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## [FREE] Fun Math Games and Activities Packs for Kindergarten to Grade 5

Ready to go, printable packs that teachers can use in the classroom.

## Ratio Questions And Practice Problems: Differentiated Practice Questions Included

## Beki Christian

## What is ratio?

## Uses of ratio

## Ratio in Middle School and High School

## Proportion and ratio

Take the example of a box containing 7 counters; 3 red counters and 4 blue counters:

The ratio of red counters:blue counters is 3:4.

For every 3 red counters there are four blue counters.

The proportion of red counters is \frac{3}{7} and the proportion of blue counters is \frac{4}{7}

3 out of every 7 counters are red and 4 out of every 7 counters are blue.

## Direct proportion and inverse proportion

## How to solve a ratio problem

If you have been given the whole amount you can follow these steps to answer the question:

- Add together the parts of the ratio to find the total number of shares
- Divide the total amount by the total number of shares
- Multiply by the number of shares required

If you have been been given a part of the whole you can follow these steps:

- Identify which part you have been given and how many shares it is worth
- Use equivalent ratios to find the other parts
- Use the values you have to answer your problem

## How to solve a proportion problem

Proportion problems can often be solved using scaling. To do this you can follow these steps:

- Identify the values that you have been given which are proportional to each other
- Use division to find an equivalent relationship
- Use multiplication to find the required relationship

## Real life ratio problems and proportion problems

Ratio is all around us. Let’s look at some examples of where we may see ratio and proportion:

## Cooking ratio question

Here we know the full amount – 1000ml.

The ratio is 1:9 and we want to find the amount of milk.

- Total number of shares = 1 + 9 = 10
- Value of each share: 1000 ÷ 10 = 100
- The milk is 9 shares so 9 × 100 = 900

## Maps ratio question

The scale on a map is 1:10000. What distance would 3.5cm on the map represent in real life?

Here we know one part is 3.5. We can use equivalent ratios to find the other part.

The distance in real life would be 35000cm or 350m.

## Speed proportion question

I travelled 60 miles in 2 hours. Assuming my speed doesn’t change, how far will I travel in 3 hours?

This is a proportion question.

- I travelled 60 miles in 2 hours.
- Dividing by 2, I travelled 30 miles in one hour
- Multiplying by 3, I would travel 90 miles in 3 hours

## Middle School ratio questions

Example Middle School worded question

## Ratio questions for 6th grade

Gertie divides $30 in the ratio 2:4.

The total number of shares is 2 + 4 = 6.

Each share is worth $30 ÷ 6 = $5.

Jasmine gets 2 shares, 2 x $5 = $10.

Holly gets 4 shares, 4 x $5 = $20.

## Ratio questions 7th grade

3. The ratio of men:women working in a company is 3:5. What proportion of the employees are women?

In this company, the ratio of men:women is 3:5 so for every 3 men there are 5 women.

This means that for every 8 employees, 5 of them are women.

Therefore \frac{5}{8} of the employees are women.

## Ratio questions 8th grade

5. The angles in a triangle are in the ratio 3:4:5. Work out the size of each angle.

30^{\circ} , 40^{\circ} and 50^{\circ}

22.5^{\circ}, 30^{\circ} and 37.5^{\circ}

60^{\circ} , 60^{\circ} and 60^{\circ}

45^{\circ} , 60^{\circ} and 75^{\circ}

The total number of shares is 3 + 4 + 5 = 12.

Each share is worth 180 ÷ 12 = 15 ^{\circ} .

3 shares is 3 x 15 = 45 ^{\circ} .

4 shares is 4 x 15 = 60 ^{\circ} .

5 shares is 5 x 15 = 75 ^{\circ} .

6. Paint Pro makes pink paint by mixing red paint and white paint in the ratio 3:4.

Colour Co makes pink paint by mixing red paint and white paint in the ratio 5:7.

Which company uses a higher proportion of red paint in their mixture?

The proportion of red paint for Paint Pro is \frac{3}{7}

The proportion of red paint for Colour Co is \frac{5}{12}

We can compare fractions by putting them over a common denominator using equivalent fractions

\frac{3}{7} = \frac{36}{84} \hspace{3cm} \frac{5}{12}=\frac{35}{84}

\frac{3}{7} is a bigger fraction so Paint Pro uses a higher proportion of red paint.

## High school ratio questions

## Ratio high school questions (low difficulty)

We have been given one part so we can work this out using equivalent ratios.

The total number of students is 8 + 4 + 16 = 28

8. A bag contains counters. 40% of the counters are red and the rest are yellow.

Write down the ratio of red counters:yellow counters. Give your answer in the form 1:n.

Jim receives 2 shares more than Rosie, so 2 shares is equal to 12.

Therefore 1 share is equal to 6. Rosie receives 5 shares: 5 × 6 = 30.

How long will it take Rahim to save for his new bike?

Rahim’s earnings of $1500 are divided in the ratio of 8:3:4.

The total number of shares is 8 + 3 + 4 = 15.

Each share is worth $ 1500 ÷ 15 = £100 .

Rahim spends 4 shares on extras so 4 × $ 100 = $400 .

The number of months it will take Rahim is $ 480 ÷ $ 80 = 6

## Ratio GCSE exam questions higher

12. In a school the ratio of girls:boys is 2:3.

25% of the girls have school dinners.

30% of the boys have school dinners.

What is the total percentage of students at the school who have school dinners?

100% in the ratio 2:3 is 40%:60% so 40% of the students are girls and 60% are boys.

The total percentage of students who have school dinners is 10 + 18 = 28%.

13. For the cuboid below, a:b = 3:1 and a:c = 1:2.

Find an expression for the volume of the cuboid in terms of a.

If a:b = 3:1 then b=\frac{1}{3}a

## Ratio high school questions (average difficulty)

Calculate the total amount of money won by Bill and Ben.

The new ratio is 3a:4a-40 and this is equal to the ratio 6:7.

Since 3a:4a-40 is equivalent to 6:7, 7 lots of 3a must be equal to 6 lots of 4a-40.

The initial amounts were 3a:4a. a is 80 so Bill received $240 and Ben received $320.

The total amount won was $560.

What fraction of the animals on the farm are babies?

The easiest way to solve this is to think about fractions.

\\ \frac{4}{5} of the animals are pigs, \frac{1}{5} of the animals are goats.

## Looking for more middle school and high school math questions?

- 15 Algebra questions
- 15 Probability questions
- 15 Trigonometry questions
- 15 Simultaneous equations questions
- 15 Venn diagram questions
- Long division questions

The activities are designed to be fun, flexible and suitable for a range of abilities.

## Privacy Overview

## How to Solve Questions About Ratios

## What Is a Ratio?

Here are some everyday examples of times when you could use ratios:

- When you convert your Pounds to Dollars or Euros when you go on holiday
- When you calculate your winnings on a bet
- When you work out how many bottles of beer you need for a party
- When you share a packet of sweets fairly among your friends
- When you calculate how much tax you must pay on your income

## Different Ways of Presenting Ratios

## Scaling a Ratio

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## Question 1: Scaling Ratios

What quantity of the ingredients will she need to use?

## Reducing a Ratio

Sometimes ratios are not presented in their simplest form, which makes them harder to manipulate.

## Question 2: Reducing Ratios

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## Finding Unknown Quantities From Existing Equivalent Ratios

## Question 3: Finding Unknown Quantities From Existing Equivalent Ratios

How much wine do they need in total?

## Common Mistakes and Things to Look Out For

## Question 4: Scaling Ratios

## Question 5: Reducing Ratios

Hugo and Claudia share 600 g chocolate using the ratio 4:2.

How much chocolate does Claudia get?

## Question 6: Scaling Ratios

## Frequently Asked Questions

What is an easy way to solve ratio questions.

In this case, that’s 3 + 1 = 4.

That 5 is then used in the third and final step to create the answer.

## What are the most common mistakes in ratio questions?

## How do I solve ratio questions and get an answer in minutes?

Once you work out which type of question it is you can get an answer in minutes.

## Are there any tricks to solve ratio questions in bank/any other competitive exams?

## What is an example of a ratio question?

## Do ratios perform a proportion?

## How are ratios used in everyday life?

## What are the rules of ratio?

For example, a 1:2 ratio could be expressed as 1/2 or with the words '1 to 2'.

## How does ratio and proportion help me as a student?

## What prior knowledge is needed for ratios?

## How do you teach students ratios?

## How are ratios used in cooking?

Therefore just doubling the initial measurements is a way of using ratios.

You might also be interested in these other WikiJob articles:

Or explore the Aptitude Tests / Test Types sections.

## Algebra: Ratio Word Problems

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

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

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.

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.

## How To Solve Proportion Word Problems?

- 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

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.

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

## Algebra And Ratios With Three Terms

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

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## Ratios and proportions and how to solve them

A ratio can be written in three different ways and all are read as "the ratio of x to y"

A proportion is read as "x is to y as z is to w"

$$\frac{x}{y}=\frac{z}{w} \: where\: y,w\neq 0$$

If one number in a proportion is unknown you can find that number by solving the proportion.

If we write the unknown number in the nominator then we can solve this as any other equation

$$\frac{x}{100}=\frac{2}{20}$$

$${\color{green} {100\, \cdot }}\, \frac{x}{100}={\color{green} {100\, \cdot }}\, \frac{2}{20}$$

If we again use the example with the cookie mix used above

$$\frac{{\color{green} {20}}}{{\color{blue} {1}}}=\frac{{\color{blue} {40}}}{{\color{green} {2}}}$$

$${\color{blue} {1}}\cdot {\color{blue} {40}}={\color{green} {2}}\cdot {\color{green} {20}}=40$$

It is said that in a proportion if

$$20\cdot 1:4=20\cdot \frac{1}{4}=5$$

## Video lesson

$$\frac{x}{x + 20} = \frac{24}{54}$$

- The coordinate plane
- Linear equations in the coordinate plane
- The slope of a linear function
- The slope-intercept form of a linear equation
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- Algebra 2 Overview
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## Word Problems: Ratios

Write the ratio as a fraction.

So the ratio of sunfish to rainbow shiners is 2 : 5 .

(Note that the ratio of rainbow shiners to sunfish is the reciprocal : 5 2 or 5 : 2 .)

Ms. Ekpebe's class has 32 students, of which 20 are girls. Write the ratio of girls to boys.

Subtract 20 from 32 to find the number of boys in the class.

There are 12 boys in the class. So, ratio of girls to boys is 20 : 12 .

In simplest form, this ratio is 5 : 3 .

Some ratio word problems require you to solve a proportion.

The ratio 2 : 3 means that for every 2 cups of butter, you should use 3 cups of sugar.

Here you're using 6 cups of butter, or 3 times as much.

So you need to multiply the amount of sugar by 3 .

So, you need to use 9 cups of sugar.

You can think of this in terms of equivalent fractions :

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## How Do You Solve a Word Problem Using Ratios?

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## What's a Numerator and What's A Denominator?

## Ratio Definitions

## What's a Ratio?

## What are Equivalent Ratios?

## Working with Ratios

## How Do You Find Equivalent Ratios?

## Finding Equivalent Fractions

## What are Equivalent Fractions?

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## Unit 1: Lesson 4

## Part to whole ratio word problem using tables

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## Ratio word problems

## Interesting ratio word problems

Solution: The ratio of women to men is 30 to 40, 30:40, or 30/40

The ratio of length to width is 20 to 15, 20:15 or 20/15

## Hard ratio word problems

100/6000 = 1/60 The ratio of the length to the area in simplest form is 1/60

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The six steps of problem solving involve problem definition, problem analysis, developing possible solutions, selecting a solution, implementing the solution and evaluating the outcome. Problem solving models are used to address issues that...

An example of a ratio word problem is: “In a bag of candy, there is a ratio of red to green candies of 3:4. If the bag contains 120 pieces of candy, how many red candies are there?” Another example of a ratio word problem is: “A recipe call...

When multiplying or dividing different bases with the same exponent, combine the bases, and keep the exponent the same. For example, X raised to the third power times Y raised to the third power becomes the product of X times Y raised to th...

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

Solving Proportions with an Unknown Ratio ... To check the accuracy of our answer, simply divide the two sides of the equation and compare the

How to solve a ratio problem · Identify which part you have been given and how many shares it is worth · Use equivalent ratios to find the other

What makes you unique? Why are you applying for this position? ... What interests you about this job? Where do you see yourself in five years?

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

A proportion on the other hand is an equation that says that two ratios are equivalent. For instance if one package of cookie mix results in 20 cookies than

Example 1: A backyard pond has 12 sunfish and 30 rainbow shiners. Write the ratio of sunfish to rainbow shiners in simplest form . Write

This tutorial shows you how to use a ratio to create equivalent ratios. Then, use a multiplier to find a missing value and solve the word problem.

How do we write ratios? · Determine whether the ratio is part to part or part to whole. · Calculate the parts and the whole if needed. · Plug values into the ratio

... specific to this particular problem in this video, but I hope these examples help you know how to solve part to whole ratio problems.

Ratio word problems · Example #1: · Solution: The ratio of women to men is 30 to 40, 30:40, or 30/40 · Example #2: The length of a rectangular garden is 20 feet