Proportion

A recipe is an example of direct proportion. When you double the amount of cakes you make you double the amount of each ingredient that you use. The ingredients are always in the same ratio.

Example 1: Here is a recipe to make 30 cookies

Cookie Recipe
150g Butter
180g Sugar
225g Flour
210g Chocolate Chips

Work out how much of each ingredient is needed to make 20 cookies

There are lots of ways to answer questions like this.
We could work out the amount of each ingredient needed for each cookie by dividing by 30 (30 ÷ 30 = 1), and then multiply by 20 for 20 cookies.

Another option is to start by working out the amounts needed for 10 cookies.
We can work out the amounts needed for 10 cookies by dividing by 3
30 cookies ÷ 3 = 10 cookies

For 10 cookies we need:
Butter: 150g ÷ 3 = 50g
Sugar: 180g ÷ 3 = 60g
Flour: 225g ÷ 3 = 75g
Chocolate Chips: 210g ÷ 3 = 70g

We can now either take the amount for 10 cookies away from the amount for 30 cookies
or we can double the amount for 10 cookies to get 20 cookies

For 20 cookies we need:
Butter: 50g × 2 = 100g
Sugar: 60g × 2 = 120g
Flour: 75g × 2 = 150g
Chocolate Chips: 70g × 2 = 140g

Example 2: Here is a recipe to make 12 flapjacks

Flapjack Recipe
240g Butter
80g Sugar
400g Oats
4 tbsp Honey

Work out how much of each ingredient is needed to make 30 flapjacks

Again there are lots of ways to approach this question.

One way is to halve the recipe. This will give us the amounts for 6 flapjacks. We can then multiply by 5 (6 × 5 = 30).

For 6 flapjacks we need:
Butter: 240g ÷ 2 = 120g
Sugar: 80g ÷ 2 = 40g
Oats: 400g ÷ 2 = 200g
Honey: 4tbsp ÷ 2 = 2tbsp

We can now multiply the amounts needed for 6 flapjacks by 5 to get the amounts for 30 flapjacks.

For 30 flapjacks we need:
Butter: 120g × 5 = 600g
Sugar: 40g × 5 = 200g
Oats: 200g × 5 = 1000g
Honey: 2tbsp × 5 = 10tbsp

Try these:

Proportion is about keeping the same balance between quantities. In recipe questions, the ingredients are in direct proportion to the number of items made.

If the number made changes, every ingredient must be scaled by the same multiplier. You can calculate the multiplier using the following formula:

\text{multiplier} = \frac{\text{new number made}}{\text{old number made}}

Once the multiplier is found, apply it to the original quantities to find the updated amounts:

\text{new amount} = \text{old amount} \times \text{multiplier}

A multiplier greater than 1 scales up, and a multiplier between 0 and 1 scales down. Keep units with your answers, such as g, ml, kg or number of eggs.

Here is a list of ingredients for making 10 Flapjacks.

Ingredients for 10 Flapjacks

80 g rolled oats
60 g butter
30 ml golden syrup
36 g light brown sugar

Two quantities are in direct proportion when they increase or decrease by the [ ].

A recipe is an example of direct proportion. When you double the amount of cakes you make you double the amount of each ingredient that you use. The ingredients are always in the same ratio.

Example 1: Here is a recipe to make 30 cookies

Cookie Recipe
150g Butter
180g Sugar
225g Flour
210g Chocolate Chips

Work out how much of each ingredient is needed to make 20 cookies

There are lots of ways to answer questions like this.
We could work out the amount of each ingredient needed for each cookie by dividing by 30 (30 ÷ 30 = 1), and then multiply by 20 for 20 cookies.

Another option is to start by working out the amounts needed for 10 cookies.
We can work out the amounts needed for 10 cookies by dividing by 3
30 cookies ÷ 3 = 10 cookies

For 10 cookies we need:
Butter: 150g ÷ 3 = 50g
Sugar: 180g ÷ 3 = 60g
Flour: 225g ÷ 3 = 75g
Chocolate Chips: 210g ÷ 3 = 70g

We can now either take the amount for 10 cookies away from the amount for 30 cookies
or we can double the amount for 10 cookies to get 20 cookies

For 20 cookies we need:
Butter: 50g × 2 = 100g
Sugar: 60g × 2 = 120g
Flour: 75g × 2 = 150g
Chocolate Chips: 70g × 2 = 140g

Practise questions

1 of 3

A recipe makes 30 cookies using 150 g of butter. How much butter is needed to make 45 cookies?

Example 2: Here is a recipe to make 12 flapjacks

Flapjack Recipe
240g Butter
80g Sugar
400g Oats
4 tbsp Honey

Work out how much of each ingredient is needed to make 30 flapjacks

Again there are lots of ways to approach this question.

One way is to halve the recipe. This will give us the amounts for 6 flapjacks. We can then multiply by 5 (6 × 5 = 30).

For 6 flapjacks we need:
Butter: 240g ÷ 2 = 120g
Sugar: 80g ÷ 2 = 40g
Oats: 400g ÷ 2 = 200g
Honey: 4tbsp ÷ 2 = 2tbsp

We can now multiply the amounts needed for 6 flapjacks by 5 to get the amounts for 30 flapjacks.

For 30 flapjacks we need:
Butter: 120g × 5 = 600g
Sugar: 40g × 5 = 200g
Oats: 200g × 5 = 1000g
Honey: 2tbsp × 5 = 10tbsp

Practise questions

1 of 3

A recipe makes 12 flapjacks using 240 g of butter. How much butter is needed for 18 flapjacks?

Try these:

Practise questions

1 of 3

If $y$ is directly proportional to x, and $y = 12$ when x=3, what is the value of $y$ when x=5?

Proportion is about keeping the same balance between quantities. In recipe questions, the ingredients are in direct proportion to the number of items made.

If the number made changes, every ingredient must be scaled by the same multiplier. You can calculate the multiplier using the following formula:

\text{multiplier} = \frac{\text{new number made}}{\text{old number made}}

Once the multiplier is found, apply it to the original quantities to find the updated amounts:

\text{new amount} = \text{old amount} \times \text{multiplier}

A multiplier greater than 1 scales up, and a multiplier between 0 and 1 scales down. Keep units with your answers, such as g, ml, kg or number of eggs.

Here is a list of ingredients for making 10 Flapjacks.

Ingredients for 10 Flapjacks

80 g rolled oats
60 g butter
30 ml golden syrup
36 g light brown sugar

Two quantities are in direct proportion when they increase or decrease by the [ ].

A recipe makes 30 cookies using 150 g of butter. How much butter is needed to make 45 cookies?

A recipe makes 12 flapjacks using 240 g of butter. How much butter is needed for 18 flapjacks?

If $y$ is directly proportional to x, and $y = 12$ when x=3, what is the value of $y$ when x=5?

Review Proportion by teaching Genie

Recap your knowledge with an interactive lesson

Put it into practice with exam-style questions

Ingredients for 10 Flapjacks

Remember key concepts with flashcards

Proportion

Practise questions

Practise questions

Practise questions

Review Proportion by teaching Genie

Recap your knowledge with an interactive lesson

Put it into practice with exam-style questions

Ingredients for 10 Flapjacks

Remember key concepts with flashcards

Practise questions

Practise questions

Practise questions

Proportion

Review Proportion by teaching Genie

Recap your knowledge with an interactive lesson

Put it into practice with exam-style questions

Ingredients for 10 Flapjacks

Remember key concepts with flashcards

Proportion Revision Guide

Proportion

Practise questions

Practise questions

Practise questions

Review Proportion by teaching Genie

Recap your knowledge with an interactive lesson

Put it into practice with exam-style questions

Ingredients for 10 Flapjacks

Remember key concepts with flashcards

Proportion Revision Guide

Practise questions

Practise questions

Practise questions