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Top 10 Pre-Algebra Practice Questions

Top 10 Pre-Algebra Practice Questions

Preparing for Pre-Algebra test? The best way to prepare for your Pre-Algebra test is to work through as many Pre-Algebra practice questions as possible. Here are the top 10 Pre-Algebra practice questions to help you review the most important Pre-Algebra concepts. These Pre-Algebra practice questions are designed to cover mathematics concepts and topics that are found on the actual test. The questions have been fully updated to reflect the latest 2022 Pre-Algebra guidelines. Answers and full explanations are provided at the end of the post.

Start your Pre-Algebra test prep journey right now with these sample Pre-Algebra questions.

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Pre-algebra practice questions.

1- What is the value of the expression \((5(x-2y)+(2-x)^2) \) when \(x=3\) and \(y=-2\) ?

2- What is the slope of a line that is perpendicular to the line \(4x-2y=12\) ?

D.\(-\frac{1}{2}\)

3- Which of the following is equal to the expression below? \((2x+2y)(2x-y)\)

A. \(4x^2- 2y^2\)

B. \(2x^2+6xy-2y^2\)

C. \(24x^2+2xy-2y^2\)

D. \(4x^2+2xy-2y^2\)

4- What is the product of all possible values of x in the following equation? \(|x-10| = 3\)

5- \( [6 \times (- 24) + 8] – (-4) + [4 \times 5] \div 2 = ? \)

B. \(-112\)

C. \(-122\)

D. \(-144\)

6- What is the value of x in the following system of equations? \(2x+5y=11\) \(4x-2y=-14\)

7- What is the median of these numbers? 2, 27, 28, 19, 67, 44, 35

8- A swimming pool holds 2,000 cubic feet of water. The swimming pool is 25 feet long and 10 feet wide. How deep is the swimming pool?_______

9- The area of a circle is \(64 π\). Which of the following is the circumference of the circle?

A. 8\(\pi\)

B. 12\(\pi\)

C. 16\(\pi\)

D. 64\(\pi\)

10- What is the value of \(3^6 \) ?______

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1- D Plug in the value of \(x\) and \(y\). \(x=3\) and \(y=-2\) \((5(x-2y)+(2-x)^2)=(5(3-2(-2))+(2-3)^2)=(5(3+4)+(-1)^2) = 35+1=36\)

2- D The equation of a line in slope intercept form is: \(y=mx+b\) Solve for \(y\). \(4x-2y=12 {\Rightarrow} -2y=12-4x {\Rightarrow} y=(12-4x){\div}(-2) {\Rightarrow} y=2x-6\) The slope of this line is 2. The product of the slopes of two perpendicular lines is -1. Therefore, the slope of a line that is perpendicular to this line is: \(m_{1} {\times} m_{2} = -1 {\Rightarrow} 2 {\times} m_{2} = -1 {\Rightarrow} m_{2} = \frac{-1}{2}\)

3- D Use FOIL method. \((2x+2y)(2x-y) = 4x^2-2xy+4xy-2y^2=4x^2+2xy-2y^2\)

4- D To solve absolute values equations, write two equations. \(x-10\) could be positive 3, or negative 3. Therefore, \(x-10=3 \Rightarrow x=13\) \(x-10=-3 \Rightarrow x=7\) Find the product of solutions: \(7 \times 13 = 91\)

5- C Use PEMDAS (order of operation): \([6 {\times} (- 24) + 8] – (- 4) + [4 × 5] {\div} 2 \) \( [- 144 + 8] – (- 4) + [20] {\div} 2 = [- 144 + 8] – (- 4) + 10 \) \([- 136] – (- 4) + 10 = [- 136] + 4 + 10 = – 122\)

6- D Solving Systems of Equations by Elimination Multiply the first equation by (-2), then add it to the second equation. \({-2(2x+5y= 11) \ 4x-2y=-14} {\Rightarrow} {-4x-10y= -22 \ 4x-2y=-14} {\Rightarrow} {-12y= -36} {\Rightarrow} {y= 3}\) Plug in the value of y into one of the equations and solve for x. \(2x+5(3)= 11 {\Rightarrow} 2x+15= 11 {\Rightarrow} 2x= -4 {\Rightarrow} x= -2\)

7- B Write the numbers in order: 2, 19, 27, 28, 35, 44, 67 Median is the number in the middle. So, the median is 28

8- 8 Use formula of rectangle prism volume. \(V = (length) (width) (height) {\Rightarrow} 2000 = (25) (10) (height) {\Rightarrow} height = 2000 {\div} 250 = 8\)

9- C The area of the circle is \(16 π\). Use the formula of areas of circles. \(Area = πr^2 ⇒ 64 π> πr^2⇒ 64 > r^2⇒ r < 8\) The radius of the circle is 8. Let’s put 8 for the radius. Now, use the circumference formula: \(Circumference =2πr=2π (8)=16π\)

10- 729 \((3^6 ) = 3 × 3 × 3 × 3 × 3 × 3 = 729\)

Looking for the best resource to help you succeed on the Pre-Algebra Math test?

The Best Books to Ace Algebra

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.

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

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  • 9.1 Use a Problem Solving Strategy
  • Introduction
  • 1.1 Introduction to Whole Numbers
  • 1.2 Add Whole Numbers
  • 1.3 Subtract Whole Numbers
  • 1.4 Multiply Whole Numbers
  • 1.5 Divide Whole Numbers
  • Key Concepts
  • Review Exercises
  • Practice Test
  • Introduction to the Language of Algebra
  • 2.1 Use the Language of Algebra
  • 2.2 Evaluate, Simplify, and Translate Expressions
  • 2.3 Solving Equations Using the Subtraction and Addition Properties of Equality
  • 2.4 Find Multiples and Factors
  • 2.5 Prime Factorization and the Least Common Multiple
  • Introduction to Integers
  • 3.1 Introduction to Integers
  • 3.2 Add Integers
  • 3.3 Subtract Integers
  • 3.4 Multiply and Divide Integers
  • 3.5 Solve Equations Using Integers; The Division Property of Equality
  • Introduction to Fractions
  • 4.1 Visualize Fractions
  • 4.2 Multiply and Divide Fractions
  • 4.3 Multiply and Divide Mixed Numbers and Complex Fractions
  • 4.4 Add and Subtract Fractions with Common Denominators
  • 4.5 Add and Subtract Fractions with Different Denominators
  • 4.6 Add and Subtract Mixed Numbers
  • 4.7 Solve Equations with Fractions
  • Introduction to Decimals
  • 5.1 Decimals
  • 5.2 Decimal Operations
  • 5.3 Decimals and Fractions
  • 5.4 Solve Equations with Decimals
  • 5.5 Averages and Probability
  • 5.6 Ratios and Rate
  • 5.7 Simplify and Use Square Roots
  • Introduction to Percents
  • 6.1 Understand Percent
  • 6.2 Solve General Applications of Percent
  • 6.3 Solve Sales Tax, Commission, and Discount Applications
  • 6.4 Solve Simple Interest Applications
  • 6.5 Solve Proportions and their Applications
  • Introduction to the Properties of Real Numbers
  • 7.1 Rational and Irrational Numbers
  • 7.2 Commutative and Associative Properties
  • 7.3 Distributive Property
  • 7.4 Properties of Identity, Inverses, and Zero
  • 7.5 Systems of Measurement
  • Introduction to Solving Linear Equations
  • 8.1 Solve Equations Using the Subtraction and Addition Properties of Equality
  • 8.2 Solve Equations Using the Division and Multiplication Properties of Equality
  • 8.3 Solve Equations with Variables and Constants on Both Sides
  • 8.4 Solve Equations with Fraction or Decimal Coefficients
  • 9.2 Solve Money Applications
  • 9.3 Use Properties of Angles, Triangles, and the Pythagorean Theorem
  • 9.4 Use Properties of Rectangles, Triangles, and Trapezoids
  • 9.5 Solve Geometry Applications: Circles and Irregular Figures
  • 9.6 Solve Geometry Applications: Volume and Surface Area
  • 9.7 Solve a Formula for a Specific Variable
  • Introduction to Polynomials
  • 10.1 Add and Subtract Polynomials
  • 10.2 Use Multiplication Properties of Exponents
  • 10.3 Multiply Polynomials
  • 10.4 Divide Monomials
  • 10.5 Integer Exponents and Scientific Notation
  • 10.6 Introduction to Factoring Polynomials
  • 11.1 Use the Rectangular Coordinate System
  • 11.2 Graphing Linear Equations
  • 11.3 Graphing with Intercepts
  • 11.4 Understand Slope of a Line
  • A | Cumulative Review
  • B | Powers and Roots Tables
  • C | Geometric Formulas

Learning Objectives

By the end of this section, you will be able to:

  • Approach word problems with a positive attitude
  • Use a problem solving strategy for word problems
  • Solve number problems

Be Prepared 9.1

Before you get started, take this readiness quiz.

Translate “6 “6 less than twice x ” x ” into an algebraic expression. If you missed this problem, review Example 2.25 .

Be Prepared 9.2

Solve: 2 3 x = 24 . 2 3 x = 24 . If you missed this problem, review Example 8.16 .

Be Prepared 9.3

Solve: 3 x + 8 = 14 . 3 x + 8 = 14 . If you missed this problem, review Example 8.20 .

Approach Word Problems with a Positive Attitude

The world is full of word problems. How much money do I need to fill the car with gas? How much should I tip the server at a restaurant? How many socks should I pack for vacation? How big a turkey do I need to buy for Thanksgiving dinner, and what time do I need to put it in the oven? If my sister and I buy our mother a present, how much will each of us pay?

Now that we can solve equations, we are ready to apply our new skills to word problems. Do you know anyone who has had negative experiences in the past with word problems? Have you ever had thoughts like the student in Figure 9.2 ?

When we feel we have no control, and continue repeating negative thoughts, we set up barriers to success. We need to calm our fears and change our negative feelings.

Start with a fresh slate and begin to think positive thoughts like the student in Figure 9.3 . Read the positive thoughts and say them out loud.

If we take control and believe we can be successful, we will be able to master word problems.

Think of something that you can do now but couldn't do three years ago. Whether it's driving a car, snowboarding, cooking a gourmet meal, or speaking a new language, you have been able to learn and master a new skill. Word problems are no different. Even if you have struggled with word problems in the past, you have acquired many new math skills that will help you succeed now!

Use a Problem-solving Strategy for Word Problems

In earlier chapters, you translated word phrases into algebraic expressions, using some basic mathematical vocabulary and symbols. Since then you've increased your math vocabulary as you learned about more algebraic procedures, and you've had more practice translating from words into algebra.

You have also translated word sentences into algebraic equations and solved some word problems. The word problems applied math to everyday situations. You had to restate the situation in one sentence, assign a variable, and then write an equation to solve. This method works as long as the situation is familiar to you and the math is not too complicated.

Now we'll develop a strategy you can use to solve any word problem. This strategy will help you become successful with word problems. We'll demonstrate the strategy as we solve the following problem.

Example 9.1

Pete bought a shirt on sale for $18 , $18 , which is one-half the original price. What was the original price of the shirt?

Step 1. Read the problem. Make sure you understand all the words and ideas. You may need to read the problem two or more times. If there are words you don't understand, look them up in a dictionary or on the Internet.

  • In this problem, do you understand what is being discussed? Do you understand every word?

Step 2. Identify what you are looking for. It's hard to find something if you are not sure what it is! Read the problem again and look for words that tell you what you are looking for!

  • In this problem, the words “what was the original price of the shirt” tell you that what you are looking for: the original price of the shirt.

Step 3. Name what you are looking for. Choose a variable to represent that quantity. You can use any letter for the variable, but it may help to choose one that helps you remember what it represents.

  • Let p = p = the original price of the shirt

Step 4. Translate into an equation. It may help to first restate the problem in one sentence, with all the important information. Then translate the sentence into an equation.

Step 5. Solve the equation using good algebra techniques. Even if you know the answer right away, using algebra will better prepare you to solve problems that do not have obvious answers.

Step 6. Check the answer in the problem and make sure it makes sense.

  • We found that p = 36 , p = 36 , which means the original price was $36 . $36 . Does $36 $36 make sense in the problem? Yes, because 18 18 is one-half of 36 , 36 , and the shirt was on sale at half the original price.
  • Step 7. Answer the question with a complete sentence.
  • The problem asked “What was the original price of the shirt?” The answer to the question is: “The original price of the shirt was $36 .” $36 .”

If this were a homework exercise, our work might look like this:

Joaquin bought a bookcase on sale for $120 , $120 , which was two-thirds the original price. What was the original price of the bookcase?

Two-fifths of the people in the senior center dining room are men. If there are 16 16 men, what is the total number of people in the dining room?

We list the steps we took to solve the previous example.

Problem-Solving Strategy

  • Step 1. Read the word problem. Make sure you understand all the words and ideas. You may need to read the problem two or more times. If there are words you don't understand, look them up in a dictionary or on the internet.
  • Step 2. Identify what you are looking for.
  • Step 3. Name what you are looking for. Choose a variable to represent that quantity.
  • Step 4. Translate into an equation. It may be helpful to first restate the problem in one sentence before translating.
  • Step 5. Solve the equation using good algebra techniques.
  • Step 6. Check the answer in the problem. Make sure it makes sense.

Let's use this approach with another example.

Example 9.2

Yash brought apples and bananas to a picnic. The number of apples was three more than twice the number of bananas. Yash brought 11 11 apples to the picnic. How many bananas did he bring?

Guillermo bought textbooks and notebooks at the bookstore. The number of textbooks was 3 3 more than the number of notebooks. He bought 5 5 textbooks. How many notebooks did he buy?

Gerry worked Sudoku puzzles and crossword puzzles this week. The number of Sudoku puzzles he completed is seven more than the number of crossword puzzles. He completed 14 14 Sudoku puzzles. How many crossword puzzles did he complete?

In Solve Sales Tax, Commission, and Discount Applications , we learned how to translate and solve basic percent equations and used them to solve sales tax and commission applications. In the next example, we will apply our Problem Solving Strategy to more applications of percent.

Example 9.3

Nga's car insurance premium increased by $60 , $60 , which was 8% 8% of the original cost. What was the original cost of the premium?

Pilar's rent increased by 4% . 4% . The increase was $38 . $38 . What was the original amount of Pilar's rent?

Steve saves 12% 12% of his paycheck each month. If he saved $504 $504 last month, how much was his paycheck?

Solve Number Problems

Now we will translate and solve number problems . In number problems, you are given some clues about one or more numbers, and you use these clues to build an equation. Number problems don't usually arise on an everyday basis, but they provide a good introduction to practicing the Problem Solving Strategy . Remember to look for clue words such as difference , of , and and .

Example 9.4

The difference of a number and six is 13 . 13 . Find the number.

The difference of a number and eight is 17 . 17 . Find the number.

The difference of a number and eleven is −7 . −7 . Find the number.

Example 9.5

The sum of twice a number and seven is 15 . 15 . Find the number.

The sum of four times a number and two is 14 . 14 . Find the number.

Try It 9.10

The sum of three times a number and seven is 25 . 25 . Find the number.

Some number word problems ask you to find two or more numbers. It may be tempting to name them all with different variables, but so far we have only solved equations with one variable. We will define the numbers in terms of the same variable. Be sure to read the problem carefully to discover how all the numbers relate to each other.

Example 9.6

One number is five more than another. The sum of the numbers is twenty-one. Find the numbers.

Try It 9.11

One number is six more than another. The sum of the numbers is twenty-four. Find the numbers.

Try It 9.12

The sum of two numbers is fifty-eight. One number is four more than the other. Find the numbers.

Example 9.7

The sum of two numbers is negative fourteen. One number is four less than the other. Find the numbers.

Try It 9.13

The sum of two numbers is negative twenty-three. One number is 7 7 less than the other. Find the numbers.

Try It 9.14

The sum of two numbers is negative eighteen. One number is 40 40 more than the other. Find the numbers.

Example 9.8

One number is ten more than twice another. Their sum is one. Find the numbers.

Try It 9.15

One number is eight more than twice another. Their sum is negative four. Find the numbers.

Try It 9.16

One number is three more than three times another. Their sum is negative five. Find the numbers.

Consecutive integers are integers that immediately follow each other. Some examples of consecutive integers are:

Notice that each number is one more than the number preceding it. So if we define the first integer as n , n , the next consecutive integer is n + 1 . n + 1 . The one after that is one more than n + 1 , n + 1 , so it is n + 1 + 1 , n + 1 + 1 , or n + 2 . n + 2 .

Example 9.9

The sum of two consecutive integers is 47 . 47 . Find the numbers.

Try It 9.17

The sum of two consecutive integers is 95 . 95 . Find the numbers.

Try It 9.18

The sum of two consecutive integers is −31 . −31 . Find the numbers.

Example 9.10

Find three consecutive integers whose sum is 42 . 42 .

Try It 9.19

Find three consecutive integers whose sum is 96 . 96 .

Try It 9.20

Find three consecutive integers whose sum is −36 . −36 .

Links To Literacy

Practice makes perfect.

In the following exercises, use the problem-solving strategy for word problems to solve. Answer in complete sentences.

Two-thirds of the children in the fourth-grade class are girls. If there are 20 20 girls, what is the total number of children in the class?

Three-fifths of the members of the school choir are women. If there are 24 24 women, what is the total number of choir members?

Zachary has 25 25 country music CDs, which is one-fifth of his CD collection. How many CDs does Zachary have?

One-fourth of the candies in a bag of are red. If there are 23 23 red candies, how many candies are in the bag?

There are 16 16 girls in a school club. The number of girls is 4 4 more than twice the number of boys. Find the number of boys in the club.

There are 18 18 Cub Scouts in Troop 645 . 645 . The number of scouts is 3 3 more than five times the number of adult leaders. Find the number of adult leaders.

Lee is emptying dishes and glasses from the dishwasher. The number of dishes is 8 8 less than the number of glasses. If there are 9 9 dishes, what is the number of glasses?

The number of puppies in the pet store window is twelve less than the number of dogs in the store. If there are 6 6 puppies in the window, what is the number of dogs in the store?

After 3 3 months on a diet, Lisa had lost 12% 12% of her original weight. She lost 21 21 pounds. What was Lisa's original weight?

Tricia got a 6% 6% raise on her weekly salary. The raise was $30 $30 per week. What was her original weekly salary?

Tim left a $9 $9 tip for a $50 $50 restaurant bill. What percent tip did he leave?

Rashid left a $15 $15 tip for a $75 $75 restaurant bill. What percent tip did he leave?

Yuki bought a dress on sale for $72 . $72 . The sale price was 60% 60% of the original price. What was the original price of the dress?

Kim bought a pair of shoes on sale for $40.50 . $40.50 . The sale price was 45% 45% of the original price. What was the original price of the shoes?

In the following exercises, solve each number word problem.

The sum of a number and eight is 12 . 12 . Find the number.

The sum of a number and nine is 17 . 17 . Find the number.

The difference of a number and twelve is 3 . 3 . Find the number.

The difference of a number and eight is 4 . 4 . Find the number.

The sum of three times a number and eight is 23 . 23 . Find the number.

The sum of twice a number and six is 14 . 14 . Find the number.

The difference of twice a number and seven is 17 . 17 . Find the number.

The difference of four times a number and seven is 21 . 21 . Find the number.

Three times the sum of a number and nine is 12 . 12 . Find the number.

Six times the sum of a number and eight is 30 . 30 . Find the number.

One number is six more than the other. Their sum is forty-two. Find the numbers.

One number is five more than the other. Their sum is thirty-three. Find the numbers.

The sum of two numbers is twenty. One number is four less than the other. Find the numbers.

The sum of two numbers is twenty-seven. One number is seven less than the other. Find the numbers.

A number is one more than twice another number. Their sum is negative five. Find the numbers.

One number is six more than five times another. Their sum is six. Find the numbers.

The sum of two numbers is fourteen. One number is two less than three times the other. Find the numbers.

The sum of two numbers is zero. One number is nine less than twice the other. Find the numbers.

One number is fourteen less than another. If their sum is increased by seven, the result is 85 . 85 . Find the numbers.

One number is eleven less than another. If their sum is increased by eight, the result is 71 . 71 . Find the numbers.

The sum of two consecutive integers is 77 . 77 . Find the integers.

The sum of two consecutive integers is 89 . 89 . Find the integers.

The sum of two consecutive integers is −23 . −23 . Find the integers.

The sum of two consecutive integers is −37 . −37 . Find the integers.

The sum of three consecutive integers is 78 . 78 . Find the integers.

The sum of three consecutive integers is 60 . 60 . Find the integers.

Find three consecutive integers whose sum is −3 . −3 .

Everyday Math

Shopping Patty paid $35 $35 for a purse on sale for $10 $10 off the original price. What was the original price of the purse?

Shopping Travis bought a pair of boots on sale for $25 $25 off the original price. He paid $60 $60 for the boots. What was the original price of the boots?

Shopping Minh spent $6.25 $6.25 on 5 5 sticker books to give his nephews. Find the cost of each sticker book.

Shopping Alicia bought a package of 8 8 peaches for $3.20 . $3.20 . Find the cost of each peach.

Shopping Tom paid $1,166.40 $1,166.40 for a new refrigerator, including $86.40 $86.40 tax. What was the price of the refrigerator before tax?

Shopping Kenji paid $2,279 $2,279 for a new living room set, including $129 $129 tax. What was the price of the living room set before tax?

Writing Exercises

Write a few sentences about your thoughts and opinions of word problems. Are these thoughts positive, negative, or neutral? If they are negative, how might you change your way of thinking in order to do better?

When you start to solve a word problem, how do you decide what to let the variable represent?

ⓐ After completing the exercises, use this checklist to evaluate your mastery of the objectives of this section.

ⓑ If most of your checks were:

…confidently. Congratulations! You have achieved the objectives in this section. Reflect on the study skills you used so that you can continue to use them. What did you do to become confident of your ability to do these things? Be specific.

…with some help. This must be addressed quickly because topics you do not master become potholes in your road to success. In math, every topic builds upon previous work. It is important to make sure you have a strong foundation before you move on. Whom can you ask for help? Your fellow classmates and instructor are good resources. Is there a place on campus where math tutors are available? Can your study skills be improved?

…no—I don’t get it! This is a warning sign and you must not ignore it. You should get help right away or you will quickly be overwhelmed. See your instructor as soon as you can to discuss your situation. Together you can come up with a plan to get you the help you need.

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  • Authors: Lynn Marecek, MaryAnne Anthony-Smith, Andrea Honeycutt Mathis
  • Publisher/website: OpenStax
  • Book title: Prealgebra 2e
  • Publication date: Mar 11, 2020
  • Location: Houston, Texas
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  • Section URL: https://openstax.org/books/prealgebra-2e/pages/9-1-use-a-problem-solving-strategy

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Pre Algebra

Pre-algebra is a primary branch of algebra designed to prepare students for a standard high school algebraic course. Students are introduced to integers, fractions, square roots, step equations, linear equations, and decimals and are taught how to solve basic equations using variables. Taking a pre-algebra course can give students initial exposure to the fundamentals of algebra and help them perform better in future courses.

What is Pre-Algebra?

Pre-algebra is a branch of mathematics that deals with the topics to be covered before algebra 1 , and algebra 2 to develop the basic understanding in students. The topics in pre-algebra consist of factors and multiples, patterns, ratios, percentages, exponents intro, order of operations, variables & expressions, linear equations. Let us discuss these listed topics in detail in our next section

Pre-Algebra Topics

Pre-algebra is divided into multiple sub-topics. There are seven-plus chapters in this branch and each chapter is divided into several sub-topics.

Number Theory

  • Whole Numbers
  • Roman Numerals
  • Rational Numbers
  • Real Numbers
  • Pythagorean Theorem
  • Absolute Value

Factors and Multiples

  • Prime numbers and Composite numbers
  • Prime factorization
  • Linear Equations
  • Algebraic Expressions
  • Solving Linear Systems by Substitution
  • System of Equations Solver
  • Solutions of a Linear Equation
  • Variable expressions
  • Ratio and Proportion

Exponents and Square Root

  • Order of Operations
  • Square root
  • Mean, Median, Mode
  • Probability

Pre Algebra Formulas

Here are a few formulas related to pre-algebra which you may feel are handy to have.

  • Speed = Distance/Time
  • Pythagoras Theorem: c 2  = a 2  + b 2 , where 'c' is the hypotenuse and 'a' and 'b' are two legs of a right triangle .
  • Profit = Selling price - Cost price
  • Loss = Cost price - Selling price
  • Profit percentage = profit/cost price × 100
  • Loss percentage = loss/cost price × 100
  • Discount = List Price - Selling Price and Discount (%) = (Discount/List Price) × 100
  • Slope of a line joining the points (x 1 , y 1 ) and (x 2 , y 2 ) is m = (y 2   - y 1 ) / (x 2  - x 1 )
  • The point slope formula of a line is y - y 1  = m (x - x 1 )
  • Distance between two points (x 1 , y 1 ) and (x 2 , y 2 ) is d = √[(x 2  – x 1 ) 2  + (y 2  – y 1 ) 2 ]

Difference Between Algebra and Pre Algebra

Pre-algebra and algebra can be distinguished based on the complexity of the topics covered under both branches separately. The following table explains the important differences between pre-algebra and algebra.

Pre Algebra Worksheets

Pre-Algebra worksheets are extremely helpful for students to prepare for higher grade algebra. Below mentioned are few readily downloadable resources for your practice.

Pre Algebra Examples

Example 1: Using pre-algebra basic rules evaluate the expression (7 × (y + 2)), where y = 3.

Given, y = 3. Putting the value of y (by substitution property ) in (7 × (y + 2)), we get, 7 × (3 + 2) = 7 × 5 = 35.

Answer:  35

Example 2: Solve the given pre-algebraic expression for the value of x, 10 - (- 2) = x.

Given, 10 - (- 2) = x. We will simply do the subtraction of the given expression and get the value of x. 10 + 2 is equal to 12, or x = 12.

Therefore, the value of x is 12.

Answer:  x = 12

Example 3: Using pre-algebra rule solve the equation for the value of y. 10y + 2 = 3.

Given, 10y + 2 = 3. We will simplify the given expression and get the value of y. 10y = 1 y = 1/10

Therefore, the value of y is 1/10.

Answer:  y = 1/10

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Practice Questions on Pre Algebra

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FAQs on Pre Algebra

Why is pre-algebra important.

Pre-algebra provides students an opportunity to learn the basics to understand the complexity of algebra. It develops a basic understanding of variables, equations , and exponents along with the knowledge of how to use the order of operations with algebraic expressions.

How Do You Start Pre-Algebra for Beginners?

Pre-algebra is a building block of mathematics. If you are a beginner you can definitely follow the below-listed points while practicing pre-algebra. These points are:

  • One must aware of arithmetic operations .
  • Remember PEMDAS or BODMAS .
  • Must know how to solve negative numbers .
  • Learn the difference between variables , exponents, equations, and  coefficients .
  • Solve more practice questions.

Is Pre-Algebra Harder than Algebra?

As a name described Pre-algebra is a primary branch of algebra where all the basic concepts are covered to understand the further complex topics of algebra. It is not at all difficult if learned with the best-sophisticated approach.

What do You Learn in Pre-Algebra?

In pre-algebra, we learn about the following listed topics.

  • Variables, coefficient, degree

What Comes After Pre-Algebra?

After pre-algebra, the next subject is algebra 1, algebra 2. These have advanced concepts that require a pre-requisite understanding of the concepts covered in pre-algebra.

What is the First Thing you Learn in Pre-Algebra?

The first thing students learn in algebra 1 is real numbers and their operations. The basic concepts covered under pre-algebra form the basis of the advanced algebraic concepts.

What is Standard Form in Pre-Algebra?

A standard form in pre-algebra is a form of writing a given mathematical concept like an equation, number, or an expression in a form that follows certain rules.

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The Art Of Problem Solving Prealgebra By Richard Rusczyck, David Patrick, Ravi Boppana (z Lib.org)

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COMMENTS

  1. Pre-algebra

    Unit 1: Factors and multiples 0/800 Mastery points Factors and multiples Prime and composite numbers Prime factorization Unit 2: Patterns 0/1000 Mastery points Math patterns Writing expressions Number patterns Unit 3: Ratios and rates

  2. Mathway

    Mathway | Pre-Algebra Problem Solver Mathway Visit Mathway on the web Start 7-day free trial on the app Start 7-day free trial on the app Download free on Amazon Download free in Windows Store getGo Pre-Algebra Basic Math Pre-Algebra Algebra Trigonometry Precalculus Calculus Statistics Finite Math Linear Algebra Chemistry Physics Graphing Upgrade

  3. Pre-algebra word problems

    To solve a pre-algebra word problem: Identify the quantity to be calculated. Determine the operations and numbers needed to calculate the desired quantity. Write and evaluate the expressions to get the desired quantity. If the context requires rounding, round the answer. [Example] Your turn! TRY: FINDING THE GROUP SIZE

  4. Top 10 Pre-Algebra Practice Questions

    The best way to prepare for your Pre-Algebra test is to work through as many Pre-Algebra practice questions as possible. Here are the top 10 Pre-Algebra practice questions to help you review the most important Pre-Algebra concepts.

  5. Pre-Algebra Worksheets

    On this page you will find printable pre-algebra worksheets that have basic problems for addition, subtraction, multiplication and division, as well as worksheets with various combinations of the operators. These worksheets can be introduced as part of the process of learning basic math facts, or as a lead-in to algebra topics in 5th grade or ...

  6. Equations & inequalities introduction

    Math Pre-algebra Unit 7: Equations & inequalities introduction 2,200 possible mastery points Mastered Proficient Familiar Attempted Not started Quiz Unit test About this unit In this topic, we will look at 1- and 2-step equations, as well as expressions and inequalities. Algebraic equations basics Learn Variables, expressions, & equations

  7. Prealgebra Textbook

    Prealgebra Richard Rusczyk, David Patrick, Ravi Boppana Paperback Text: 608 pages. Solutions: 224 pages. Prealgebra prepares students for the rigors of algebra and also teaches students problem-solving techniques to prepare them for prestigious middle school math contests such as MATHCOUNTS, MOEMS, and the AMC 8.

  8. Pre Algebra Calculator

    Send us Feedback. Free pre algebra calculator - Find Factors and Multipliers, Decimals, Fractions and Percent step-by-step.

  9. 9.1 Use a Problem Solving Strategy

    Problem-Solving Strategy. Step 1. Read the word problem. Make sure you understand all the words and ideas. You may need to read the problem two or more times. If there are words you don't understand, look them up in a dictionary or on the internet. Step 2. Identify what you are looking for. Step 3.

  10. Pre-Algebra

    Solve Pre-Algebra Mean Mode Greatest Common Factor Least Common Multiple Order of Operations Fractions Mixed Fractions Prime Factorization Exponents Radicals Learn about pre-algebra using our free math solver with step-by-step solutions.

  11. Prealgebra 1 Online Math Course

    Our weekly live Prealgebra 1 course brings together eager young problem solvers from around the world for 75-minute classes with an experienced instructor and multiple assistants. Students also learn from our Prealgebra textbook and videos, while honing their skills on several types of homework problems.

  12. Pre-Algebra Lessons at Cool math .com

    Pre-Algebra solving equations lessons with lots of worked examples and practice problems. Very easy to understand!

  13. Pre Algebra

    Example 2: Solve the given pre-algebraic expression for the value of x, 10 - (- 2) = x. Solution: Given, 10 - (- 2) = x. We will simply do the subtraction of the given expression and get the value of x. 10 + 2 is equal to 12, or x = 12. Therefore, the value of x is 12. Answer: x = 12. Example 3: Using pre-algebra rule solve the equation for the ...

  14. Pre-Algebra

    Free math worksheets, charts and calculators Ready-to-Use Pre-Algebra Lesson With Step By Step Instructions, Problems, Solutions and Interactive Exercises.

  15. Variables & expressions

    Start Course challenge Math Pre-algebra Unit 6: Variables & expressions 1,500 possible mastery points Mastered Proficient Familiar Attempted Not started Quiz Unit test Parts of algebraic expressions Learn What is a variable? Terms, factors, & coefficients Why aren't we using the multiplication sign? Terms, factors, and coefficients review Practice

  16. Ratios and rates

    Start Course challenge Math Pre-algebra Unit 3: Ratios and rates 1,700 possible mastery points Mastered Proficient Familiar Attempted Not started Quiz Unit test About this unit Learn all about proportional relationships. How are they connected to ratios and rates? What do their graphs look like?

  17. Solving Simple Equations in Pre-Algebra Problems

    When dealing with simple algebraic expressions, you don't always need algebra to solve them. The following practice questions ask you to use three different methods: inspecting, rewriting the problem, and guessing and checking. Practice questions In the following questions, solve for x in each case just by looking at the equation. 1. 18 - x = 12

  18. Pre Algebra Calculator & Problem Solver

    Understand Pre Algebra, one step at a time. Step by steps for fractions, factoring, and prime factorization. Enter your math expression. x2 − 2x + 1 = 3x − 5. Get Chegg Math Solver. $9.95 per month (cancel anytime).

  19. The Art Of Problem Solving Prealgebra By Richard Rusczyck, David

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  20. Videos

    We offer hundreds of free videos featuring AoPS founder Richard Rusczyk. Below are videos aligned to our Prealgebra text, the first half of our Introduction to Algebra text, and our Introduction to Counting & Probability text. We also regularly produce MATHCOUNTS Minis featuring problems from State-level MATHCOUNTS competitions, as well as ...

  21. Pre-Algebra (Problem-Solving Approach)

    Pre-Algebra (Problem-Solving Approach) Information. Class meets three times a week for 50-55 minutes, or twice per week for one hour and fifteen minutes. Class cap: 15 students. Designed for grades 6-8. Course may be listed as "honors" on transcript.

  22. Multi-step equations

    Math Pre-algebra Unit 12: Multi-step equations 700 possible mastery points Mastered Proficient Familiar Attempted Quiz Unit test Equations with variables on both sides

  23. Videos

    a There has been an unexpected error. Please contact [email protected] and tell them exactly what you were doing to trigger this, and include this magic code: E_NOACTION OK OK These videos complement the Art of Problem Solving textbook Prealgebra. They are used in our Prealgebra 1 and Prealgebra 2 courses.

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    Solve problems from Pre Algebra to Calculus step-by-step . Frequently Asked Questions (FAQ) Is there a step by step calculator for math? Symbolab is the best step by step calculator for a wide range of math problems, from basic arithmetic to advanced calculus and linear algebra. It shows you the solution, graph, detailed steps and explanations ...