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Sharing in a Ratio: Worksheets with Answers

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Ratio Problem Solving

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

There are also ratio problem solving worksheets based on Edexcel, AQA and OCR exam questions, along with further guidance on where to go next if you’re still stuck.

What is ratio problem solving?

Ratio problem solving is a collection of 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 we can use to help us 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 we can use when given certain pieces of information.

When solving ratio 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?

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

Then we multiply each part of the ratio by 5.

3 x 5:5 x 5 = 15:25

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

• Dividing ratios

Step-by-step guide: Dividing ratios (coming soon)

Ratios and fractions (proportion problems)

We also need to consider problems involving fractions. These are usually proportion questions where we are stating the proportion of the total amount as a fraction.

Simplifying and equivalent ratios

• Simplifying ratios

Equivalent ratios

Units and conversions ratio questions

Units and conversions are usually equivalent ratio problems (see above).

• If £1:\$1.37 and we wanted to convert £10 into dollars, we would multiply both sides of the ratio by 10 to get £10 is equivalent to \$13.70.
• The scale on a map is 1:25,000. I measure 12cm on the map. How far is this in real life, in kilometres? After multiplying both parts of the ratio by 12 you must then convert 12 \times 25000=300000 \ cm to km by dividing the solution by 100 \ 000 to get 3km.

Notice that for all three of these examples, the units are important. For example if we write the mapping example as the ratio 4cm:1km, this means that 4cm on the map is 1km in real life.

Top tip: if you are converting units, always write the units in your ratio.

Usually with ratio problem solving questions, the problems are quite wordy . They can involve missing values , calculating ratios , graphs , equivalent fractions , negative numbers , decimals and percentages .

Highlight the important pieces of information from the question, know what you are trying to find or calculate , and use the steps above to help you start practising how to solve problems involving ratios.

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.

Explain how to do ratio problem solving

Ratio problem solving worksheet

Get your free ratio problem solving worksheet of 20+ questions and answers. Includes reasoning and applied questions.

Related lessons on ratio

Ratio problem solving is part of our series of lessons to support revision on ratio . You may find it helpful to start with the main ratio lesson for a summary of what to expect, or use the step by step guides below for further detail on individual topics. Other lessons in this series include:

• How to work out ratio  
• Ratio to fraction
• Ratio scale
• Ratio to percentage

Ratio problem solving examples

Example 1: part:part ratio.

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

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

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

We could write this as

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

We know that 465 students have school dinner.

2 Know what you are trying to calculate.

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

We need to find the value of p.

3 Use prior knowledge to structure a solution.

We are looking for an equivalent ratio to 5:7. So we need to calculate the multiplier. We do this by dividing the known values on the same side of the ratio by each other.

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} (GBP) to Euros \bf{€} (EUR).

The two values in the table that are important are GBP and EUR. Writing this as a ratio, we can state

We know that we have £520.

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

To get from 1 to 520, we multiply by 520 and so to calculate the number of Euros for £520, we 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 500ml of concentrated plant food must be diluted into 2l 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{500ml} of concentrated plant food must be diluted into \bf{2l} 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, we can now state the ratio of plant food to water as 500ml:2l. As we can convert litres into millilitres, we could convert 2l into millilitres by multiplying it by 1000.

2l = 2000ml

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

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

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

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 pocket money per week proportional to their age. Kieran is 3 years older than Josh. Luke is twice Josh’s age. If Josh receives £8 pocket money, how much money do the three siblings receive in total?

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

We 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, we have

We also know that Luke receives £8.

We want to calculate the total amount of pocket money for the three siblings.

We need to find the value of x first. As Luke receives £8, we can state the equation 2x=8 and so x=4.

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

The total amount of pocket money is therefore 4+7+8=£19.

Example 5: simplifying ratios

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

Express this data as a ratio in its simplest form.

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

We need to simplify this ratio.

To simplify a ratio, we 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 , we get

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 .

We know the two ratios

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

Using equivalent ratios we can say that the ratio of silica:soda is equivalent to 15:3 by multiplying the ratio by 3.

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

Example 7: using bar modelling

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

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

We want to find the original quantity.

Drawing a bar model of this problem, we have

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

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

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

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

We can fill in each share to be 25g.

Adding up each share, we get

India = 5 \times 25=125g

Beau = 2 \times 25=50g

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

Common misconceptions

• 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 millilitres. We did not mix ml and l in the ratio.

• Ratio written 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.

• Ratios and fractions confusion

Take care when writing ratios as fractions and vice-versa. Most ratios we come across are part:part. The ratio here of red:yellow is 1:2. So the fraction which is red is \frac{1}{3} (not \frac{1}{2} ).

• 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:n}

The assumption can be incorrectly made that n must be greater than 1 , but n can be any number, including a decimal.

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?

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

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

3. 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.

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

5. A clothing company has a sale on tops, dresses and shoes. \frac{1}{3} of sales were for tops, \frac{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.

6. 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.

Ratio problem solving GCSE questions

1. One mole of water weighs 18 grams and contains 6.02 \times 10^{23} water molecules.

Write this in the form 1gram:n where n represents the number of water molecules in standard form.

2. A plank of wood is sawn into three pieces in the ratio 3:2:5. The first piece is 36cm shorter than the third piece.

Calculate the length of the plank of wood.

5-3=2 \ parts = 36cm so 1 \ part = 18cm

3. (a) Jenny is x years old. Sally is 4 years older than Jenny. Kim is twice Jenny’s age. Write their ages in a ratio J:S:K.

(b) Sally is 16 years younger than Kim. Calculate the sum of their ages.

Learning checklist

You have now learned how to:

• Relate the language of ratios and the associated calculations to the arithmetic of fractions and to linear functions
• Develop their mathematical knowledge, in part through solving problems and evaluating the outcomes, including multi-step problems
• Make and use connections between different parts of mathematics to solve problems

The next lessons are

• Compound measures
• Best buy maths

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Solving ratio problems

Ratio problems take different forms, which may include:

linking ratios and fractions

part-part problems - where the value of one part of the ratio is given and the value of another ratio part has to be found

part-whole problems - where the value of one part of the ratio is given and the value of the whole has to be found

comparison problems - where the ratio and the difference between the values is given

• problems where values change, giving a new ratio

In order to solve ratio problems, an understanding of the structure of the problem is needed. A bar model may help to clarify this.

An understanding of equivalent ratios and simplifying ratios , as well as division in a given ratio is needed to solve ratio problems.

Solving problems involving ratios and fractions

To solve a problem involving ratios and fractions, you may be given the ratio or the fraction .

When given the ratio :

Add the ratio parts together to find the denominator of the fraction.

The numerator of the fraction is the ratio part that is the focus of the question.

When given the fraction :

• The numerator of the fraction gives one of the ratio parts.
• Find the other ratio part by subtracting the numerator from the denominator.
• Write the ratio in the correct order.

The ratio of horses to donkeys at an animal sanctuary is 5 : 2. What fraction of the animals are donkeys?

Add the ratio parts (5 and 2) to find the denominator of the fraction. 5 + 2 = 7. The denominator is 7

The numerator of the fraction is the ratio part that is the focus of the question (donkeys). The numerator is 2. The fraction of the animals that are donkeys is 2⁄7

To make pink paint, 2⁄5 red paint is mixed with white paint. How much white paint is needed? What is the ratio of red to white paint?

The numerator of the fraction of red paint is 2. This is the ratio part for red paint. To find the ratio part for the white paint, subtract the numerator from the denominator. 5 – 2 = 3. The ratio part for white paint is 3. 3⁄5 of the paint is white. The ratio of red to white paint is 2 : 3

A farm has sheep and goats in the ratio 7 : 5 (sheep : goats). What fraction of the animals are sheep?

Add the ratio parts (7 and 5) to find the denominator of the fraction.

7 + 5 = 12. The denominator is 12

The numerator of the fraction is the ratio part that is the focus of the question (sheep). The numerator is 7

The fraction of animals that are sheep is \( \frac{7}{12} \)

Solving part-part and part-whole ratio problems

A part-part ratio problem is where the value of one part of the ratio is given and the value of another ratio part has to be found. A part-whole problem is where the value of one part of the ratio is given and the value of the whole has to be found.

Given a ratio and the value of one part of the ratio, find the value of another ratio part or the value of the whole.

Draw a bar model split into the total number of parts. Label with the given information to represent the problem.

Find the value of one part by dividing the given value by the associated number of parts.

To find the value of another ratio part in a part-part problem, multiply the value of one part by the number of parts asked for.

To find the whole in a part-whole problem, multiply the value of one part by the total number of parts.

A box contains toffees and truffles in the ratio 7 : 6. There are 24 truffles. How many toffees are there?

Draw a bar model and label it to illustrate the problem. The ratio of toffees to truffles is 7 : 6. Draw 7 parts for the toffees and 6 for the truffles. Label the truffle bar with 24. To work out the total number of toffees, the value of one part needs to be found.

To work the value of one part, divide the number of truffles (24) by the number of parts given (6). This gives the value of one part. 24 ÷ 6 = 4

Multiply the value of one part (4) by the number of parts asked for: the toffees (7). 4 × 7 = 28. There are 28 toffees in the box.

A library stocks books for children and books for adults in the ratio 3 : 5. There are 450 books for children. How many books are in the library?

Draw a bar model and label it to illustrate the problem. The ratio of books for children to books for adults is 3 : 5. Draw 3 parts for books for children and 5 parts for books for adults. Label the books for children bar with 450. To work out the total number of books, the value of one part needs to be found.

To find the value of one part, divide the amount of books for children (450) by the number of parts given (3). 450 ÷ 3 = 150. The value of one part is 150

Multiply the value of one part (150) by the number of parts asked for: the number of books in the library. This is the total of books for children parts and the books for adults parts. (3 + 5 = 8). The calculation is 150 × 8. The total number of books in the library is 1200.

The ratio of desserts to pizzas in a supermarket freezer is 4 : 3 There are a total of 620 desserts. How many pizzas are in the freezer?

Draw a bar model to illustrate the problem. The ratio of desserts to pizzas is 4 : 3 . Draw 4 parts for desserts and 3 parts for pizzas.

Label it to illustrate the problem. Label the dessert bar with 620. To find the number of pizzas in the freezer, work out the value of one part.

To find the value of one part, divide the share for desserts (620) by the number of parts (4). 620 ÷ 4 = 155. The value of one part is 155

Multiply the value of one part (155) by the number of parts asked for: pizzas (3). 155 x 3 = 465

The number of pizzas in the freezer is 465

Solving ratio problems involving comparisons

Some ratio problems involve a comparison between values. The comparison is the value difference between two parts of the ratio.

Given a ratio and a comparison between values:

Draw a bar model to illustrate the problem.

Label the given information.

Find the value of one part by dividing the comparison value by the number of parts given.

Multiply the value of one part by the number of parts of the object of the question.

Everyone at a fancy dress party is dressed up as either a vampire or a wizard. The ratio of people dressed as vampires to wizards is 5 : 2. If there are 6 more vampires than wizards, how many people are at the party?

Draw a bar model to illustrate the problem. The ratio of vampires to wizards is 5 : 2. There are 5 parts for the vampires and 2 parts for the wizards.

Label the given information. There are 6 more vampires than wizards. The diagram shows the comparison between the vampires bar and the wizards bar. To work out the total number of people at the party, the value of one part needs to be found.

To find the value of one part, divide the difference value (6) by the number of parts that make up the difference (3). 6 ÷ 3 = 2. The value of one part is 2

Multiply the value of one part (2) by the number of parts asked for (all the people so all the parts, 7). 2 × 7 = 14. The total number of people at the party is 14

The ratio of the number of tulips to daffodils in a flower display is 3 : 7. There are 96 fewer tulips than daffodils. Find the number of daffodils in the display.

Draw a bar model to illustrate the problem. The ratio of tulips to daffodils is 3 : 7. There are 3 parts for tulips and 7 parts for daffodils.

Label the given information. There are 96 fewer tulips than daffodils. The diagram shoes the comparison between the tulips bar and the daffodils bar. To work out the number of daffodils in the display, the value of one part needs to be found.

To find the value of one part, divide the comparison value (96) by the number of parts that make up the difference (4). 96 ÷ 4 = 24. The value of one part is 24

Multiply the value of one part (24) by the number of parts asked for (all the daffodils, 7 parts). 24 × 7 = 168. The number of daffodils in the display is 168

The ratio of the number of robins to sparrows to blackbirds in a survey of garden birds is 1 : 3 : 8 (robins : sparrows : blackbirds)

There were 70 fewer robins than sparrows. How many birds were observed in this survey?

Draw a bar model to illustrate the problem. The ratio of robins to sparrows to blackbirds is 1 : 3 : 8. There is 1 part for robins, 3 for sparrows and 8 for blackbirds.

Label the given information. There are 70 fewer robins than sparrows. This is the difference between the robins bar and the sparrows bar. To find the total number of birds in the survey, the value of one part needs to be found.

To find the value of one part, divide the difference value (70) by the number of parts that make up the difference (2). 70 ÷ 2 = 35. The value of one part is 35

Multiply the value of one part (35) by the number of parts asked for (all the parts, 12). 35 x 12 = 420

Solving ratio problems with changing amounts

Given a ratio and total amount, find the new changing amounts and find the new ratio:

A total amount and ratio is given. Draw a bar model to illustrate this starting information.

Divide the total amount in the initial ratio.

• Find the value of one part by dividing the total amount by the sum of the parts.
• Multiply the value of one part by the number of parts for each share of the ratio.

Adjust the shared amounts according to the given information in the question.

Write the new amounts as a ratio and simplify, if necessary, by dividing the parts by their highest common factor (HCF).

In this example, you need to be able to divide in a given ratio and simplify ratios.

A market stall has 60 T-shirts. The ratio of small, medium and large T-shirts being sold on the stall is 2 : 3 : 1. The stallholder sells 26 medium and 2 large T-shirts. What is the ratio of small, medium and large T-shirts now?

Draw a bar model to illustrate the starting information. Draw 2 parts for small T-shirts, 3 for medium and 1 for large. The total number of T-shirts is 60

Divide 60 in the ratio 2 : 3 : 1. To find the value of one part, divide the total number (60) by the sum of the parts (2 + 3 + 1 = 6). 60 ÷ 6 = 10. The value of one part is 10

2 parts are small, so 2 × 10 = 20 small T-shirts. 3 parts are medium, so 3 × 10 = 30 medium T-shirts. 1 part is large, so 1 × 10 = 10 large T-shirts.

Adjust the shared amounts according to the given information in the question. At the start there were 20 small, 30 medium and 10 large T-shirts. 26 medium and 2 large T-shirts are sold. The remaining T-shirts are 20 small, 4 medium and 8 large T-shirts.

The ratio of small to medium to large T-shirts is now 20 : 4 : 8. This ratio can be simplified.

To simplify the ratio, divide each part by their highest common factor (HCF). The HCF of 20, 4 and 8 is 4. Divide each part by 4. The new simplified ratio of small to medium to large T-shirts is 5 : 1 : 2

There are 55 big cats in a safari park. The ratio of lions to tigers is 3 : 2 12 lion cubs and 5 tiger cubs are born. What is the ratio of lions to tigers now?

A total amount and ratio is given. Draw a bar model to illustrate this starting information. Draw 3 parts for lions and 2 parts for tigers, with a total of 55

Divide the total number of big cats (55) in the ratio 3 : 2. To find the value of one part, divide the amount (55) by the total number of parts (5). 55 ÷ 5 = 11. The value of one part is 11. Multiply one part by the number of parts for each big cat. There are 11 × 3 = 33 lions. There are 11 × 2 = 22 tigers.

Adjust the shared amounts according to given information in the question. After the cubs have been born there are 33 + 12 = 45 lions and 22 + 5 = 27 tigers.

Write the new shares as a ratio and simplify. The new ratio of lions to tigers is 45 : 27. This ratio can be simplified by finding the HCF of 45 and 27. This is 9. Divide each ratio share by 9. The ratio simplifies to 5 : 3

The ratio of lions to tigers is now 5 : 3

Practise solving ratio problems

Practise solving ratio problems in this quiz. You may need a pen and paper to complete these questions.

Real-world maths

Ratio problems occur in many different contexts.

Successful cookery relies on the ratio of the ingredients used. For example:

To make meringues, you need a ratio of 2 parts sugar to 1 part egg white.

To make Yorkshire puddings, you need equal amounts of egg, flour and milk (and a pinch of salt). The ratio of egg, flour and milk is 1 : 1 : 1

In construction, fencing companies use a fixed ratio of concrete mix to water to secure fence posts. For a given amount of concrete mix, the amount of water needed is worked out. This is a part-to-part ratio problem.

Game - Divided Islands

Divided Islands

Use your maths skills to help the islanders of Ichi build bridges and bring light back to the islands in this free game from BBC Bitesize.

Division in a given ratio

Scale drawings

Map scales and ratio

Corbettmaths

Videos, worksheets, 5-a-day and much more, percentages practice questions, percentages (non-calculator), click here for questions, click here for answers, percentages (calculator).

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Praxis Core Math

Course: praxis core math   >   unit 1.

• Rational number operations | Lesson
• Rational number operations | Worked example

Ratios and proportions | Lesson

• Ratios and proportions | Worked example
• Percentages | Lesson
• Percentages | Worked example
• Rates | Lesson
• Rates | Worked example
• Naming and ordering numbers | Lesson
• Naming and ordering numbers | Worked example
• Number concepts | Lesson
• Number concepts | Worked example
• Counterexamples | Lesson
• Counterexamples | Worked example
• Pre-algebra word problems | Lesson
• Pre-algebra word problems | Worked example
• Unit reasoning | Lesson
• Unit reasoning | Worked example

What are ratios and proportions?

What skills are tested.

• Identifying and writing equivalent ratios
• Solving word problems involving ratios
• Solving word problems using proportions

How do we write ratios?

• The ratio of lemon juice to sugar is a part-to-part ratio. It compares the amount of two ingredients.
• The ratio of lemon juice to lemonade is a part-to-whole ratio. It compares the amount of one ingredient to the sum of all ingredients.
• 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.
• Simplify the ratio if needed. Integer-to-integer ratios are preferred.

How do we use proportions?

• Write an equation using equivalent ratios.
• Plug in known values and use a variable to represent the unknown quantity.
• If the numeric part of one ratio is a multiple of the corresponding part of the other ratio, we can calculate the unknown quantity by multiplying the other part of the given ratio by the same number.
• If the relationship between the two ratios is not obvious, solve for the unknown quantity by isolating the variable representing it.
• (Choice A)   1 : 4 ‍   A 1 : 4 ‍  
• (Choice B)   1 : 2 ‍   B 1 : 2 ‍  
• (Choice C)   1 : 1 ‍   C 1 : 1 ‍  
• (Choice D)   2 : 1 ‍   D 2 : 1 ‍  
• (Choice E)   4 : 1 ‍   E 4 : 1 ‍  
• (Choice A)   1 6 ‍   A 1 6 ‍  
• (Choice B)   1 3 ‍   B 1 3 ‍  
• (Choice C)   2 5 ‍   C 2 5 ‍  
• (Choice D)   1 2 ‍   D 1 2 ‍  
• (Choice E)   2 3 ‍   E 2 3 ‍  
• Your answer should be
• an integer, like 6 ‍  
• a simplified proper fraction, like 3 / 5 ‍  
• a simplified improper fraction, like 7 / 4 ‍  
• a mixed number, like 1   3 / 4 ‍  
• an exact decimal, like 0.75 ‍  
• a multiple of pi, like 12   pi ‍   or 2 / 3   pi ‍  

Things to remember

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