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Ratio problem solving

Here you will learn about ratio problem solving, including how to set up and solve problems. You will also look at real life ratio word problems.

Students will first learn about ratio problem solving as part of ratio and proportion in 6 th grade and 7 th grade.

What is ratio problem solving?

Ratio problem solving is a collection of ratio and proportion word problems that link together aspects of ratio and proportion into more real life questions. This requires you to be able to take key information from a question and use your knowledge of ratios (and other areas of the curriculum) to solve the problem.

A ratio is a relationship between two or more quantities. They are usually written in the form a : b where a and b are two quantities. When problem solving with a ratio, the key facts that you need to know are:

  • What is the ratio involved?
  • What order are the quantities in the ratio?
  • What is the total amount / what is the part of the total amount known?
  • What are you trying to calculate ?

As with all problem solving, there is not one unique method to solve a problem. However, this does not mean that there aren’t similarities between different problems that you can use to help you find an answer.

The key to any problem solving is being able to draw from prior knowledge and use the correct piece of information to allow you to get to the next step and then the solution.

Let’s look at a couple of methods you can use when given certain pieces of information.

When solving ratio word problems, it is very important that you are able to use ratios. This includes being able to use ratio notation.

For example, Charlie and David share some sweets in the ratio of 3 : 5. This means that for every 3 sweets Charlie gets, David receives 5 sweets.

Charlie and David share 40 sweets, how many sweets do they each get?

You use the ratio to divide 40 sweets into 8 equal parts.

40 \div 8=5

Then you multiply each part of the ratio by 5.

3\times 5:5\times 5=15 : 25

This means that Charlie will get 15 sweets and David will get 25 sweets.

There can be ratio word problems involving different operations and types of numbers.

Here are some examples of different types of ratio word problems:

What is ratio problem solving?

Common Core State Standards

How does this relate to 6 th grade math?

  • Grade 6 – Ratios and Proportional Relationships (6.RP.A.3) Use ratio and rate reasoning to solve real-world and mathematical problems, for example, by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations.
  • Grade 7 – Ratio and Proportional Relationships (7.RP.A.2) Recognize and represent proportional relationships between quantities.

How to do ratio problem solving

In order to solve problems including ratios:

Identify key information within the question.

Know what you are trying to calculate.

Use prior knowledge to structure a solution.

[FREE] Ratio Check for Understanding Quiz (Grade 6 and 7)

[FREE] Ratio Check for Understanding Quiz (Grade 6 and 7)

Use this quiz to check your 6th and 7th grade students’ understanding of ratios. 10+ questions with answers covering a range of 6th and 7th grade ratio topics to identify areas of strength and support!

Ratio problem solving examples

Example 1: part:part ratio.

Within a school, the total number of students who have school lunches to packed lunches is 5 : 7. If 465 students have a school lunch, how many students have a packed lunch?

Within a school, the number of students who have school lunches to packed lunches is \textbf{5 : 7} . If \textbf{465} students have a school lunch, how many students have a packed lunch?

Here you can see that the ratio is 5 : 7, where the first part of the ratio represents school lunches (S) and the second part of the ratio represents packed lunches (P).

You could write this as:

Ratio Problem Solving Image 2 US

Where the letter above each part of the ratio links to the question.

You know that 465 students have school lunch.

2 Know what you are trying to calculate.

From the question, you need to calculate the number of students that have a packed lunch, so you can now write a ratio below the ratio 5 : 7 that shows that you have 465 students who have school lunches, and p students who have a packed lunch.

Ratio Problem Solving Image 3 US

You need to find the value of p.

3 Use prior knowledge to structure a solution.

You are looking for an equivalent ratio to 5 : 7. So you need to calculate the multiplier.

You do this by dividing the known values on the same side of the ratio by each other.

465\div 5 = 93

This means to create an equivalent ratio, you can multiply both sides by 93.

Ratio Problem Solving Image 4 US

So the value of p is equal to 7 \times 93=651.

There are 651 students that have a packed lunch.

Example 2: unit conversions

The table below shows the currency conversions on one day.

Use the table above to convert £520 \; (GBP) to Euros € \; (EUR).

Use the table above to convert \bf{£520} \textbf{ (GBP)} to Euros \textbf{€ } \textbf{(EUR)}.

The two values in the table that are important are \text{GBP} and EUR. Writing this as a ratio, you can state,

Ratio Problem Solving Image 7 US

You know that you have £520.

You need to convert GBP to EUR and so you are looking for an equivalent ratio with GBP=£520 and EUR=E.

Ratio Problem Solving Image 8 US

To get from 1 to 520, you multiply by 520 and so to calculate the number of Euros for £520, you need to multiply 1.17 by 520.

1.17 \times 520=608.4

So £520=€608.40.

Example 3: writing a ratio 1 : n

Liquid plant food is sold in concentrated bottles. The instructions on the bottle state that the 500 \, ml of concentrated plant food must be diluted into 2 \, l of water. Express the ratio of plant food to water, respectively, in the ratio 1 : n.

Liquid plant food is sold in concentrated bottles. The instructions on the bottle state that the \bf{500 \, ml} of concentrated plant food must be diluted into \bf{2 \, l} of water. Express the ratio of plant food to water respectively as a ratio in the form 1 : n.

Using the information in the question, you can now state the ratio of plant food to water as 500 \, ml : 2 \, l. As you can convert liters into milliliters, you could convert 2 \, l into milliliters by multiplying it by 1000.

2 \, l=2000 \, ml

So you can also express the ratio as 500 : 2000 which will help you in later steps.

You want to simplify the ratio 500 : 2000 into the form 1:n.

You need to find an equivalent ratio where the first part of the ratio is equal to 1. You can only do this by dividing both parts of the ratio by 500 (as 500 \div 500=1 ).

Ratio Problem Solving Image 9 US

So the ratio of plant food to water in the form 1 : n is 1 : 4.

Example 4: forming and solving an equation

Three siblings, Josh, Kieran and Luke, receive an allowance each week proportional to their age. Kieran is 3 years older than Josh. Luke is twice Josh’s age. If Josh receives \$ 8 allowance, how much money do the three siblings receive in total?

Three siblings, Josh, Kieran and Luke, receive an allowance each week proportional to their ages. Kieran is \bf{3} years older than Josh. Luke is twice Josh’s age. If Luke receives \bf{\$ 8} allowance, how much money do the three siblings receive in total?

You can represent the ages of the three siblings as a ratio. Taking Josh as x years old, Kieran would therefore be x+3 years old, and Luke would be 2x years old. As a ratio, you have:

Ratio Problem Solving Image 10 US

You also know that Luke receives \$ 8.

You want to calculate the total amount of allowance for the three siblings.

You need to find the value of x first. As Luke receives \$ 8, you can state the equation 2x=8 and so x=4.

Now you know the value of x, you can substitute this value into the other parts of the ratio to obtain how much money the siblings each receive.

Ratio Problem Solving Image 11 US

The total amount of allowance is therefore 4+7+8=\$ 19.

Example 5: simplifying ratios

Below is a bar chart showing the results for the colors of counters in a bag.

Ratio Problem Solving Image 12 US

Express this data as a ratio in its simplest form.

From the bar chart, you can read the frequencies to create the ratio.

Ratio Problem Solving Image 13 US

You need to simplify this ratio.

To simplify a ratio, you need to find the highest common factor of all the parts of the ratio. By listing the factors of each number, you can quickly see that the highest common factor is 2.

\begin{aligned} & 12 = 1, {\color{red}2}, 3, 4, 6, 12 \\\\ & 16 = 1, {\color{red}2}, 4, 8, 16 \\\\ & 10 = 1, {\color{red}2}, 5, 10 \end{aligned}

HCF(12,16,10) = 2

Dividing all the parts of the ratio by 2, you get

Ratio Problem Solving Image 14 US

Our solution is 6 : 8 : 5.

Example 6: combining two ratios

Glass is made from silica, lime and soda. The ratio of silica to lime is 15 : 2. The ratio of silica to soda is 5 : 1. State the ratio of silica:lime:soda.

Glass is made from silica, lime and soda. The ratio of silica to lime is \bf{15 : 2}. The ratio of silica to soda is \bf{5 : 1}. State the ratio of silica:lime:soda.

You know the two ratios

Ratio Problem Solving Image 15 US

You are trying to find the ratio of all 3 components: silica, lime and soda.

Using equivalent ratios you can say that the ratio of Silica:Soda is equivalent to 15 : 3 by multiplying the ratio by 3.

Ratio Problem Solving Image 16 US

You now have the same amount of silica in both ratios and so you can now combine them to get the ratio 15 : 2 : 3.

Ratio Problem Solving Image 17 US

Example 7: using bar modeling

India and Beau share some popcorn in the ratio of 5 : 2. If India has 75 \, g more popcorn than Beau, what was the original quantity?

India and Beau share some popcorn in the ratio of \bf{5 : 2} . If India has \bf{75 \, g} more popcorn than Beau, what was the original quantity?

You know that the initial ratio is 5 : 2 and that India has three more parts than Beau.

You want to find the original quantity.

Drawing a bar model of this problem, you have:

Ratio Problem Solving Image 18 US

Where India has 5 equal shares, and Beau has 2 equal shares.

Each share is the same value and so if you can find out this value, you can then find the total quantity.

From the question, India’s share is 75 \, g more than Beau’s share so you can write this on the bar model.

Ratio Problem Solving Image 19 US

You can find the value of one share by working out 75 \div 3=25 \, g.

Ratio Problem Solving Image 20 US

You can fill in each share to be 25 \, g.

Ratio Problem Solving Image 21 US

Adding up each share, you get

India=5 \times 25=125 \, g

Beau=2 \times 25=50 \, g

The total amount of popcorn was 125+50=175 \, g.

Teaching tips for ratio problem solving

  • Continue to remind students that when solving ratio word problems, it’s important to identify the quantities being compared and express the ratio in its simplest form.
  • Create practice problems for students using the information in your classroom. For example, ask students to find the ratio of boys to the ratio of girls using the total number of students in your classroom, then the school.
  • To find more practice questions, utilize educational websites and apps instead of worksheets. Some of these may also provide tutorials for struggling students. These can also be helpful for test prep as they are more engaging for students.
  • Use a variety of numbers in your ratio word problems – whole numbers, fractions, decimals, and mixed numbers – to give students a variety of practice.
  • Provide students with a step-by-step process for problem solving, like the one shown above, that can be applied to every ratio word problem.

Easy mistakes to make

  • Mixing units Make sure that all the units in the ratio are the same. For example, in example 6, all the units in the ratio were in milliliters. You did not mix ml and l in the ratio.
  • Writing ratios in the wrong order For example, the number of dogs to cats is given as the ratio 12 : 13 but the solution is written as 13 : 12.

Ratio Problem Solving Image 22 US

  • Counting the number of parts in the ratio, not the total number of shares For example, the ratio 5 : 4 has 9 shares, and 2 parts. This is because the ratio contains 2 numbers but the sum of these parts (the number of shares) is 5+4=9. You need to find the value per share, so you need to use the 9 shares in your next line of working.
  • Ratios of the form \bf{1 : \textbf{n}} The assumption can be incorrectly made that n must be greater than 1, but n can be any number, including a decimal.

Related ratio lessons

  • Unit rate math
  • Simplifying ratios
  • Ratio to fraction
  • How to calculate exchange rates
  • Ratio to percent
  • How to write a ratio

Practice ratio problem solving questions

1. An online shop sells board games and computer games. The ratio of board games to the total number of games sold in one month is 3 : 8. What is the ratio of board games to computer games?

GCSE Quiz True

8-3=5 computer games sold for every 3 board games.

2. The ratio of prime numbers to non-prime numbers from 1-200 is 45 : 155. Express this as a ratio in the form 1 : n.

You need to simplify the ratio so that the first number is 1. That means you need to divide each number in the ratio by 45.

45 \div 45=1

155\div{45}=3\cfrac{4}{9}

3. During one month, the weather was recorded into 3 categories: sunshine, cloud and rain. The ratio of sunshine to cloud was 2 : 3 and the ratio of cloud to rain was 9 : 11. State the ratio that compares sunshine:cloud:rain for the month.

3 \times S : C=6 : 9

4. The angles in a triangle are written as the ratio x : 2x : 3x. Calculate the size of each angle.

You should know that the 3 angles in a triangle always equal 180^{\circ}.

\begin{aligned} & x+2 x+3 x=180 \\\\ & 6 x=180 \\\\ & x=30^{\circ} \\\\ & 2 x=60^{\circ} \\\\ & 3 x=90^{\circ} \end{aligned}

5. A clothing company has a sale on tops, dresses and shoes. \cfrac{1}{3} of sales were for tops, \cfrac{1}{5} of sales were for dresses, and the rest were for shoes. Write a ratio of tops to dresses to shoes sold in its simplest form.

\cfrac{1}{3}+\cfrac{1}{5}=\cfrac{5+3}{15}=\cfrac{8}{15}

1-\cfrac{8}{15}=\cfrac{7}{15}

6. The volume of gas is directly proportional to the temperature (in degrees Kelvin). A balloon contains 2.75 \, l of gas and has a temperature of 18^{\circ}K. What is the volume of gas if the temperature increases to 45^{\circ}K?

The given ratio in the word problem is 2. 75 \mathrm{~L}: 18^{\circ} \mathrm{K}

Divide 45 by 18 to see the relationship between the two temperatures.

45 \div 18=2.5

45 is 2.5 times greater than 18. So we multiply 2.75 by 2.5 to get the amount of gas.

2.75 \times 2.5=6.875 \mathrm{~l}

Ratio problem solving FAQs

A ratio is a comparison of two or more quantities. It shows how much one quantity is related to another.

A recipe calls for 2 cups of flour and 1 cup of sugar. What is the ratio of flour to sugar? (2 : 1)

In middle school ( 7 th grade and 8 th grade), students transition from understanding basic ratios to working with more complex and real-life applications of ratios and proportions. They gain a deeper understanding of how ratios relate to different mathematical concepts, making them more prepared for higher-level math topics in high school.

The next lessons are

  • Properties of equality
  • Multiplication and division

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Ratio Word Problem Worksheets

We are delighted to share this set of extensively well-researched ratio word problem worksheets which will help students in grade 5 through grade 8 to grasp the basics of ratio calculations. These printable worksheets include simple theme-based ratio word problems, finding the ratio between two quantities, word problems that require children to find a part from the whole, part-to-part, a whole from the part, reading pictographs, bar graphs, and pie graphs. Click on the free icon to sample our worksheets.

Express in ratio: Read the themes

Express in ratio: Read the themes

Look at the vivid themes and answer the word problems in these 5th grade worksheets. Express in ratio and reduce it to the lowest term. Use the answer key to verify your responses.

  • Download the set

Find the ratio between two quantities

Find the ratio between two quantities

This set of well-researched ratio word problem pdf worksheets includes factual and educative real-life scenarios. Find the ratio between the two quantities. Express your answer in the simplest form.

Ratio word problems: Part-to-part

Ratio word problems: Part-to-part

Based on the data given in these colorful worksheets, read and answer the extremely engaging part-to-part ratio word problems that ensue. You have an option to download this set of worksheets in a single click.

Ratio word problems: A part from the whole

Ratio word problems: A part from the whole

This collection of ratio word problems printable worksheets will require 6th grade and 7th grade students to find the parts from the given ratio and the whole. Set up the simple equation and solve the word problems.

Ratio word problems: The whole from the part

Ratio word problems: The whole from the part

Based on one part of the number and the ratio provided in these word problems, the children need to find the share of the other part and the whole. There are five word problems in each worksheet.

Ratio word problems: Mixed bag

Ratio word problems: Mixed bag

This set of assorted word problems for 7th grade and 8th grade students contains a mix of finding part-to-part, part-to-whole, and finding the ratio. Some word problems may require you to find the ratio based on the increase or decrease in quantity and vice versa.

Finding the Ratio from Pictographs

Finding the Ratio from Pictographs

Use the key to find the total of each item. Read the pictograph and answer the word problems. The word problems are based on finding ratio between the quantities. Do not forget to reduce the ratio to the lowest term.

Finding the Ratio from Bar Graphs

Finding the Ratio from Bar Graphs

The data provided in these bar graphs are borrowed from real-life scenarios. Read the bar graphs and write the ratio in the simplest form.

Finding the Ratio from Pie Graphs

Finding the Ratio from Pie Graphs

The printable worksheet pdfs in this section contain ratio word problems based on pie graphs. Read the pie graph, find the ratio and solve the word problems.

Related Worksheets

» Proportions

» Fractions

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» Decimal Word Problems

» Division Word Problems

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Algebra: Ratio Word Problems

Related Pages Two-Term Ratio Word Problems More Ratio Word Problems Algebra Lessons

In these lessons, we will learn how to solve ratio word problems that have two-term ratios or three-term ratios.

Ratio problems are word problems that use ratios to relate the different items in the question.

The main things to be aware about for ratio problems are:

  • Change the quantities to the same unit if necessary.
  • Write the items in the ratio as a fraction .
  • Make sure that you have the same items in the numerator and denominator.

Ratio Problems: Two-Term Ratios

Example 1: In a bag of red and green sweets, the ratio of red sweets to green sweets is 3:4. If the bag contains 120 green sweets, how many red sweets are there?

Solution: Step 1: Assign variables: Let x = number of red sweets.

Step 2: Solve the equation. Cross Multiply 3 × 120 = 4 × x 360 = 4 x

Answer: There are 90 red sweets.

Example 2: John has 30 marbles, 18 of which are red and 12 of which are blue. Jane has 20 marbles, all of them either red or blue. If the ratio of the red marbles to the blue marbles is the same for both John and Jane, then John has how many more blue marbles than Jane?

Solution: Step 1: Sentence: Jane has 20 marbles, all of them either red or blue. Assign variables: Let x = number of blue marbles for Jane 20 – x = number red marbles for Jane

Step 2: Solve the equation

Cross Multiply 3 × x = 2 × (20 – x ) 3 x = 40 – 2 x

John has 12 blue marbles. So, he has 12 – 8 = 4 more blue marbles than Jane.

Answer: John has 4 more blue marbles than Jane.

How To Solve Word Problems Using Proportions?

This is another word problem that involves ratio or proportion.

Example: A recipe uses 5 cups of flour for every 2 cups of sugar. If I want to make a recipe using 8 cups of flour. How much sugar should I use?

How To Solve Proportion Word Problems?

When solving proportion word problems remember to have like units in the numerator and denominator of each ratio in the proportion.

  • Biologist tagged 900 rabbits in Bryer Lake National Park. At a later date, they found 6 tagged rabbits in a sample of 2000. Estimate the total number of rabbits in Bryer Lake National Park.
  • Mel fills his gas tank up with 6 gallons of premium unleaded gas for a cost of $26.58. How much would it costs to fill an 18 gallon tank? 3 If 4 US dollars can be exchanged for 1.75 Euros, how many Euros can be obtained for 144 US dollars?

Ratio problems: Three-term Ratios

Example 1: A special cereal mixture contains rice, wheat and corn in the ratio of 2:3:5. If a bag of the mixture contains 3 pounds of rice, how much corn does it contain?

Solution: Step 1: Assign variables: Let x = amount of corn

Step 2: Solve the equation Cross Multiply 2 × x = 3 × 5 2 x = 15

Answer: The mixture contains 7.5 pounds of corn.

Example 2: Clothing store A sells T-shirts in only three colors: red, blue and green. The colors are in the ratio of 3 to 4 to 5. If the store has 20 blue T-shirts, how many T-shirts does it have altogether?

Solution: Step 1: Assign variables: Let x = number of red shirts and y = number of green shirts

Step 2: Solve the equation Cross Multiply 3 × 20 = x × 4 60 = 4 x x = 15

5 × 20 = y × 4 100 = 4 y y = 25

The total number of shirts would be 15 + 25 + 20 = 60

Answer: There are 60 shirts.

Algebra And Ratios With Three Terms

Let’s study how algebra can help us think about ratios with more than two terms.

Example: There are a total of 42 computers. Each computer runs one of three operating systems: OSX, Windows, Linux. The ratio of the computers running OSX, Windows, Linux is 2:5:7. Find the number of computers that are running each of the operating systems.

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how to solve ratio word problems 8th grade

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Last modified on August 3rd, 2023

Ratio Word Problems

Here, we will learn to do some practical word problems involving ratios.

Amelia and Mary share $40 in a ratio of 2:3. How much do they get separately?

There is a total reward of $40 given.  Let Amelia get = 2x and Mary get = 3x Then, 2x + 3x = 40 Now, we solve for x => 5x = 40 => x = 8 Thus, Amelia gets = 2x = 2 × 8 = $16 Mary gets = 3x = 3 × 8 = $24

In a bag of blue and red marbles, the ratio of blue marbles to red marbles is 3:4. If the bag contains 120 green marbles, how many blue marbles are there?

Let the total number of blue marbles be x Thus, ${\dfrac{3}{4}=\dfrac{x}{120}}$ x = ${\dfrac{3\times 120}{4}}$ x = 90 So, there are 90 blue marbles in the bag.

Gregory weighs 75.7 kg. If he decreases his weight in the ratio of 5:4, find his reduced weight.

Let the decreased weight of Gregory be = x kg Thus, 5x = 75.7 x = \dfrac{75\cdot 7}{5} = 15.14 Thus his reduced weight is 4 × 15.14 = 60.56 kg

A recipe requires butter and sugar to be in the ratio of 2:3. If we require 8 cups of butter, find how many cups of sugar are required. Write the equivalent fraction.

Thus, for every 2 cups of butter, we use 3 cups of sugar Here we are using 8 cups of butter, or 4 times as much So you need to multiply the amount of sugar by 4 3 × 4 = 12 So, we need to use 12 cups of sugar Thus, the equivalent fraction is ${\dfrac{2}{3}=\dfrac{8}{12}}$

Jerry has 16 students in his class, of which 10 are girls. Write the ratio of girls to boys in his class. Reduce your answer to its simplest form.

Total number of students = 16 Number of girls = 10 Number of boys = 16 – 10 = 6 Thus the ratio of girls to boys is ${\dfrac{10}{6}=\dfrac{5}{3}}$

A bag containing chocolates is divided into a ratio of 5:7. If the larger part contains 84 chocolates, find the total number of chocolates in the bag.

Let the total number of chocolates be x

Then the two parts are:

${\dfrac{5x}{5+7}}$ and ${\dfrac{7x}{5+7}}$

${\dfrac{7x}{5+7}}$ = 84

=> ${\dfrac{7x}{12}}$ = 84

Thus, the total number of chocolates that were present in the bag was 144

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Word Problems Involving Rates and Ratios

Word Problems Involving Rates and Ratios

The ratio is to compare two numbers. Rate is one type of ratio and is used to measure the variety of one thing or quantity in comparison to other. Word problems involving comparing rates deal with distances, time, rates, wind or water current, money, and age.

A step-by-step guide to solving rates and ratios word problems

To solve the word problems involving rates and ratios, follow these steps: Step 1: Find the known ratio and the unknown ratio. Step 2: Write the proportion. Step 3: Use cross-multiply and solve. Step 4: Plug the result into the unknown ratio to check the answers.

Word Problems Involving Rates and Ratios – Examples 1

If 11 apple pies cost $88, what will 8 apple pies cost? Solution: Write as a rate. \(\frac{88÷11}{11÷11}=\frac{8}{1}\) Write a proportion to know the cost of 8 apple pies. \(\frac{8}{1}=\frac{x}{6}→8×6=1×x→x=48\)

Word Problems Involving Rates and Ratios – Examples 2

If 6 cookbooks cost $120, how much would a dozen cookbooks cost? Solution: Write as a rate. \(\frac{120÷6}{6÷6}=\frac{20}{1}\) Write a proportion to know the cost of 12 cookbooks. \(\frac{20}{1}=\frac{x}{12}→20×12=1×x→x=240\)

by: Effortless Math Team about 1 year ago (category: Articles )

Effortless Math Team

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  • Word Problems on Ratio

We will learn how to divide a quantity in a given ratio and its application in the word problems on ratio.

1. John weights 65.7 kg. If he reduces his weight in the ratio 5 : 4, find his reduced weight.

Let the previous weight be 5x.

x = \(\frac{65.7}{5}\)

Therefore, the reduce weight = 4 × 13.14 = 52.56 kg.

2. Robin leaves $ 1245500 behind. According to his wish, the money is to be divided between his son and daughter in the ratio 3 : 2. Find the sum received by his son.

We know if a quantity x is divided in the ratio a : b then the two parts are \(\frac{ax}{a + b}\) and \(\frac{bx}{a + b}\).

Therefore, the sum received by his son = \(\frac{3}{3 + 2}\) × $ 1245500  

= \(\frac{3}{5}\) × $ 1245500

= 3 × $ 249100

= $ 747300  

3. Two numbers are in the ratio 3 : 2. If 2 is added to the first and 6 is added to the second number, they are in the ratio 4 : 5. Find the numbers.

Let the numbers be 3x and 2x.

According to the problem,

\(\frac{3x + 2}{2x + 6}\) = \(\frac{4}{5}\)

⟹ 5(3x + 2) = 4

⟹ 15x + 10 = 8x + 24

⟹ 15x – 8x = 24 - 10

⟹ x = \(\frac{14}{7}\)

Therefore, the original numbers are: 3x = 3 × 2 = 6 and 2x = 2 × 2 = 4.

Thus, the numbers are 6 and 4.

4. If a quantity is divided in the ratio 5 : 7, the larger part is 84. Find the quantity.

Let the quantity be x.

Then the two parts will be \(\frac{5x}{5 + 7}\) and \(\frac{7x}{5 + 7}\).

Hence, the larger part is 84, we get

\(\frac{7x}{5 + 7}\) = 84

⟹ \(\frac{7x}{12}\) = 84

⟹ 7x = 84 × 12

⟹ 7x = 1008

⟹ x = \(\frac{1008}{7}\)

Therefore, the quantity is 144.

●  Ratio and proportion

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Welcome to our Ratio Word Problems page. Here you will find our range of 6th Grade Ratio Problem worksheets which will help your child apply and practice their Math skills to solve a range of ratio problems.

For full functionality of this site it is necessary to enable JavaScript.

Here are the instructions how to enable JavaScript in your web browser .

Here you will find a range of problem solving worksheets about ratio.

The sheets involve using and applying knowledge to ratios to solve problems.

The sheets have been put in order of difficulty, with the easiest first. They are aimed at students in 6th grade.

Each problem sheet comes complete with an answer sheet.

Using these sheets will help your child to:

  • apply their ratio skills;
  • apply their knowledge of fractions;
  • solve a range of word problems.
  • Ratio Problems 1
  • PDF version
  • Ratio Problems 2
  • Ratio Problems 3
  • Ratio Problems 4

Ratio and Probability Problems

  • Ration and Probability Problems 1
  • Sheet 1 Answers
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  • Sheet 2 Answers

More Recommended Math Worksheets

Take a look at some more of our worksheets similar to these.

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These sheets are a great way to introduce ratio of one object to another using visual aids.

The sheets in this section are at a more basic level than those on this page.

We also have some ratio and proportion worksheets to help learn these interrelated concepts.

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Take a look at our percentage worksheets for finding the percentage of a number or money amount.

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Real World Algebra by Edward Zaccaro

Algebra is often taught abstractly with little or no emphasis on what algebra is or how it can be used to solve real problems. Just as English can be translated into other languages, word problems can be "translated" into the math language of algebra and easily solved. Real World Algebra explains this process in an easy to understand format using cartoons and drawings. This makes self-learning easy for both the student and any teacher who never did quite understand algebra. Includes chapters on algebra and money, algebra and geometry, algebra and physics, algebra and levers and many more. Designed for children in grades 4-9 with higher math ability and interest but could be used by older students and adults as well. Contains 22 chapters with instruction and problems at three levels of difficulty.

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IMAGES

  1. Ratio Word Problems

    how to solve ratio word problems 8th grade

  2. Ratio and Proportion Word Problems Worksheet for 8th Grade

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  3. Ratio word problems

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  5. Solve Three Part Ratio Problems (Word Problems) Worksheets [PDF] (6.RP

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  6. Ratio And Rates Word Problems Worksheets With Answers

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VIDEO

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  5. ratio and proportion Word Problems Business and general MATHEMATICS for SMIU fast IBA CBM

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COMMENTS

  1. IXL

    Skill plans. IXL plans. Washington state standards. Textbooks. Test prep. Awards. Improve your math knowledge with free questions in "Word problems involving ratios" and thousands of other math skills.

  2. Free worksheets for ratio word problems

    Generator Use the generator to make customized ratio worksheets. Experiment with the options to see what their effect is. Ratio Worksheets Columns: Rows: (These determine the number of problems) Level: Level 1: write a ratio Level 2: write a ratio and simplify it Numbers used (only for levels 1 & 2):

  3. Solving Ratio Word Problems (the easy way!)

    This video focuses on how to solve ratio word problems. In particular, I show students the trick of multiplying each term in the ratio by x to help set up an...

  4. Ratio Problem Solving

    3+5=8 3 + 5 = 8 40 \div 8=5 40 ÷ 8 = 5 Then you multiply each part of the ratio by 5. 5. 3\times 5:5\times 5=15 : 25 3 × 5: 5 × 5 = 15: 25 This means that Charlie will get 15 15 sweets and David will get 25 25 sweets. There can be ratio word problems involving different operations and types of numbers.

  5. Solve Ratio Word Problems

    Solve Ratio Word Problems Derek Banas 1.28M subscribers Subscribe Subscribed 156 20K views 3 years ago Learn Algebra In this video I'll show you how to solve multiple types of Ratio...

  6. Ratio Word Problems Worksheets

    Pre-Algebra > Ratio > Word Problems Ratio Word Problem Worksheets We are delighted to share this set of extensively well-researched ratio word problem worksheets which will help students in grade 5 through grade 8 to grasp the basics of ratio calculations.

  7. Ratio Word Problems (video lessons, examples and solutions)

    Step 1: Assign variables: Let x = number of red sweets. Write the items in the ratio as a fraction. Step 2: Solve the equation. Cross Multiply 3 × 120 = 4 × x 360 = 4 x Isolate variable x Answer: There are 90 red sweets. Example 2: John has 30 marbles, 18 of which are red and 12 of which are blue.

  8. Ratio and Proportion Word Problems

    This math video tutorial provides a basic introduction into ratio and proportion word problems. Here is a list of examples and practice problems:Percentages...

  9. IXL

    Math. English. Science. Recommendations. Skill plans. Provincial curriculum. Awards. Improve your math knowledge with free questions in "Ratios and rates: word problems" and thousands of other math skills.

  10. Ratio Word Problems Solved

    Write the ratio of girls to boys in his class. Reduce your answer to its simplest form. Solution: Total number of students = 16. Number of girls = 10. Number of boys = 16 - 10 = 6. Thus the ratio of girls to boys is 10 6 = 5 3. A bag containing chocolates is divided into a ratio of 5:7. If the larger part contains 84 chocolates, find the ...

  11. How to Solve Ratio Word Problems

    Express each ratio of two quantities by writing its numerical values as a fraction. Remember, that's one of the three ways to write a ratio. Find an equivalent ratio, and then set these fractions ...

  12. Word Problems Involving Rates and Ratios

    A step-by-step guide to solving rates and ratios word problems. To solve the word problems involving rates and ratios, follow these steps: Step 1: Find the known ratio and the unknown ratio. Step 2: Write the proportion. Step 3: Use cross-multiply and solve. Step 4: Plug the result into the unknown ratio to check the answers. Word Problems ...

  13. Word Problems on Ratio

    Solution: Let the numbers be 3x and 2x. According to the problem, 3 x + 2 2 x + 6 = 4 5 5 (3x + 2) = 4 15x + 10 = 8x + 24 15x - 8x = 24 - 10 7x = 14 x = 14 7 x = 2 Therefore, the original numbers are: 3x = 3 × 2 = 6 and 2x = 2 × 2 = 4. Thus, the numbers are 6 and 4. 4. If a quantity is divided in the ratio 5 : 7, the larger part is 84.

  14. Ratio Word Problems

    Here you will find a range of problem solving worksheets about ratio. The sheets involve using and applying knowledge to ratios to solve problems. The sheets have been put in order of difficulty, with the easiest first. They are aimed at students in 6th grade. Each problem sheet comes complete with an answer sheet. solve a range of word problems.

  15. IXL

    Spanish. Recommendations. Skill plans. IXL plans. Virginia state standards. Textbooks. Test prep. Awards. Improve your math knowledge with free questions in "Solve proportions: word problems" and thousands of other math skills.

  16. PDF Proportion Word Problems

    8) If you can buy four bulbs of elephant garlic for $8 then how many can you buy with $32? 10) The money used in Jordan is called the Dinar. The exchange rate is $3 to 2 Dinars. Find how many dollars you would receive if you exchanged 22 Dinars. 13) Castel bought four bunches of fennel for $9. How many bunches of fennel can Mofor buy if he has $18?

  17. How to Solve Ratio Word Problems

    http://www.mathtestace.comhttp://www.mathtestace.com/fraction-word-problems/Need help solving word problems with ratios and fractions? This video will walk y...

  18. Part to whole ratio word problem using tables

    3 comments ( 14 votes) Coding4el 4 years ago Hi Annet. You need to find the sum to be able to find the ratio. Example: The ratio of girls to boys in a school is (5:6). If there are 33 students, how many boys are there and girls are there? 1. 5 + 6 = 11 2. 6/11 = boy part of the school/total students 3. 11 x ? = 33, so 6 x ? = ? boys

  19. Proportion word problems (practice)

    Worked example: Solving proportions Math > 7th grade > Proportional relationships > Writing & solving proportions Proportion word problems Google Classroom Sam used 6 loaves of elf bread on an 8 day hiking trip. He wants to know how many loaves of elf bread ( b) he should pack for a 12 day hiking trip if he eats the same amount of bread each day.

  20. Free proportion worksheets for grades 6, 7, and 8

    Proportion Worksheets Create proportion worksheets to solve proportions or word problems (e.g. speed/distance or cost/amount problems) — available both as PDF and html files. These are most useful when students are first learning proportions in 6th, 7th, and 8th grade.

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    This video focuses on how to solve ratio word problem in algebra 1. I show how to carefully translate the verbal portions of the problem in algebraic express...

  22. Setting up proportions to solve word problems

    Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/math/cc-seventh-grade-math/cc-7th-r...

  23. Ratio Word Problems (Simplifying Math)

    For an entire 6th grade math course with lessons, examples, supported practice, assessments and an end of course certificate, go to the link below! It can be...