Percent Maths Problems

  • + ACCUPLACER Mathematics
  • + ACT Mathematics
  • + AFOQT Mathematics
  • + ALEKS Tests
  • + ASVAB Mathematics
  • + ATI TEAS Math Tests
  • + Common Core Math
  • + DAT Math Tests
  • + FSA Tests
  • + FTCE Math
  • + GED Mathematics
  • + Georgia Milestones Assessment
  • + GRE Quantitative Reasoning
  • + HiSET Math Exam
  • + HSPT Math
  • + ISEE Mathematics
  • + PARCC Tests
  • + Praxis Math
  • + PSAT Math Tests
  • + PSSA Tests
  • + SAT Math Tests
  • + SBAC Tests
  • + SIFT Math
  • + SSAT Math Tests
  • + STAAR Tests
  • + TABE Tests
  • + TASC Math
  • + TSI Mathematics
  • + ACT Math Worksheets
  • + Accuplacer Math Worksheets
  • + AFOQT Math Worksheets
  • + ALEKS Math Worksheets
  • + ASVAB Math Worksheets
  • + ATI TEAS 6 Math Worksheets
  • + FTCE General Math Worksheets
  • + GED Math Worksheets
  • + 3rd Grade Mathematics Worksheets
  • + 4th Grade Mathematics Worksheets
  • + 5th Grade Mathematics Worksheets
  • + 6th Grade Math Worksheets
  • + 7th Grade Mathematics Worksheets
  • + 8th Grade Mathematics Worksheets
  • + 9th Grade Math Worksheets
  • + HiSET Math Worksheets
  • + HSPT Math Worksheets
  • + ISEE Middle-Level Math Worksheets
  • + PERT Math Worksheets
  • + Praxis Math Worksheets
  • + PSAT Math Worksheets
  • + SAT Math Worksheets
  • + SIFT Math Worksheets
  • + SSAT Middle Level Math Worksheets
  • + 7th Grade STAAR Math Worksheets
  • + 8th Grade STAAR Math Worksheets
  • + THEA Math Worksheets
  • + TABE Math Worksheets
  • + TASC Math Worksheets
  • + TSI Math Worksheets
  • + AFOQT Math Course
  • + ALEKS Math Course
  • + ASVAB Math Course
  • + ATI TEAS 6 Math Course
  • + CHSPE Math Course
  • + FTCE General Knowledge Course
  • + GED Math Course
  • + HiSET Math Course
  • + HSPT Math Course
  • + ISEE Upper Level Math Course
  • + SHSAT Math Course
  • + SSAT Upper-Level Math Course
  • + PERT Math Course
  • + Praxis Core Math Course
  • + SIFT Math Course
  • + 8th Grade STAAR Math Course
  • + TABE Math Course
  • + TASC Math Course
  • + TSI Math Course
  • + Number Properties Puzzles
  • + Algebra Puzzles
  • + Geometry Puzzles
  • + Intelligent Math Puzzles
  • + Ratio, Proportion & Percentages Puzzles
  • + Other Math Puzzles

How to Solve Percent Problems? (+FREE Worksheet!)

Learn how to calculate and solve percent problems using the percent formula.

How to Solve Percent Problems? (+FREE Worksheet!)

Related Topics

  • How to Find Percent of Increase and Decrease
  • How to Find Discount, Tax, and Tip
  • How to Do Percentage Calculations
  • How to Solve Simple Interest Problems

Step by step guide to solve percent problems

  • In each percent problem, we are looking for the base, or part or the percent.
  • Use the following equations to find each missing section. Base \(= \color{black}{Part} \ ÷ \ \color{blue}{Percent}\) \(\color{ black }{Part} = \color{blue}{Percent} \ ×\) Base \(\color{blue}{Percent} = \color{ black }{Part} \ ÷\) Base

Percent Problems – Example 1:

\(2.5\) is what percent of \(20\)?

In this problem, we are looking for the percent. Use the following equation: \(\color{blue}{Percent} = \color{ black }{Part} \ ÷\) Base \(→\) Percent \(=2.5 \ ÷ \ 20=0.125=12.5\%\)

The Absolute Best Books to Ace Pre-Algebra to Algebra II

The Ultimate Algebra Bundle From Pre-Algebra to Algebra II

Percent problems – example 2:.

\(40\) is \(10\%\) of what number?

Use the following formula: Base \(= \color{ black }{Part} \ ÷ \ \color{blue}{Percent}\) \(→\) Base \(=40 \ ÷ \ 0.10=400\) \(40\) is \(10\%\) of \(400\).

Percent Problems – Example 3:

\(1.2\) is what percent of \(24\)?

In this problem, we are looking for the percent. Use the following equation: \(\color{blue}{Percent} = \color{ black }{Part} \ ÷\) Base \(→\) Percent \(=1.2÷24=0.05=5\%\)

The Best Book to Help You Ace Pre-Algebra

Pre-Algebra for Beginners The Ultimate Step by Step Guide to Preparing for the Pre-Algebra Test

Percent problems – example 4:.

\(20\) is \(5\%\) of what number?

Use the following formula: Base \(= \color{black}{Part} \ ÷ \ \color{blue}{Percent}\) \(→\) Base \(=20÷0.05=400\) \( 20\) is \(5\%\) of \(400\).

Exercises for Calculating Percent Problems

Solve each problem..

  • \(51\) is \(340\%\) of what?
  • \(93\%\) of what number is \(97\)?
  • \(27\%\) of \(142\) is what number?
  • What percent of \(125\) is \(29.3\)?
  • \(60\) is what percent of \(126\)?
  • \(67\) is \(67\%\) of what?

Download Percent Problems Worksheet

  • \(\color{blue}{15}\)
  • \(\color{blue}{104.3}\)
  • \(\color{blue}{38.34}\)
  • \(\color{blue}{23.44\%}\)
  • \(\color{blue}{47.6\%}\)
  • \(\color{blue}{100}\)

The Greatest Books for Students to Ace the Algebra

Pre-Algebra Exercise Book A Comprehensive Workbook + PreAlgebra Practice Tests

Pre-algebra in 10 days the most effective pre-algebra crash course, college algebra practice workbook the most comprehensive review of college algebra, high school algebra i a comprehensive review and step-by-step guide to mastering high school algebra 1, 10 full length clep college algebra practice tests the practice you need to ace the clep college algebra test.

by: Effortless Math Team about 4 years ago (category: Articles , Free Math Worksheets )

Effortless Math Team

Related to this article, more math articles.

  • Best Smartphones for Math Teachers
  • The Rules of Integral: Complex Subject Made Easy
  • PSAT 10 Math Worksheets: FREE & Printable
  • How is the TASC Test Scored?
  • 10 Must-Know Expert Tips for the HiSET Math Test
  • Gain Access to the Answers: Explore the Solution Manual for “CHSPE Math for Beginners”
  • 10 Most Common 5th Grade PSSA Math Questions
  • How to Get Better at Math: 7 Comprehensive Tips for Parents with Kids Struggling
  • 4th Grade OAA Math Worksheets: FREE & Printable
  • Best Laptops for Back to School

What people say about "How to Solve Percent Problems? (+FREE Worksheet!) - Effortless Math: We Help Students Learn to LOVE Mathematics"?

No one replied yet.

Leave a Reply Cancel reply

You must be logged in to post a comment.

Pre-Algebra Practice Workbook The Most Comprehensive Review of Pre-Algebra

Algebra i practice workbook the most comprehensive review of algebra 1, algebra ii practice workbook the most comprehensive review of algebra 2, algebra i for beginners the ultimate step by step guide to acing algebra i, algebra ii for beginners the ultimate step by step guide to acing algebra ii, pre-algebra tutor everything you need to help achieve an excellent score.

  • ATI TEAS 6 Math
  • ISEE Upper Level Math
  • SSAT Upper-Level Math
  • Praxis Core Math
  • 8th Grade STAAR Math

Limited time only!

Save Over 45 %

It was $89.99 now it is $49.99

Login and use all of our services.

Effortless Math services are waiting for you. login faster!

Register Fast!

Password will be generated automatically and sent to your email.

After registration you can change your password if you want.

  • Math Worksheets
  • Math Courses
  • Math Topics
  • Math Puzzles
  • Math eBooks
  • GED Math Books
  • HiSET Math Books
  • ACT Math Books
  • ISEE Math Books
  • ACCUPLACER Books
  • Premium Membership
  • Youtube Videos
  • Google Play
  • Apple Store

Effortless Math provides unofficial test prep products for a variety of tests and exams. All trademarks are property of their respective trademark owners.

  • Bulk Orders
  • Refund Policy

OML Search

Solving Percent Problems

Percent Problems

Mathway Calculator Widget

We welcome your feedback, comments and questions about this site or page. Please submit your feedback or enquiries via our Feedback page.

Library homepage

  • school Campus Bookshelves
  • menu_book Bookshelves
  • perm_media Learning Objects
  • login Login
  • how_to_reg Request Instructor Account
  • hub Instructor Commons
  • Download Page (PDF)
  • Download Full Book (PDF)
  • Periodic Table
  • Physics Constants
  • Scientific Calculator
  • Reference & Cite
  • Tools expand_more
  • Readability

selected template will load here

This action is not available.

Mathematics LibreTexts

4.2: Percents Problems and Applications of Percent

  • Last updated
  • Save as PDF
  • Page ID 142718

  • Morgan Chase
  • Clackamas Community College via OpenOregon

You may use a calculator throughout this module.

sale-tag.jpg

Recall: The amount is the answer we get after finding the percent of the original number. The base is the original number, the number we find the percent of. We can call the percent the rate.

When we looked at percents in a previous module, we focused on finding the amount. In this module, we will learn how to find the percentage rate and the base.

\(\text{Amount}=\text{Rate}\cdot\text{Base}\)

\(A=R\cdot{B}\)

We can translate from words into algebra.

  • “is” means equals
  • “of” means multiply
  • “what” means a variable

Solving Percent Problems: Finding the Rate

Suppose you earned \(56\) points on a \(60\)-point quiz. To figure out your grade as a percent, you need to answer the question “\(56\) is what percent of \(60\)?” We can translate this sentence into the equation \(56=R\cdot60\).

Exercises \(\PageIndex{1}\)

1. \(56\) is what percent of \(60\)?

2. What percent of \(120\) is \(45\)?

1. \(93\%\) or \(93.3\%\)

2. \(37.5\%\)

Be aware that this method gives us the answer in decimal form and we must move the decimal point to convert the answer to a percent.

Also, if the instructions don’t explicitly tell you how to round your answer, use your best judgment: to the nearest whole percent or nearest tenth of a percent, to two or three significant figures, etc.

Solving Percent Problems: Finding the Base

Suppose you earn \(2\%\) cash rewards for the amount you charge on your credit card. If you want to earn $ \(50\) in cash rewards, how much do you need to charge on your card? To figure this out, you need to answer the question “\(50\) is \(2\%\) of what number?” We can translate this into the equation \(50=0.02\cdot{B}\).

3. $ \(50\) is \(2\%\) of what number?

4. \(5\%\) of what number is \(36\)?

3. $ \(2,500\)

5. An \(18\%\) tip will be added to a dinner that cost $ \(107.50\). What is the amount of the tip?

6. The University of Oregon women’s basketball team made \(13\) of the \(29\) three-points shots they attempted during a game against UNC. What percent of their three-point shots did the team make?

7. \(45\%\) of the people surveyed answered “yes” to a poll question. If \(180\) people answered “yes”, how many people were surveyed altogether?

5. $ \(19.35\)

6. \(44.8\%\) or \(45\%\)

7. \(400\) people were surveyed

Solving Percent Problems: Percent Increase

When a quantity changes, it is often useful to know by what percent it changed. If the price of a candy bar is increased by \(50\) cents, you might be annoyed because it’s it’s a relatively large percentage of the original price. If the price of a car is increased by \(50\) cents, though, you wouldn’t care because it’s such a small percentage of the original price.

To find the percent of increase:

  • Subtract the two numbers to find the amount of increase.
  • Using this result as the amount and the original number as the base, find the unknown percent.

Notice that we always use the original number for the base, the number that occurred earlier in time. In the case of a percent increase, this is the smaller of the two numbers.

8. The price of a candy bar increased from $ \(0.89\) to $ \(1.39\). By what percent did the price increase?

9. The population of Portland in 2010 was \(583,793\). The estimated population in 2019 was \(654,741\). Find the percent of increase in the population. [1]

8. \(56.2\%\) increase

9. \(12.2\%\) increase

Solving Percent Problems: Percent Decrease

Finding the percent decrease in a number is very similar.

To find the percent of decrease:

  • Subtract the two numbers to find the amount of decrease.

Again, we always use the original number for the base, the number that occurred earlier in time. For a percent decrease, this is the larger of the two numbers.

10. During a sale, the price of a candy bar was reduced from $ \(1.39\) to $ \(0.89\). By what percent did the price decrease?

11. The number of students enrolled at Clackamas Community College decreased from \(7,439\) in Summer 2019 to \(4,781\) in Summer 2020. Find the percent of decrease in enrollment.

10. \(36.0\%\) decrease

11. \(35.7\%\) decrease

Relative Error

In an earlier module, we said that a measurement will always include some error, no matter how carefully we measure. It can be helpful to consider the size of the error relative to the size of what is being measured. As we saw in the examples above, a difference of \(50\) cents is important when we’re pricing candy bars but insignificant when we’re pricing cars. In the same way, an error of an eighth of an inch could be a deal-breaker when you’re trying to fit a screen into a window frame, but an eighth of an inch is insignificant when you’re measuring the length of your garage.

The expected outcome is what the number would be in a perfect world. If a window screen is supposed to be exactly \(25\) inches wide, we call this the expected outcome, and we treat it as though it has infinitely many significant digits. In theory, the expected outcome is \(25.000000...\)

To find the absolute error , we subtract the measurement and the expected outcome. Because we always treat the expected outcome as though it has unlimited significant figures, the absolute error should have the same precision (place value) as the measurement , not the expected outcome .

To find the relative error , we divide the absolute error by the expected outcome. We usually express the relative error as a percent. In fact, the procedure for finding the relative error is identical to the procedures for finding a percent increase or percent decrease!

To find the relative error:

  • Subtract the two numbers to find the absolute error.
  • Using the absolute error as the amount and the expected outcome as the base, find the unknown percent.

Exercisew \(\PageIndex{1}\)

12. A window screen is measured to be \(25\dfrac{3}{16}\) inches wide instead of the advertised \(25\) inches. Determine the relative error, rounded to the nearest tenth of a percent.

13. The contents of a box of cereal are supposed to weigh \(10.8\) ounces, but they are measured at \(10.67\) ounces. Determine the relative error, rounded to the nearest tenth of a percent.

12. \(0.1875\div25\approx0.8\%\)

13. \(0.13\div10.8\approx1.2\%\)

6509400855_aaaf915871.jpg

The tolerance is the maximum amount that a measurement is allowed to differ from the expected outcome. For example, the U.S. Mint needs its coins to have a consistent size and weight so that they will work in vending machines. A dime (10 cents) weighs \(2.268\) grams, with a tolerance of \(\pm0.091\) grams. [2] This tells us that the minimum acceptable weight is \(2.268-0.091=2.177\) grams, and the maximum acceptable weight is \(2.268+0.091=2.359\) grams. A dime with a weight outside of the range \(2.177\leq\text{weight}\leq2.359\) would be unacceptable.

dime-under-microscope-300x225.jpg

A U.S. nickel (5 cents) weighs \(5.000\) grams with a tolerance of \(\pm0.194\) grams.

14. Determine the lowest acceptable weight and highest acceptable weight of a nickel.

15. Determine the relative error of a nickel that weighs \(5.21\) grams.

A U.S. quarter (25 cents) weighs \(5.670\) grams with a tolerance of \(\pm0.227\) grams.

16. Determine the lowest acceptable weight and highest acceptable weight of a quarter.

17. Determine the relative error of a quarter that weighs \(5.43\) grams.

14. \(4.806\) g; \(5.194\) g

15. \(0.21\div5.000=4.2\%\)

16. \(5.443\) g; \(5.897\) g

17. \(0.24\div5.670\approx4.2\%\)

  • www.census.gov/quickfacts/fact/table/portlandcityoregon,OR,US/PST045219 ↵
  • https://www.usmint.gov/learn/coin-and-medal-programs/coin-specifications and https://www.thesprucecrafts.com/how-much-do-coins-weigh-4171330 ↵

Solving Percent Problems

Learning Objective(s)

·          Identify the amount, the base, and the percent in a percent problem.

·          Find the unknown in a percent problem.

Introduction

Percents are a ratio of a number and 100. So they are easier to compare than fractions, as they always have the same denominator, 100. A store may have a 10% off sale. The amount saved is always the same portion or fraction of the price, but a higher price means more money is taken off. Interest rates on a saving account work in the same way. The more money you put in your account, the more money you get in interest. It’s helpful to understand how these percents are calculated.

Parts of a Percent Problem

Jeff has a coupon at the Guitar Store for 15% off any purchase of $100 or more. He wants to buy a used guitar that has a price tag of $220 on it. Jeff wonders how much money the coupon will take off the original $220 price.

Problems involving percents have any three quantities to work with: the percent , the amount , and the base .

The percent has the percent symbol (%) or the word “percent.” In the problem above, 15% is the percent off the purchase price.

The base is the whole amount. In the problem above, the whole price of the guitar is $220, which is the base.

The amount is the number that relates to the percent. It is always part of the whole. In the problem above, the amount is unknown. Since the percent is the percent off , the amount will be the amount off of the price .

You will return to this problem a bit later. The following examples show how to identify the three parts, the percent, the base, and the amount.

The previous problem states that 30 is a portion of another number. That means 30 is the amount. Note that this problem could be rewritten: 20% of what number is 30?

Solving with Equations

Percent problems can be solved by writing equations. An equation uses an equal sign (= ) to show that two mathematical expressions have the same value.

Percents are fractions, and just like fractions, when finding a percent (or fraction, or portion) of another amount, you multiply.

The percent of the base is the amount.

Percent of the Base is the Amount.

Percent · Base = Amount

Once you have an equation, you can solve it and find the unknown value. To do this, think about the relationship between multiplication and division. Look at the pairs of multiplication and division facts below, and look for a pattern in each row.

Multiplication and division are inverse operations. What one does to a number, the other “undoes.”

When you have an equation such as 20% · n = 30, you can divide 30 by 20% to find the unknown: n =  30 ÷ 20%.

You can solve this by writing the percent as a decimal or fraction and then dividing.

n = 30 ÷ 20% =  30 ÷ 0.20 = 150

You can estimate to see if the answer is reasonable. Use 10% and 20%, numbers close to 12.5%, to see if they get you close to the answer.

10% of 72 = 0.1 · 72 = 7.2

20% of 72 = 0.2 · 72 = 14.4

Notice that 9 is between 7.2 and 14.4, so 12.5% is reasonable since it is between 10% and 20%.

This problem is a little easier to estimate. 100% of 24 is 24. And 110% is a little bit more than 24. So, 26.4 is a reasonable answer.

Using Proportions to Solve Percent Problems

Let’s go back to the problem that was posed at the beginning. You can now solve this problem as shown in the following example.

You can estimate to see if the answer is reasonable. Since 15% is half way between 10% and 20%, find these numbers.

10% of 220 = 0.1 · 220 = 22

20% of 220 = 0.2 · 220 = 44

The answer, 33, is between 22 and 44. So $33 seems reasonable.

There are many other situations that involve percents. Below are just a few.

Corbettmaths

Percentages Practice Questions

Percentages (non-calculator), click here for questions, click here for answers, percentages (calculator), gcse revision cards.

sample problem solving percentage

5-a-day Workbooks

sample problem solving percentage

Primary Study Cards

sample problem solving percentage

Privacy Policy

Terms and Conditions

Corbettmaths © 2012 – 2024

A free service from Mattecentrum

Solving problems with percentages

  • Price difference I
  • Price difference II
  • How many students?

To solve problems with percent we use the percent proportion shown in "Proportions and percent".

$$\frac{a}{b}=\frac{x}{100}$$

$$\frac{a}{{\color{red} {b}}}\cdot {\color{red} {b}}=\frac{x}{100}\cdot b$$

$$a=\frac{x}{100}\cdot b$$

x/100 is called the rate.

$$a=r\cdot b\Rightarrow Percent=Rate\cdot Base$$

Where the base is the original value and the percentage is the new value.

47% of the students in a class of 34 students has glasses or contacts. How many students in the class have either glasses or contacts?

$$a=r\cdot b$$

$$47\%=0.47a$$

$$=0.47\cdot 34$$

$$a=15.98\approx 16$$

16 of the students wear either glasses or contacts.

We often get reports about how much something has increased or decreased as a percent of change. The percent of change tells us how much something has changed in comparison to the original number. There are two different methods that we can use to find the percent of change.

The Mathplanet school has increased its student body from 150 students to 240 from last year. How big is the increase in percent?

We begin by subtracting the smaller number (the old value) from the greater number (the new value) to find the amount of change.

$$240-150=90$$

Then we find out how many percent this change corresponds to when compared to the original number of students

$$90=r\cdot 150$$

$$\frac{90}{150}=r$$

$$0.6=r= 60\%$$

We begin by finding the ratio between the old value (the original value) and the new value

$$percent\:of\:change=\frac{new\:value}{old\:value}=\frac{240}{150}=1.6$$

As you might remember 100% = 1. Since we have a percent of change that is bigger than 1 we know that we have an increase. To find out how big of an increase we've got we subtract 1 from 1.6.

$$1.6-1=0.6$$

$$0.6=60\%$$

As you can see both methods gave us the same answer which is that the student body has increased by 60%

Video lessons

A skirt cost $35 regulary in a shop. At a sale the price of the skirtreduces with 30%. How much will the skirt cost after the discount?

Solve "54 is 25% of what number?"

  • Pre-Algebra
  • The mean, the median and the mode
  • Stem-and-Leaf Plots and Box-and-Whiskers Plot
  • Calculating the outcome
  • Combinations and permutations
  • Finding the odds
  • Probability of events
  • Geometry – fundamental statements
  • Circle graphs
  • Angles and parallel lines
  • Quadrilaterals, polygons and transformations
  • Measure areas
  • Pyramids, prisms, cylinders and cones
  • Square roots and real numbers
  • The Pythagorean Theorem
  • Trigonometry
  • Algebra 1 Overview
  • Algebra 2 Overview
  • Geometry Overview
  • SAT Overview
  • ACT Overview

Percentages Worksheets

Welcome to the percentages math worksheet page where we are 100% committed to providing excellent math worksheets. This page includes Percentages worksheets including calculating percentages of a number, percentage rates, and original amounts and percentage increase and decrease worksheets.

As you probably know, percentages are a special kind of decimal. Most calculations involving percentages involve using the percentage in its decimal form. This is achieved by dividing the percentage amount by 100. There are many worksheets on percentages below. In the first few sections, there are worksheets involving the three main types of percentage problems: calculating the percentage value of a number, calculating the percentage rate of one number compared to another number, and calculating the original amount given the percentage value and the percentage rate.

Most Popular Percentages Worksheets this Week

Calculating the Percent Value of Whole Number Amounts and All Percents

Percentage Calculations

sample problem solving percentage

Calculating the percentage value of a number involves a little bit of multiplication. One should be familiar with decimal multiplication and decimal place value before working with percentage values. The percentage value needs to be converted to a decimal by dividing by 100. 18%, for example is 18 ÷ 100 = 0.18. When a question asks for a percentage value of a number, it is asking you to multiply the two numbers together.

Example question: What is 18% of 2800? Answer: Convert 18% to a decimal and multiply by 2800. 2800 × 0.18 = 504. 504 is 18% of 2800.

  • Calculating the Percentage Value (Whole Number Results) Calculating the Percentage Value (Whole Number Results) (Percents from 1% to 99%) Calculating the Percentage Value (Whole Number Results) (Select percents) Calculating the Percentage Value (Whole Number Results) (Percents that are multiples of 5%) Calculating the Percentage Value (Whole Number Results) (Percents that are multiples of 25%)
  • Calculating the Percentage Value (Decimal Number Results) Calculating the Percentage Value (Decimal Number Results) (Percents from 1% to 99%) Calculating the Percentage Value (Decimal Number Results) (Select percents) Calculating the Percentage Value (Decimal Number Results) (Percents that are multiples of 5%) Calculating the Percentage Value (Decimal Number Results) (Percents that are multiples of 25%)
  • Calculating the Percentage Value (Whole Dollar Results) Calculating the Percentage Value (Whole Dollar Results) (Percents from 1% to 99%) Calculating the Percentage Value (Whole Dollar Results) (Select percents) Calculating the Percentage Value (Whole Dollar Results) (Percents that are multiples of 5%) Calculating the Percentage Value (Whole Dollar Results) (Percents that are multiples of 25%)
  • Calculating the Percentage Value (Decimal Dollar Results) Calculating the Percentage Value (Decimal Dollar Results) (Percents from 1% to 99%) Calculating the Percentage Value (Decimal Dollar Results) (Select percents) Calculating the Percentage Value (Decimal Dollar Results) (Percents that are multiples of 5%) Calculating the Percentage Value (Decimal Dollar Results) (Percents that are multiples of 25%)

Calculating what percentage one number is of another number is the second common type of percentage calculation. In this case, division is required followed by converting the decimal to a percentage. If the first number is 100% of the value, the second number will also be 100% if the two numbers are equal; however, this isn't usually the case. If the second number is less than the first number, the second number is less than 100%. If the second number is greater than the first number, the second number is greater than 100%. A simple example is: What percentage of 10 is 6? Because 6 is less than 10, it must also be less than 100% of 10. To calculate, divide 6 by 10 to get 0.6; then convert 0.6 to a percentage by multiplying by 100. 0.6 × 100 = 60%. Therefore, 6 is 60% of 10.

Example question: What percentage of 3700 is 2479? First, recognize that 2479 is less than 3700, so the percentage value must also be less than 100%. Divide 2479 by 3700 and multiply by 100. 2479 ÷ 3700 × 100 = 67%.

  • Calculating the Percentage a Whole Number is of Another Whole Number Calculating the Percentage a Whole Number is of Another Whole Number (Percents from 1% to 99%) Calculating the Percentage a Whole Number is of Another Whole Number (Select percents) Calculating the Percentage a Whole Number is of Another Whole Number (Percents that are multiples of 5%) Calculating the Percentage a Whole Number is of Another Whole Number (Percents that are multiples of 25%)
  • Calculating the Percentage a Decimal Number is of a Whole Number Calculating the Percentage a Decimal Number is of a Whole Number (Percents from 1% to 99%) Calculating the Percentage a Decimal Number is of a Whole Number (Select percents) Calculating the Percentage a Decimal Number is of a Whole Number (Percents that are multiples of 5%) Calculating the Percentage a Decimal Number is of a Whole Number (Percents that are multiples of 25%)
  • Calculating the Percentage a Whole Dollar Amount is of Another Whole Dollar Amount Calculating the Percentage a Whole Dollar Amount is of Another Whole Dollar Amount (Percents from 1% to 99%) Calculating the Percentage a Whole Dollar Amount is of Another Whole Dollar Amount (Select percents) Calculating the Percentage a Whole Dollar Amount is of Another Whole Dollar Amount (Percents that are multiples of 5%) Calculating the Percentage a Whole Dollar Amount is of Another Whole Dollar Amount (Percents that are multiples of 25%)
  • Calculating the Percentage a Decimal Dollar Amount is of a Whole Dollar Amount Calculating the Percentage a Decimal Dollar Amount is of a Whole Dollar Amount (Percents from 1% to 99%) Calculating the Percentage a Decimal Dollar Amount is of a Whole Dollar Amount (Select percents) Calculating the Percentage a Decimal Dollar Amount is of a Whole Dollar Amount (Percents that are multiples of 5%) Calculating the Percentage a Decimal Dollar Amount is of a Whole Dollar Amount (Percents that are multiples of 25%)

The third type of percentage calculation involves calculating the original amount from the percentage value and the percentage. The process involved here is the reverse of calculating the percentage value of a number. To get 10% of 100, for example, multiply 100 × 0.10 = 10. To reverse this process, divide 10 by 0.10 to get 100. 10 ÷ 0.10 = 100.

Example question: 4066 is 95% of what original amount? To calculate 4066 in the first place, a number was multiplied by 0.95 to get 4066. To reverse this process, divide to get the original number. In this case, 4066 ÷ 0.95 = 4280.

  • Calculating the Original Amount from a Whole Number Result and a Percentage Calculating the Original Amount (Percents from 1% to 99%) ( Whole Numbers ) Calculating the Original Amount (Select percents) ( Whole Numbers ) Calculating the Original Amount (Percents that are multiples of 5%) ( Whole Numbers ) Calculating the Original Amount (Percents that are multiples of 25%) ( Whole Numbers )
  • Calculating the Original Amount from a Decimal Number Result and a Percentage Calculating the Original Amount (Percents from 1% to 99%) ( Decimals ) Calculating the Original Amount (Select percents) ( Decimals ) Calculating the Original Amount (Percents that are multiples of 5%) ( Decimals ) Calculating the Original Amount (Percents that are multiples of 25%) ( Decimals )
  • Calculating the Original Amount from a Whole Dollar Result and a Percentage Calculating the Original Amount (Percents from 1% to 99%) ( Dollar Amounts and Whole Numbers ) Calculating the Original Amount (Select percents) ( Dollar Amounts and Whole Numbers ) Calculating the Original Amount (Percents that are multiples of 5%) ( Dollar Amounts and Whole Numbers ) Calculating the Original Amount (Percents that are multiples of 25%) ( Dollar Amounts and Whole Numbers )
  • Calculating the Original Amount from a Decimal Dollar Result and a Percentage Calculating the Original Amount (Percents from 1% to 99%) ( Dollar Amounts and Decimals ) Calculating the Original Amount (Select percents) ( Dollar Amounts and Decimals ) Calculating the Original Amount (Percents that are multiples of 5%) ( Dollar Amounts and Decimals ) Calculating the Original Amount (Percents that are multiples of 25%) ( Dollar Amounts and Decimals )
  • Mixed Percentage Calculations with Whole Number Percentage Values Mixed Percentage Calculations (Percents from 1% to 99%) ( Whole Numbers ) Mixed Percentage Calculations (Select percents) ( Whole Numbers ) Mixed Percentage Calculations (Percents that are multiples of 5%) ( Whole Numbers ) Mixed Percentage Calculations (Percents that are multiples of 25%) ( Whole Numbers )
  • Mixed Percentage Calculations with Decimal Percentage Values Mixed Percentage Calculations (Percents from 1% to 99%) ( Decimals ) Mixed Percentage Calculations (Select percents) ( Decimals ) Mixed Percentage Calculations (Percents that are multiples of 5%) ( Decimals ) Mixed Percentage Calculations (Percents that are multiples of 25%) ( Decimals )
  • Mixed Percentage Calculations with Whole Dollar Percentage Values Mixed Percentage Calculations (Percents from 1% to 99%) ( Dollar Amounts and Whole Numbers ) Mixed Percentage Calculations (Select percents) ( Dollar Amounts and Whole Numbers ) Mixed Percentage Calculations (Percents that are multiples of 5%) ( Dollar Amounts and Whole Numbers ) Mixed Percentage Calculations (Percents that are multiples of 25%) ( Dollar Amounts and Whole Numbers )
  • Mixed Percentage Calculations with Decimal Dollar Percentage Values Mixed Percentage Calculations (Percents from 1% to 99%) ( Dollar Amounts and Decimals ) Mixed Percentage Calculations (Select percents) ( Dollar Amounts and Decimals ) Mixed Percentage Calculations (Percents that are multiples of 5%) ( Dollar Amounts and Decimals ) Mixed Percentage Calculations (Percents that are multiples of 25%) ( Dollar Amounts and Decimals )

Percentage Increase/Decrease Worksheets

sample problem solving percentage

The worksheets in this section have students determine by what percentage something increases or decreases. Each question includes an original amount and a new amount. Students determine the change from the original to the new amount using a formula: ((new - original)/original) × 100 or another method. It should be straight-forward to determine if there is an increase or a decrease. In the case of a decrease, the percentage change (using the formula) will be negative.

  • Percentage Increase/Decrease With Whole Number Percentage Values Percentage Increase/Decrease Whole Numbers with 1% Intervals Percentage Increase/Decrease Whole Numbers with 5% Intervals Percentage Increase/Decrease Whole Numbers with 25% Intervals
  • Percentage Increase/Decrease With Decimal Number Percentage Values Percentage Increase/Decrease Decimals with 1% Intervals Percentage Increase/Decrease Decimals with 5% Intervals Percentage Increase/Decrease Decimals with 25% Intervals
  • Percentage Increase/Decrease With Whole Dollar Percentage Values Percentage Increase/Decrease Whole Dollar Amounts with 1% Intervals Percentage Increase/Decrease Whole Dollar Amounts with 5% Intervals Percentage Increase/Decrease Whole Dollar Amounts with 25% Intervals
  • Percentage Increase/Decrease With Decimal Dollar Percentage Values Percentage Increase/Decrease Decimal Dollar Amounts with 1% Intervals Percentage Increase/Decrease Decimal Dollar Amounts with 5% Intervals Percentage Increase/Decrease Decimal Dollar Amounts with 25% Intervals

Copyright © 2005-2024 Math-Drills.com You may use the math worksheets on this website according to our Terms of Use to help students learn math.

Word Problems on Percentage

Word problems on percentage will help us to solve various types of problems related to percentage. Follow the procedure to solve similar type of percent problems.

Word problems on percentage:

1.  In an exam Ashley secured 332 marks. If she secured 83 % makes, find the maximum marks.

Let the maximum marks be m.

Ashley’s marks = 83% of m

Ashley secured 332 marks

Therefore, 83% of m = 332

⇒ 83/100 × m = 332

⇒ m = (332 × 100)/83

⇒ m =33200/83

Therefore, Ashley got 332 marks out of 400 marks.

2. An alloy contains 26 % of copper. What quantity of alloy is required to get 260 g of copper?

Let the quantity of alloy required = m g

Then 26 % of m =260 g

⇒ 26/100 × m = 260 g

⇒ m = (260 × 100)/26 g

⇒ m = 26000/26 g

⇒ m = 1000 g

3. There are 50 students in a class. If 14% are absent on a particular day, find the number of students present in the class.

Solution:             

Number of students absent on a particular day = 14 % of 50

                                          i.e., 14/100 × 50 = 7

Therefore, the number of students present = 50 - 7 = 43 students.

4. In a basket of apples, 12% of them are rotten and 66 are in good condition. Find the total number of apples in the basket.

Solution:             

Let the total number of apples in the basket be m

12 % of the apples are rotten, and apples in good condition are 66

Therefore, according to the question,

88% of m = 66

⟹ 88/100 × m = 66

⟹ m = (66 × 100)/88

⟹ m = 3 × 25

Therefore, total number of apples in the basket is 75.

5. In an examination, 300 students appeared. Out of these students; 28 % got first division, 54 % got second division and the remaining just passed. Assuming that no student failed; find the number of students who just passed.

The number of students with first division = 28 % of 300

                                                             = 28/100 × 300

                                                             = 8400/100

                                                             = 84

And, the number of students with second division = 54 % of 300

                                                                        = 54/100 × 300

                                                                        =16200/100

                                                                        = 162

Therefore, the number of students who just passed = 300 – (84 + 162)

                                                                           = 54

Questions and Answers on Word Problems on Percentage:

1. In a class 60% of the students are girls. If the total number of students is 30, what is the number of boys?

2. Emma scores 72 marks out of 80 in her English exam. Convert her marks into percent.

Answer: 90%

3. Mason was able to sell 35% of his vegetables before noon. If Mason had 200 kg of vegetables in the morning, how many grams of vegetables was he able to see by noon?

Answer: 70 kg

4. Alexander was able to cover 25% of 150 km journey in the morning. What percent of journey is still left to be covered?

Answer:  112.5 km

5. A cow gives 24 l milk each day. If the milkman sells 75% of the milk, how many liters of milk is left with him?

Answer: 6 l

Word Problems on Percentage

6.  While shopping Grace spent 90% of the money she had. If she had $ 4500 on shopping, what was the amount of money she spent?

Answer:  $ 4050

Fraction into Percentage

Percentage into Fraction

Percentage into Ratio

Ratio into Percentage

Percentage into Decimal

Decimal into Percentage

Percentage of the given Quantity

How much Percentage One Quantity is of Another?

Percentage of a Number

Increase Percentage

Decrease Percentage

Basic Problems on Percentage

Solved Examples on Percentage

Problems on Percentage

Real Life Problems on Percentage

Application of Percentage

8th Grade Math Practice From Word Problems on Percentage to HOME PAGE

New! Comments

Didn't find what you were looking for? Or want to know more information about Math Only Math . Use this Google Search to find what you need.

  • Preschool Activities
  • Kindergarten Math
  • 1st Grade Math
  • 2nd Grade Math
  • 3rd Grade Math
  • 4th Grade Math
  • 5th Grade Math
  • 6th Grade Math
  • 7th Grade Math
  • 8th Grade Math
  • 9th Grade Math
  • 10th Grade Math
  • 11 & 12 Grade Math
  • Concepts of Sets
  • Probability
  • Boolean Algebra
  • Math Coloring Pages
  • Multiplication Table
  • Cool Maths Games
  • Math Flash Cards
  • Online Math Quiz
  • Math Puzzles
  • Binary System
  • Math Dictionary
  • Conversion Chart
  • Homework Sheets
  • Math Problem Ans
  • Free Math Answers
  • Printable Math Sheet
  • Funny Math Answers
  • Employment Test
  • Math Patterns
  • Link Partners
  • Privacy Policy

XML RSS

Recent Articles

RSS

Roman Numerals | System of Numbers | Symbol of Roman Numerals |Numbers

Feb 22, 24 04:21 PM

List of Roman Numerals Chart

Worksheet on Roman Numerals |Roman Numerals|Symbols for Roman Numerals

Feb 22, 24 04:15 PM

Roman Numbers Table

Roman Symbols | What are Roman Numbers? | Roman Numeration System

Feb 22, 24 02:30 PM

Roman Numbers

Place Value | Place, Place Value and Face Value | Grouping the Digits

Feb 19, 24 11:57 PM

Place-value of a Digit

Math Questions Answers | Solved Math Questions and Answers | Free Math

Feb 19, 24 11:14 PM

Math Questions Answers

Worksheet on Fraction into Percentage

Worksheet on Percentage into Fraction

Worksheet on Percentage into Ratio

Worksheet on Ratio into Percentage

Worksheet on Percentage into Decimal

Worksheet on Percentage of a Number

Worksheet on Finding Percent

Worksheet on Finding Value of a Percentage

Worksheet on Percentage of a Given Quantity

Worksheet on Word Problems on Percentage

Worksheet on Increase Percentage

Worksheet on Decrease Percentage

Worksheet on increase and Decrease Percentage

Worksheet on Expressing Percent

Worksheet on Percent Problems

Worksheet on Finding Percentage

© and ™ math-only-math.com. All Rights Reserved. 2010 - 2024.

Percents (%)

When we say "percent" we are really saying "per 100".

One percent ( 1% ) means 1 per 100.

Try it Yourself:

Using Percent

Use the slider and try some different numbers (What is 40% of 80? What is 10% of 200? What is 90% of 10?)

Because "Percent" means "per 100" think:

"this should be divided by 100"

So 75% really means 75 100

And 100% is 100 100 , or exactly 1 (100% of any number is just the number, unchanged)

And 200% is 200 100 , or exactly 2 (200% of any number is twice the number)

A Percent can also be expressed as a Decimal or a Fraction

Read more about this at Decimals, Fractions and Percentages .

Some Worked Examples

Example: calculate 25% of 80.

25% = 25 100

And   25 100 × 80 = 20

So 25% of 80 is 20

Example: 15% of 200 apples are bad. How many apples are bad?

15% = 15 100

30 apples are bad

Example: if only 10 of the 200 apples are bad, what percent is that?

As a fraction, 10 200 = 0.05

As a percentage it is: 10 200 x 100 = 5%

5% of those apples are bad

skateboard

Example: A Skateboard is reduced 25% in price. The old price was $120. Find the new price.

First, find 25% of $120:

And   25 100  × $120 = $30

25% of $120 is $30

So the reduction is $30

Take the reduction from the original price

$120 − $30 = $90

The Price of the Skateboard in the sale is $90

Calculation Trick

This little rule can make some calculations easier:

x% of y = y% of x

Example: 8% of 50

8% of 50 is the same as 50% of 8

And 50% of 8 is 4

So 8% of 50 is also 4

Percent vs Percentage

My Dictionary says "Percentage" is the "result obtained by multiplying a quantity by a percent". So 10 percent of 50 apples is 5 apples: the 5 apples is the percentage .

But in practice people use both words the same way.

Percentage Questions

Percentage Questions with answers are provided here. Students can practise these questions based on percentages to prepare for the upcoming exams. These percentage problems are prepared by our subject experts, as per the latest exam pattern. All the materials here are formulated according to the NCERT curriculum and the latest CBSE syllabus (2022-2023). Learn How to Calculate Percentage here at BYJU’S with easy steps.

sample problem solving percentage

Definition: Percentage is derived from the Latin word “per centum”. It means by the hundred. It is denoted by %. If we say, 5%, then it is equal to 5/100 = 0.05.

Percentage Questions and Solutions

Q.1: A fruit seller had some apples. He sells 40% apples and still has 420 apples. What is the total number of apples he had originally?

Solution: Let the number of apples a fruit seller had be x.

As per the given question,

(100 – 40%) of x = 420

60% of x = 420

60/100 x = 420

Hence, the fruit seller had a total of 700 apples

Q.2: A person multiplied a number by 3/5 instead of 5/3, What is the percentage error in the calculation?

Solution: Let the number be X.

X is mistakenly multiplied by ⅗ = 3X/5

X should be multiplied by 5/3 = 5X/3

Thus, the error will be = (5X/3 – 3x/5) = 16X/15

Percentage Error = (error/True value) x 100

= [(16/15) x X/(5/3) x X] x 100

Q.3: If 20% of x = y, what is the value of y% of 20 in terms of x?

Solution: Given,

20% of x = y

⇒ (20/100) x = y

=(y/100). 20

= [(20x/100) / 100] x 20

Q.4: Three students contested an election and received 1000, 5000 and 10000 votes, respectively. What is the percentage of the total votes the winning student gets?

Solution: Total number of votes = 1000 + 5000 + 10000 = 16000

The student who won the votes got 10000 votes

Hence, the percentage will be:

(10000/16000) x 100% = 62.5%

Q.5: If the price of a product is first decreased by 25% and then increased by 20%, then what is the percentage change in the price?

Solution: Let the original price be Rs. 100.

New final price = 120 % of (75 % of Rs. 100)

Therefore, the net change in price is 100 – 90 = 10.

Percentage decrease = 10%

Q.6: The value of a washing machine depreciates at the rate of 10% every year. If its present value is Rs. 8748, then what was the price of the washing machine three years ago?

Current price of the washing machine = Rs.8748

The price of the machine depreciated at the rate of 10% every year

Therefore, the price of the washing machine three years ago = 8748 ÷ (1 – 10/100) 3

Q.7: For a student to clear an examination, he must score 55% marks. If he gets 120 and fails by 78 marks, what is the total marks for the examination?

Solution: Given, the mark obtained by the student is 120 and the student fails by 78 marks

Therefore, the passing marks is = 120+78 = 198

Let us consider, the total marks be x

⇒ (55/100) × x = 198

Q.8: By how much is 80% of 40 greater than 4/5 of 25?

Solution: 80% of 40 = 80/100 × 40

⅘ of 25 = ⅘ × 25

Required value = (80/100) × 40 – (4/5) × 25

= 32 – 20

Q.9: A number is decreased by 10% and then increased by 10%. The number so obtained is 10 less than the original number. What was the original number?

Solution: Let the original number be x

Final number obtained = 110% of (90% of x)

=(110/100 × 90/100 × x)

= (99/100)x

Given the number obtained is 10 less than the original number.

x – (99/100) x = 10

Q.10: What is the percentage of ratio 5:4?

Solution: 5 : 4 = 5/4 = ( (5/4) x 100 )% = 125%.

Related Articles

  • Percent Error
  • Percentage Increase Or Decrease
  • Loss Percentage Formula
  • Fraction to Percent Conversion
  • Difference Between Percentage and Percentile

Practice Questions on Percentage

  • What is 25% of 80?
  • What is the percentage of 50 paise to 4 rupees?
  • Find the percentage change, when a number is changed from 100 to 80.
  • 50 is what percentage of 500?

Leave a Comment Cancel reply

Your Mobile number and Email id will not be published. Required fields are marked *

Request OTP on Voice Call

Post My Comment

sample problem solving percentage

  • Share Share

Register with BYJU'S & Download Free PDFs

Register with byju's & watch live videos.

close

iPhone Battery and Performance

Understand iPhone performance and its relation to your battery.

Your iPhone is designed to be simple and easy to use. This is only possible through a combination of advanced technologies and sophisticated engineering. One important technology area is battery and performance. Batteries are a complex technology, and a number of variables contribute to battery performance and related iPhone performance. All rechargeable batteries are consumables and have a limited lifespan — eventually their capacity and performance decline such that they need to be replaced. Learn more about iPhone batteries and how battery aging can affect iPhone performance.

About lithium-ion batteries

iPhone batteries use lithium-ion technology. Compared with older generations of battery technology, lithium-ion batteries charge faster, last longer, and have a higher power density for more battery life in a lighter package. Rechargeable lithium-ion technology currently provides the best technology for your device. Learn more about lithium-ion batteries .

How to maximize battery performance

“Battery life” is the amount of time a device runs before it needs to be recharged. “Battery lifespan” is the amount of time a battery lasts until it needs to be replaced. One factor affecting battery life and lifespan is the mix of things you do with your device. No matter how you use your device, there are ways to help. A battery’s lifespan is related to its “chemical age,” which is more than just the passage of time. It includes different factors, such as the number of charge cycles and how it was cared for. Follow these tips to maximize battery performance and help extend battery lifespan. For example, keep iPhone half charged when it’s stored for the long term. Also avoid charging or leaving iPhone in hot environments, including direct sun exposure, for extended periods of time.

When batteries chemically age

All rechargeable batteries are consumable components that become less effective as they chemically age.

As lithium-ion batteries chemically age, the amount of charge they can hold diminishes, resulting in shorter amounts of time before a device needs to be recharged. This can be referred to as the battery’s maximum capacity — the measure of battery capacity relative to when it was new. In addition, a battery’s ability to deliver maximum instantaneous performance, or “peak power,” might decrease. For a phone to function properly, the electronics must be able to draw upon instantaneous power from the battery. One attribute that affects this instantaneous power delivery is the battery’s impedance. A battery with a high impedance might be unable to provide sufficient power to the system that needs it. A battery's impedance can increase if a battery has a higher chemical age. A battery’s impedance will temporarily increase at a low state of charge and in a cold temperature environment. When coupled with a higher chemical age, the impedance increase will be more significant. These are characteristics of battery chemistry that are common to all lithium-ion batteries in the industry.

When power is pulled from a battery with a higher level of impedance, the battery’s voltage will drop to a greater degree. Electronic components require a minimum voltage to properly operate. This includes the device’s internal storage, power circuits, and the battery itself. The power management system determines the capability of the battery to supply this power and manages the loads to maintain operations. When the operations can no longer be supported with the full capabilities of the power management system, the system will perform a shutdown to preserve these electronic components. While this shutdown is intentional from the device perspective, it might be unexpected by the user.

Preventing unexpected shutdowns

You're more likely to experience unexpected shutdowns when your battery has a low state of charge, a higher chemical age, or when you're in colder temperatures. In extreme cases, shutdowns can occur more frequently, making the device unreliable or unusable. For iPhone 6, iPhone 6 Plus, iPhone 6s, iPhone 6s Plus, iPhone SE (1st generation), iPhone 7, and iPhone 7 Plus, iOS dynamically manages performance peaks to prevent the device from unexpectedly shutting down, so you can still use your iPhone. This performance management feature is specific to iPhone and doesn't apply to any other Apple products. Starting with iOS 12.1, iPhone 8, iPhone 8 Plus, and iPhone X include this feature; iPhone XS, iPhone XS Max, and iPhone XR include this feature starting with iOS 13.1. Learn about performance management on iPhone 11 and later .

iPhone performance management works by looking at a combination of the device temperature, battery state of charge, and battery impedance. Only if these variables require it, iOS will dynamically manage the maximum performance of some system components, such as the CPU and GPU, in order to prevent unexpected shutdowns. As a result, the device workloads will self-balance, allowing a smoother distribution of system tasks, rather than larger, quick spikes of performance all at once. In some cases, you might not notice any differences in device performance. The level of perceived change depends on how much performance management is required for your device.

In cases that require more extreme performance management, you might notice effects such as:

Longer app launch times

Lower frame rates while scrolling

Backlight dimming (which can be overridden in Control Center)

Lower speaker volume by up to -3dB

Gradual frame rate reductions in some apps

During the most extreme cases, the camera flash will be disabled as visible in the camera UI

Apps refreshing in background might require reloading upon launch

Many key areas aren't affected by this performance management feature. Some of these include:

Cellular call quality and networking throughput performance

Captured photo and video quality

GPS performance

Location accuracy

Sensors like gyroscope, accelerometer, barometer

For a low battery state of charge and colder temperatures, performance-management changes are temporary. If a device battery has chemically aged far enough, performance-management changes might be more lasting. This is because all rechargeable batteries are consumables and have a limited lifespan, eventually needing to be replaced. If you are impacted by this and would like to improve your device performance, replacing your device battery can help.

For iOS 11.3 and later

iOS 11.3 and later improve performance management by periodically assessing the level of performance management necessary to avoid unexpected shutdowns. If the battery health is able to support the observed peak power requirements, the amount of performance management will be lowered. If an unexpected shutdown occurs again, performance management will increase. This assessment is ongoing, allowing more adaptive performance management.

iPhone 8 and later use an advanced hardware and software design that provides a more accurate estimation of both power needs and the battery’s power capability to maximize overall system performance. This allows iOS to anticipate and avoid an unexpected shutdown more precisely. As a result, the effects of performance management might be less noticeable on iPhone 8 and later. Over time, the rechargeable batteries in all iPhone models will diminish in their capacity and peak performance and will eventually need to be replaced.

image alt text

Battery Health

For iPhone 6 and later, iOS 11.3 and later add new features to show battery health and recommend if you need to replace the battery. You can find these in Settings > Battery > Battery Health (with iOS 16.1 or later, find these in Settings > Battery > Battery Health & Charging).

Additionally, you can see if the performance-management feature, which dynamically manages maximum performance to prevent unexpected shutdowns, is on, and you can choose to turn it off. This feature is enabled only after an unexpected shutdown first occurs on a device with a battery that has diminished ability to deliver maximum instantaneous power. This feature applies to iPhone 6, iPhone 6 Plus, iPhone 6s, iPhone 6s Plus, iPhone SE (1st generation), iPhone 7, and iPhone 7 Plus. Starting with iOS 12.1, iPhone 8, iPhone 8 Plus, and iPhone X include this feature; iPhone XS, iPhone XS Max, and iPhone XR include this feature starting with iOS 13.1. Learn about performance management on iPhone 11 and later . The effects of performance management on these newer models might be less noticeable due to their more advanced hardware and software design.

Devices updating from iOS 11.2.6 or earlier will initially have performance management disabled; it will be reenabled if the device subsequently experiences an unexpected shutdown.

All iPhone models include fundamental performance management to ensure that the battery and overall system operates as designed and internal components are protected. This includes behavior in hot or cold temperatures, as well as internal voltage management. This type of performance management is required for safety and expected function, and cannot be turned off.

image alt text

Your battery's maximum capacity

The Battery Health screen includes information on maximum battery capacity and peak performance capability.

Maximum battery capacity measures the device battery capacity relative to when it was new. A battery will have lower capacity as the battery chemically ages, which might result in fewer hours of usage between charges. Depending upon the length of time between when the iPhone was made and when it's activated, your battery capacity might show as slightly less than 100 percent.

Batteries of iPhone 14 models and earlier are designed to retain 80 percent of their original capacity at 500 complete charge cycles under ideal conditions.* Batteries of iPhone 15 models are designed to retain 80 percent of their original capacity at 1000 complete charge cycles under ideal conditions.* With all models, the exact capacity percentage depends on how the devices are regularly used and charged. The one-year warranty includes service coverage for a defective battery in addition to rights provided under local consumer laws. If it is out of warranty, Apple offers battery service for a charge. Learn more about charge cycles.

As your battery health degrades, so can its ability to deliver peak performance. The Battery Health screen includes a section for Peak Performance Capability where the following messages might appear.

Performance is normal

When the battery condition can support normal peak performance and does not have the performance management features applied, you'll see this message:

Your battery is currently supporting normal peak performance.

image alt text

Performance management applied

When the performance management features have been applied, you'll see this message:

This iPhone has experienced an unexpected shutdown because the battery was unable to deliver the necessary peak power. Performance management has been applied to help prevent this from happening again. Disable…

Note that if you disable performance management, you can’t turn it back on. It will be turned on again automatically if an unexpected shutdown occurs. The option to disable will also be available.

image alt text

Battery health unknown

If iOS is unable to determine the device battery health, you'll see this message:

This iPhone is unable to determine battery health. An Apple Authorized Service Provider can service the battery. More about service options…

This might be due to having an improperly installed battery or an unknown battery part.

image alt text

Performance management turned off

If you disable the applied performance-management feature, you'll see this message:

This iPhone has experienced an unexpected shutdown because the battery was unable to deliver the necessary peak power. You have manually disabled performance management protections.

If the device experiences another unexpected shutdown, the performance-management features will be reapplied. The option to disable will also be available.

image alt text

Battery health degraded

If battery health has degraded significantly, the below message will also appear:

Your battery’s health is significantly degraded. An Apple Authorized Service Provider can replace the battery to restore full performance and capacity. More about service options…

This message doesn't indicate a safety issue. You can still use your battery. However, you might experience more noticeable battery and performance issues. A new replacement battery will improve your experience. More about service options .

image alt text

Important Battery Message

If you see the message below, it means the battery in your iPhone is unable to be verified. This message applies to iPhone XS, iPhone XS Max, iPhone XR, and later.

Unable to verify this iPhone has a genuine Apple battery. Health information not available for this battery. Learn more...

Reported battery health information isn't available. To have your battery checked, contact an Apple Authorized Service Provider. More about service options .

Learn more about this message as it appears on iPhone 11 and iPhone 11 Pro and later .

Getting further assistance

If your device performance has been affected by an aged battery and you would like to get help with a battery replacement, contact Apple Support for service options.

Learn more about battery service and recycling .

Recalibration of battery health reporting on iPhone 11, iPhone 11 Pro, and iPhone 11 Pro Max

iOS 14.5 and later include an update to address inaccurate estimates of battery health reporting for some users. The battery health reporting system will recalibrate maximum battery capacity and peak performance capability on iPhone 11, iPhone 11 Pro, and iPhone 11 Pro Max.

Learn more about recalibration of battery health reporting in iOS 14.5 .

* When you use your iPhone, its battery goes through charge cycles. You complete one charge cycle when you’ve used an amount that represents 100 percent of your battery’s capacity. A complete charge cycle is normalized between 80 percent and 100 percent of original capacity to account for expected diminishing battery capacity over time.

right-icon

Lorem ipsum dolor sit amet, consectetur adipiscing elit. Vivamus convallis sem tellus, vitae egestas felis vestibule ut.

Error message details.

Reuse Permissions

Request permission to republish or redistribute SHRM content and materials.

The Performance Review Problem

As the arcane annual assessment earns a failing grade, employers struggle to create a better system to measure and motivate their workers.

​After an annual review that lasted about 10 minutes, a New Jersey-based account coordinator knew it was time to leave the public relations agency where he had worked for almost a year. 

The 25-year-old, who requested anonymity, asked for the meeting because his boss had not mentioned any formal assessment process, nor had his manager ever critiqued his work. The coordinator says he sat with a trio of senior executives who did not ask him any questions beyond how he would rate himself. He says they ignored his requests for guidance on how to advance at the agency. 

Screen Shot 2023-03-15 at 85749 AM.png

This example also illustrates one of the common failures in performance management: limiting reviews to once or twice a year without having any other meaningful career discussions in between. Nearly half (49 percent) of companies give annual or semiannual reviews, according to a study of 1,000 full-time U.S. employees released late last year by software company Workhuman. 

The only situation that is worse than doing one review per year is doing none at all, experts say. The good news is that only 7 percent of companies are keeping employees in the dark about their performance, and 28 percent of organizations are conducting assessments quarterly, the Workhuman study found.  

A Pervasive Problem

Reviews generally do not work.

That doesn’t mean that more-frequent formal meetings or casual sit-downs between supervisors and their direct reports are solving the performance review quandary, either. Only about 1 in 4 companies in North America (26 percent) said their performance management systems were effective, according to a survey of 837 companies conducted last fall by consulting firm WTW. And only one-third of the organizations said employees felt their efforts were evaluated fairly. 

Meanwhile, a Gallup survey conducted last year found that 95 percent of managers are dissatisfied with their organization’s review system.

The problem is not new, though it is taking on greater importance, experts say. Millennials and members of Generation Z crave feedback and are focused on career development. Meanwhile, the tight labor market has companies searching for ways to keep high-performing employees in the fold. Fewer than 20 percent of employees feel inspired by their reviews, and disengaged employees cost U.S. companies a collective $1.6 trillion a year, according to Gallup.

Lesli Jennings, a senior director at WTW, says part of the issue is that reviews are now so much more than a discussion of past performance. They include conversations about career development, employee experience and compensation. 

“The performance management design itself is not evolving as quickly as the objectives and the purpose that we have set out for what we want it to do,” Jennings says. 

Screen Shot 2023-03-15 at 84340 AM.png

Poor Review Practices

Some argue that means it’s time to completely scrap annual reviews and stop using scales composed of numbers or adjectives to rate employees. 

“Every single human alive today is a horribly unreliable rater of other human beings,” says Marcus Buckingham, head of people and performance research at the Roseland, N.J.-based ADP Research Institute. He says people bring their own backgrounds and personalities to bear in the reviews in what is called the “idiosyncratic rating effect.” He says the ratings managers bestow on others are more a reflection of themselves than of those they’re reviewing.

Buckingham adds that very few positions have quantifiable outcomes that can be considered a measure of competence, talent or success. It’s possible to tally a salesperson’s results or test someone’s knowledge of a computer program, he says, but he’s baffled by attempts to measure attributes such as “leadership potential.”

“I’m going to rate you on a theoretical construct like ‘strategic thinking’? Everybody knows that’s rubbish,” Buckingham says. He adds that performance reviews that offer rankings give “data that’s just bad” and insists that companies rely on data analytics because they don’t trust their managers’ judgment. But instead of working on improving their managers’ skills, he says, they put data systems in place. 

“Because we don’t educate our managers on how to have some of these conversations, we’ve decided that the solution is to give them really bad ratings systems or really bad categorization systems,” Buckingham says. 

R eviewing the Data

A mong North American employers:

  • More than 9 in 10 (93 percent) cited driving organizational performance as a key objective for performance management, yet less than half (44 percent) said their performance management program is ­meeting that objective.
  • Nearly 3 in 4 (72 percent) said ­supporting the career development of their employees is a primary objective, but only 31 percent said their performance management program was meeting that objective.
  • Less than half (49 percent) agreed that managers at their organization are ­effective at assessing the performance of their direct reports. 
  • Only 1 in 3 indicated that employees feel their performance is evaluated fairly. 
  • Just 1 in 6 (16 percent) reported having altered their performance management approach to align with remote and hybrid work models, which are rapidly becoming more prevalent.

Source: WTW 2022 Performance Reset Survey of 837 organizations worldwide, including 150 North American employers.

Data Lovers

Ratings aren’t likely to disappear anytime soon, however. “Data-driven” has become a rallying cry for companies as they seek to operate more efficiently. Organizations are trying to measure everything from sales to productivity, though such efforts can cause turmoil and hurt some individuals’ careers.

A June 2022 study of nearly 30,000 workers at an unnamed North American retail chain found that women were more likely to receive higher overall ratings than men, though women were ranked lower on “potential.” 

In that study, women were 12 percent more likely to be given the lowest rating for potential, as well as 15 percent and 28 percent less likely to receive the middle and highest potential ratings, respectively, according to the professors who conducted the study, Alan Benson of the University of Minnesota, Danielle Li of MIT and Kelly Shue of Yale. The authors also said women were 14 percent less likely to get promoted than men. “Because potential is not directly observed,” they noted, “these assessments can be highly subjective, leaving room for bias.” 

Screen Shot 2023-03-15 at 85749 AM.png

Birmingham left abruptly one afternoon and did not go in to work the next day, which he says Blizzard interpreted as his resignation. Blizzard did not respond to requests for comment.

Stack ranking became popular in the 1980s after it was embraced by General Electric. Its adoption has waned, though several tech companies continue to use it. Google and Twitter relied on stack ranking to decide who to let go in their recent rounds of layoffs, according to published reports.

Birmingham says that the system can cause anxiety and competition, which can kill team cohesion, and that arbitrary lower ratings adversely affect compensation and promotion potential. These systems can also suggest that a manager is ineffective, he says. “It implies that as managers, we basically have not done our job to hire them and train them appropriately or terminate them if they really aren’t working out.”

Birmingham says he is not opposed to ranking systems but doesn’t think they’re necessary. “I feel like the conversation about how to improve your career, what the expectations are for your job and what it will take to get to the next level are all things you can do without a rating,” he says.

Measurements Matter

Grant Pruitt, president and co-founder of Whitebox Real Estate, does not give any type of rating in his performance reviews, though he believes in using data to track his employees’ performance. “What isn’t measured can’t be managed,” says Pruitt, whose company has about 20 employees in several offices across Texas. 

At the beginning of the year, Whitebox employees set goals with their managers. Discussions are held about what benchmarks are reasonable, and these targets can be changed if there is a meaningful shift in business conditions. Team leaders hold weekly department meetings with their direct reports to discuss what’s happening and track progress. Managers hold quarterly private reviews with individuals to dig deeper into whether they’re meeting their goals and if not, why.

“Was it an achievable goal? Realistic? If it was, then what do we need to do to make sure we don’t miss it the next time?” Pruitt says. Whitebox switched to quarterly reviews about four years ago to address problems earlier and avoid having issues fester, Pruitt adds.

It’s easier to set goals for people in sales than for those in other departments, Pruitt concedes. However, he adds that executives need to brainstorm about targets they can use for other roles. For example, administrative employees can be rated on how quickly and efficiently they handle requests.

Pruitt maintains that the goal system makes it easier to respond when an employee disagrees with their manager about their performance review because there are quantitative measures to examine. The data also helps eliminate any unconscious bias a manager may have and helps ensure that a leader isn’t just giving an employee a good rating because they work out at the same gym or their children go to school together.

“I think that’s really where the numbers and the data are important,” Pruitt says. “The data doesn’t know whose kids play on the same sports team.”

Whitebox employees are also judged on how well they embrace the company’s core values, such as integrity, tenacity and coachability. Some of those values may require more-subjective judgments that can be more important than hitting quantifiable goals. 

Pruitt admits that there were occasions when he looked the other way with a few individuals who were “hitting it out of the park,” even though he believed they lacked integrity. But eventually, he had to let them go and the company lost money.

“They really came back to bite me,” Pruitt says.

Screen Shot 2023-03-15 at 84352 AM.png

Grades Are Good

Diane Dooley, CHRO of Iselin, N.J.-based World Insurance Associates LLC, also believes establishing quantitative methods to gauge employees’ performance is essential. “We are living in a world of data analytics,” she says. The broker’s roughly 2,000 employees are rated on a scale of 1 to 5.

World Insurance has taken numerous steps to remove bias from reviews. For example, last year the company conducted unconscious-bias training to help managers separate personal feelings from performance reviews. And all people managers convene to go over the reviews they’ve conducted. Dooley says that process gives everyone a chance to discuss why an employee was given a certain rank and to question some decisions. “We want to make sure we’re using the same standards,” she explains.

Currently, World Insurance conducts reviews only once a year because it has been on an acquisition binge and there hasn’t been time to institute a more frequent schedule. That will change eventually, says Dooley, who adds that she wants to introduce department grids that show how an employee’s rank compares to others’ on the team. 

“It’s just a tool that helps the department or the division understand where their people are and how we can help them collectively,” says Dooley, who has used the system at other companies. 

Dooley says she isn’t worried about World Insurance holding reviews only annually, because good managers regularly check in with their employees regardless of how frequently reviews are mandated.

Such conversations can easily fall through the cracks, however. “Managers want to manage the employees, but they get so caught up in the company’s KPIs [key performance indicators] and making sure that they’re doing everything that they need to do,” says Jennifer Currence, SHRM-SCP, CEO of WithIn Leadership, a leadership development and coaching firm in Tampa, Fla. “It’s hard to set aside the time.” 

WTW’s Jennings adds that managers sometimes avoid initiating conversations with employees who are not performing well. Such discussions are often difficult, and managers may not feel equipped to conduct them. 

“Having to address underperformers is hard work,” Jennings says. 

Additionally, experts say, coaching managers to engage in such sensitive discourse can be expensive and time-consuming.

Improve Your Performance Reviews

H ere’s how to make the review process more ­palatable for both managers and their direct reports:

  • Don’t limit conversations to once or twice per year. Every team is different, so leaders should decide what schedule is most appropriate for their departments. However, it’s important to deal with any problems as they arise; don’t let them fester.
  • Set performance goals and expectations at the beginning of the year so employees understand their responsibilities. This helps lend objectivity to the process by introducing measurable targets. However, the goals should be adjusted if there are major changes to the business or an employee’s circumstances. 
  • Explain how each employee’s position, as well as each department, fits into the company’s overall ­strategy. This will help employees understand why their job matters and why it’s important.
  • Simplify the process. There’s no need for a ­double-digit number of steps or numerous
  • questions that require long-winded answers. 
  • Consider a 360-degree approach. Input from employees’ colleagues or from other managers can help give a fuller picture of employees’ capabilities and contributions.
  • Eliminate proximity bias. You may not see some employees as often as others, especially if they work remotely, but that doesn’t mean they’re not working hard. 
  • End recency bias, which is basing a review on an employee’s most recent performance while ignoring earlier efforts. Don’t let recent mistakes overshadow the employee’s other impressive accomplishments.
  • Solicit feedback from employees. Reviews should be a two-way conversation, not a lecture.
  • Train managers to give advice calmly and helpfully. This is especially important when leaders must call out an employee’s subpar performance. 
  • Don’t discuss compensation during reviews. Employees are likely to be so focused on learning about a raise or bonus that they won’t pay much attention to anything else.

Increase Conversations

Finding the right formula for performance reviews is tricky. The company’s size, values, industry and age all play a role. Currence says businesses need to think about the frequency and purpose of these meetings. Some managers may have weekly discussions with their direct reports, but the conversations might center on status updates as opposed to performance. 

“We need to have more regular conversations,” Currence says. “There has to be a happy balance.”

San Jose, Calif.-based software maker Adobe Inc. was a pioneer when it eliminated annual reviews in 2012 after employees said assessments that look backward weren’t useful and managers lamented how time-consuming they were. Instead, Adobe introduced quarterly check-ins and did away with its numerical ratings system, even though the company is “data-driven,” according to Arden Madsen, senior director of talent management.

Screen Shot 2023-03-15 at 85749 AM.png

Adobe’s system has changed over the years as the company grew from about 11,000 employees in 2012 to around 28,000 today. In the beginning, employees were not asked a universal set of questions and the information gathered was not stored in a central place accessible to all. In 2020, Adobe instituted three or four questions that must be asked at each quarterly meeting, one of which is whether the employee has feedback for the manager. Other topics covered depend on the employee, their role and their goals.

Madsen says asking consistent questions and making reviews easily accessible are important, as internal mobility within the company has grown. 

Adobe, like many businesses, separates conversations about performance from discussions about raises and bonuses, even though they’re intertwined. 

“Money is so emotionally charged,” says WithIn Leadership’s Currence. “When we tie performance review conversations with money, we as human beings do not hear anything about performance. We only focus on the money.”    

Theresa Agovino is the workplace editor for SHRM.

Illustrations by Neil Jamieson.

Related Articles

sample problem solving percentage

Rising Demand for Workforce AI Skills Leads to Calls for Upskilling

As artificial intelligence technology continues to develop, the demand for workers with the ability to work alongside and manage AI systems will increase. This means that workers who are not able to adapt and learn these new skills will be left behind in the job market.

A vast majority of U.S. professionals  think students should be prepared to use AI upon entering the workforce.

Employers Want New Grads with AI Experience, Knowledge

A vast majority of U.S. professionals say students entering the workforce should have experience using AI and be prepared to use it in the workplace, and they expect higher education to play a critical role in that preparation.

HR Daily Newsletter

New, trends and analysis, as well as breaking news alerts, to help HR professionals do their jobs better each business day.

Success title

Success caption

Read our research on: Immigration & Migration | Podcasts | Election 2024

Regions & Countries

How americans view the situation at the u.s.-mexico border, its causes and consequences, 80% say the u.s. government is doing a bad job handling the migrant influx.

sample problem solving percentage

Pew Research Center conducted this study to understand the public’s views about the large number of migrants seeking to enter the U.S. at the border with Mexico. For this analysis, we surveyed 5,140 adults from Jan. 16-21, 2024. Everyone who took part in this survey is a member of the Center’s American Trends Panel (ATP), an online survey panel that is recruited through national, random sampling of residential addresses. This way nearly all U.S. adults have a chance of selection. The survey is weighted to be representative of the U.S. adult population by gender, race, ethnicity, partisan affiliation, education and other categories. Read more about the ATP’s methodology .

Here are the questions used for the report and its methodology .

The growing number of migrants seeking entry into the United States at its border with Mexico has strained government resources, divided Congress and emerged as a contentious issue in the 2024 presidential campaign .

Chart shows Why do Americans think there is an influx of migrants to the United States?

Americans overwhelmingly fault the government for how it has handled the migrant situation. Beyond that, however, there are deep differences – over why the migrants are coming to the U.S., proposals for addressing the situation, and even whether it should be described as a “crisis.”

Factors behind the migrant influx

Economic factors – either poor conditions in migrants’ home countries or better economic opportunities in the United States – are widely viewed as major reasons for the migrant influx.

About seven-in-ten Americans (71%), including majorities in both parties, cite better economic opportunities in the U.S. as a major reason.

There are wider partisan differences over other factors.

About two-thirds of Americans (65%) say violence in migrants’ home countries is a major reason for why a large number of immigrants have come to the border.

Democrats and Democratic-leaning independents are 30 percentage points more likely than Republicans and Republican leaners to cite this as a major reason (79% vs. 49%).

By contrast, 76% of Republicans say the belief that U.S. immigration policies will make it easy to stay in the country once they arrive is a major factor. About half as many Democrats (39%) say the same.

For more on Americans’ views of these and other reasons, visit Chapter 2.

How serious is the situation at the border?

A sizable majority of Americans (78%) say the large number of migrants seeking to enter this country at the U.S.-Mexico border is eithera crisis (45%) or a major problem (32%), according to the Pew Research Center survey, conducted Jan. 16-21, 2024, among 5,140 adults.

Related: Migrant encounters at the U.S.-Mexico border hit a record high at the end of 2023 .

Chart shows Border situation viewed as a ‘crisis’ by most Republicans; Democrats are more likely to call it a ‘problem’

  • Republicans are much more likely than Democrats to describe the situation as a “crisis”: 70% of Republicans say this, compared with just 22% of Democrats.
  • Democrats mostly view the situation as a major problem (44%) or minor problem (26%) for the U.S. Very few Democrats (7%) say it is not a problem.

In an open-ended question , respondents voice their concerns about the migrant influx. They point to numerous issues, including worries about how the migrants are cared for and general problems with the immigration system.

Yet two concerns come up most frequently:

  • 22% point to the economic burdens associated with the migrant influx, including the strains migrants place on social services and other government resources.
  • 22% also cite security concerns. Many of these responses focus on crime (10%), terrorism (10%) and drugs (3%).

When asked specifically about the impact of the migrant influx on crime in the United States, a majority of Americans (57%) say the large number of migrants seeking to enter the country leads to more crime. Fewer (39%) say this does not have much of an impact on crime in this country.

Republicans (85%) overwhelmingly say the migrant surge leads to increased crime in the U.S. A far smaller share of Democrats (31%) say the same; 63% of Democrats instead say it does not have much of an impact.

Government widely criticized for its handling of migrant influx

For the past several years, the federal government has gotten low ratings for its handling of the situation at the U.S.-Mexico border. (Note: The wording of this question has been modified modestly to reflect circumstances at the time).

Chart shows Only about a quarter of Democrats and even fewer Republicans say the government has done a good job dealing with large number of migrants at the border

However, the current ratings are extraordinarily low.

Just 18% say the U.S. government is doing a good job dealing with the large number of migrants at the border, while 80% say it is doing a bad job, including 45% who say it is doing a very bad job.

  • Republicans’ views are overwhelmingly negative (89% say it’s doing a bad job), as they have been since Joe Biden became president.
  • 73% of Democrats also give the government negative ratings, the highest share recorded during Biden’s presidency.

For more on Americans’ evaluations of the situation, visit Chapter 1 .

Which policies could improve the border situation?

There is no single policy proposal, among the nine included on the survey, that majorities of both Republicans and Democrats say would improve the situation at the U.S.-Mexico border. There are areas of relative agreement, however.

A 60% majority of Americans say that increasing the number of immigration judges and staff in order to make decisions on asylum more quickly would make the situation better. Only 11% say it would make things worse, while 14% think it would not make much difference.

Nearly as many (56%) say creating more opportunities for people to legally immigrate to the U.S. would make the situation better.

Chart shows Most Democrats and nearly half of Republicans say boosting resources for quicker decisions on asylum cases would improve situation at Mexico border

Majorities of Democrats say each of these proposals would make the border situation better.

Republicans are less positive than are Democrats; still, about 40% or more of Republicans say each would improve the situation, while far fewer say they would make things worse.

Opinions on other proposals are more polarized. For example, a 56% majority of Democrats say that adding resources to provide safe and sanitary conditions for migrants arriving in the U.S. would be a positive step forward.

Republicans not only are far less likely than Democrats to view this proposal positively, but far more say it would make the situation worse (43%) than better (17%).

Chart shows Wide partisan gaps in views of expanding border wall, providing ‘safe and sanitary conditions’ for migrants

Building or expanding a wall along the U.S.-Mexico border was among the most divisive policies of Donald Trump’s presidency. In 2019, 82% of Republicans favored expanding the border wall , compared with just 6% of Democrats.

Today, 72% of Republicans say substantially expanding the wall along the U.S. border with Mexico would make the situation better. Just 15% of Democrats concur, with most saying either it would not make much of a difference (47%) or it would make things worse (24%).

For more on Americans’ reactions to policy proposals, visit Chapter 3 .

Add Pew Research Center to your Alexa

Say “Alexa, enable the Pew Research Center flash briefing”

Report Materials

Table of contents, fast facts on how greeks see migrants as greece-turkey border crisis deepens, americans’ immigration policy priorities: divisions between – and within – the two parties, from the archives: in ’60s, americans gave thumbs-up to immigration law that changed the nation, around the world, more say immigrants are a strength than a burden, latinos have become less likely to say there are too many immigrants in u.s., most popular.

About Pew Research Center Pew Research Center is a nonpartisan fact tank that informs the public about the issues, attitudes and trends shaping the world. It conducts public opinion polling, demographic research, media content analysis and other empirical social science research. Pew Research Center does not take policy positions. It is a subsidiary of The Pew Charitable Trusts .

IMAGES

  1. Solving Percent Problems (examples, solutions, worksheets, videos

    sample problem solving percentage

  2. Percentage Word Problems

    sample problem solving percentage

  3. Solve Percent Problems using the Proportion Method

    sample problem solving percentage

  4. Example 2: Solve a Percent Problem Using a Percent Equation

    sample problem solving percentage

  5. 6th Grade Math Word Problems

    sample problem solving percentage

  6. Percentage Problem 1

    sample problem solving percentage

COMMENTS

  1. 5.2.1: Solving Percent Problems

    To solve percent problems, you can use the equation, Percent ⋅ Base = Amount , and solve for the unknown numbers. Or, you can set up the proportion, Percent = amount base , where the percent is a ratio of a number to 100. You can then use cross multiplication to solve the proportion. Percents are a ratio of a number and 100, so they are ...

  2. Solved Examples on Percentage

    The solved examples on percentage will help us to understand how to solve step-by-step different types of percentage problems. Now we will apply the concept of percentage to solve various real-life examples on percentage. Solved examples on percentage: 1. In an election, candidate A got 75% of the total valid votes.

  3. Percent Maths Problems

    Problems that deal with percentage increase and decrease as well as problems of percent of quantities. ... y = 30 and solve for x which the original price. x - 0.22 x = 30 0.78 x = 30 x = $38.5 ... invested is also known 10,000 = x + y Solve the system of the equations to find x and y. x = $3000 and y = $7000 As a practice check that 7.5% of $ ...

  4. How to Solve Percent Problems? (+FREE Worksheet!)

    Learn how to calculate and solve percent problems using the percent formula. Learn how to calculate and solve percent problems using the percent formula. Effortless Math. X + eBooks ... Percent Problems - Example 3: \(1.2\) is what percent of \(24\)? Solution: In this problem, we are looking for the percent. Use the following equation:

  5. 7.3: Solving Basic Percent Problems

    Now we can solve our equation for x. 10 = 80x Original equation. 10 80 = 80x 80 Divide both sides by 80. 1 8 = x Reduce: 10 / 80 = 1 / 8. 0.125 = x Divide: 1 / 8 = 0.125. But we must express our answer as a percent. To do this, move the decimal two places to the right and append a percent symbol. Thus, 10 is 12.5% of 80.

  6. How to Solve Percentage Problems with Examples?

    While we are on the topic of percentages, one example will be, the decimal 0.35, or the fraction \(\frac{7}{20}\), which is equivalent to 35 percent, or 35%. Solving Problems Based on Percentages By solving problems based on percentages, we can find the missing values and find the values of various unknowns in a given problem.

  7. Solving Percent Problems (examples, solutions, worksheets, videos

    Examples, solutions, and videos that will help GMAT students review how to solve percent word problems. The following diagram shows some examples of solving percent problems using the part, base, rate formula. Scroll down the page for more examples and solutions of solving percent problems. Solving Percent Problems. Show Step-by-step Solutions.

  8. 4.2: Percents Problems and Applications of Percent

    Subtract the two numbers to find the amount of decrease. Using this result as the amount and the original number as the base, find the unknown percent. Again, we always use the original number for the base, the number that occurred earlier in time. For a percent decrease, this is the larger of the two numbers. Exercises 4.2.1 4.2. 1.

  9. Percentages

    Practice. Intro to percents Get 5 of 7 questions to level up! Percents from fraction models Get 3 of 4 questions to level up! Visualize percents. ... Percent word problems Get 5 of 7 questions to level up! Quiz 3. Level up on the above skills and collect up to 160 Mastery points Start quiz. Up next for you:

  10. Solving percent problems (video)

    25% is part of a whole 100%.*. *25% is 1/4 of 100%*. so, you know that (150) is 1/4 of the answer (100%) Add 150 - 4 times (Because we know that 25% X 4 = 100%) And that is equal to: (150 + 150 + 150 + 150) = *600. The method they used in the video is also correct, but i think that this one is easier, and will make it more simple to solve the ...

  11. Solving Percent Problems

    Example. Problem. Write a proportion to find the answer to the following question. 30 is 20% of what number? = The percent in this problem is 20%. Write this percent in fractional form, with 100 as the denominator. The percent is written as the ratio , the amount is 30, and the base is unknown. 20 • n = 30 • 100. 20 • n = 3,000

  12. Percentages Practice Questions

    The Corbettmaths Practice Questions on finding a percentage of an amount.

  13. Solving problems with percentages

    To solve problems with percent we use the percent proportion shown in "Proportions and percent". a b = x 100 a b = x 100. a b ⋅b = x 100 ⋅ b a b ⋅ b = x 100 ⋅ b. a = x 100 ⋅ b a = x 100 ⋅ b. x/100 is called the rate. a = r ⋅ b ⇒ Percent = Rate ⋅ Base a = r ⋅ b ⇒ P e r c e n t = R a t e ⋅ B a s e. Where the base is the ...

  14. How to Solve Percent Problems

    So, to find 35% of 80, you would rewrite it as: 35% of 80 = 0.35 80. Solve the problem using decimal multiplication. Here's what the example looks like: So 35% of 80 is 28. As another example, suppose you want to find 12% of 31. Again, start by changing the percent to a decimal and the word of to a multiplication sign:

  15. Percent problems (practice)

    Report a problem. Do 4 problems. Learn for free about math, art, computer programming, economics, physics, chemistry, biology, medicine, finance, history, and more. Khan Academy is a nonprofit with the mission of providing a free, world-class education for anyone, anywhere.

  16. Percentage, Base, and Rate Problems

    This math video tutorial explains how to solve percentage, base, and rate problems.Percentages Made Easy: https://www.youtube.com/watc...

  17. Percentages Worksheets

    In the first few sections, there are worksheets involving the three main types of percentage problems: calculating the percentage value of a number, calculating the percentage rate of one number compared to another number, and calculating the original amount given the percentage value and the percentage rate. ... Example question: What ...

  18. Math Practice Problems

    Percentages - Sample Math Practice Problems The math problems below can be generated by MathScore.com, a math practice program for schools and individual families. ... See some of our other supported math practice problems. Complexity=100, Mode=decimal. Convert the decimal into a percentage. 1. 0.42 % 2. 0.01 % Complexity=200, Mode=decimal.

  19. Basic Problems on Percentage

    Basic problems on percentage will help us to get the basic concept to solve any percentage problems. We will learn how to apply the concept of percentage for solving some real-life problems. Basic problems on percentage: 1. What is 30 % of 80? Solution: 30 % of 80 = 30/100 × 80 = (30 × 80)/100 = 2400/100 = 24

  20. Word Problems on Percentage

    Word problems on percentage will help us to solve various types of problems related to percentage. Follow the procedure to solve similar type of percent problems. 1. In an exam Ashley secured 332 marks. If she secured 83 % makes, find the maximum marks.

  21. Percentages

    p = a b × 100. This equation can be rearranged to show a or b in terms of the other values: a = p 100 × b b = a ( p 100) = 100 × a p. [Examples] In word problems involving percentages, remember that the sum of all parts of the whole is 100 % . For example, if a teacher has graded 60 % of an assignment, then they have not graded 100 − 60 % ...

  22. Introduction to Percents

    Example: A Skateboard is reduced 25% in price. The old price was $120. Find the new price. First, find 25% of $120: 25% = 25100. ... So 10 percent of 50 apples is 5 apples: the 5 apples is the percentage. But in practice people use both words the same way. 877,878,879, 1301, 1302,880, 1303, 1304, 3501, 3502.

  23. Percentage Questions (with Answers)

    Percentage Questions and Solutions. Q.1: A fruit seller had some apples. He sells 40% apples and still has 420 apples. What is the total number of apples he had originally? Solution: Let the number of apples a fruit seller had be x. As per the given question, (100 - 40%) of x = 420. 60% of x = 420. 60/100 x = 420.

  24. iPhone Battery and Performance

    For iPhone 6 and later, iOS 11.3 and later add new features to show battery health and recommend if you need to replace the battery. You can find these in Settings > Battery > Battery Health (with iOS 16.1 or later, find these in Settings > Battery > Battery Health & Charging). Additionally, you can see if the performance-management feature ...

  25. The Performance Review Problem

    More than 9 in 10 (93 percent) cited driving organizational performance as a key objective for performance management, yet less than half (44 percent) said their performance management program is ...

  26. The U.S.-Mexico Border: How Americans View the Situation, Its Causes

    Democrats mostly view the situation as a major problem (44%) or minor problem (26%) for the U.S. Very few Democrats (7%) say it is not a problem. In an open-ended question, respondents voice their concerns about the migrant influx. They point to numerous issues, including worries about how the migrants are cared for and general problems with ...