A recipe uses 200 g of flour for 4 people. How much flour is needed for 8 people?
Double the recipe.
8 is double 4, so 200 g × 2 = 400 g.
Recipes and Scaling
Scaling involves adjusting quantities proportionally, often in contexts such as recipes. This topic builds on ratio to solve real-life problems accurately.
Overview
Scaling means making all amounts bigger or smaller by the same multiplier.
In recipe questions, this lets you adjust ingredients for a different number of people.
\( \text{new amount} = \text{old amount} \times \text{scale factor} \)
If the number of servings doubles, the ingredients also double.
If the number of servings halves, the ingredients also halve.
What you should understand after this topic
- Understand what scaling means
- Find the scale factor
- Increase or decrease recipes correctly
- Keep quantities in the same ratio
- Solve real-life scaling questions
Key Definitions
Scaling
Changing all values by the same multiplier.
Scale Factor
The number you multiply by to make values bigger or smaller.
Equivalent Ratio
A ratio with the same relationship between parts.
Servings
The number of people a recipe is for.
Ingredient Quantity
The amount of each ingredient in a recipe.
Proportional Change
When all quantities change by the same multiplier.
Key Rules
Find the scale factor first
\( \text{scale factor} = \frac{\text{new servings}}{\text{old servings}} \)
Multiply every ingredient
All ingredients must change by the same factor.
If servings double, ingredients double
The ratio stays the same.
If servings halve, ingredients halve
Scale down using a factor less than 1.
Quick Scaling Patterns
Double
Multiply by 2
Half
Multiply by \( \frac{1}{2} \)
Triple
Multiply by 3
Scale to any size
Use \( \frac{\text{new}}{\text{old}} \)
How to Solve
Step 1: Understand scaling
Scaling means multiplying all quantities by the same number so the proportions stay the same.
Exam tip: Never change ingredients differently — everything scales together.
Key idea
Use one scale factor for every ingredient.
Step 2: Find the scale factor
Divide the new number of people by the original number using ideas from fractions.
\( \text{scale factor} = \frac{\text{new amount}}{\text{original amount}} \)
Example: from 4 people to 10 people → \(\frac{10}{4} = 2.5\).
Step 3: Multiply all quantities
Multiply each ingredient by the scale factor.
Apply the same multiplier to every value.
Include units in your final answer.
Step 4: Alternative unitary method
You can also find the amount for one person first, then scale up.
\( \text{amount for 1} = \frac{\text{original amount}}{\text{number of people}} \)
Then multiply by the new number of people.
Exam thinking: Use this method when numbers divide easily.
Step 5: Common mistakes
Different multipliers
All ingredients must use the same scale factor.
Wrong scale factor
Use new ÷ original, not the other way round.
Forgetting units
Always include g, ml, etc.
Step 6: Exam method summary
See ratio for the link between scaling and ratios.
- Find the scale factor.
- Multiply all quantities by the same factor.
- Check units and rounding if needed.
- This method is closely related to best value.
Example Questions
Edexcel
Exam-style questions inspired by Edexcel GCSE Mathematics, focusing on scaling recipes proportionally.
Edexcel
A recipe uses 200g of flour to make 8 pancakes. How much flour is needed to make 20 pancakes?
Edexcel
A soup recipe requires 750ml of stock to serve 6 people. How much stock is needed to serve 10 people?
Edexcel
A cake recipe uses 120g of sugar for 12 cupcakes. Find the amount of sugar needed for 30 cupcakes.
Edexcel
A smoothie recipe uses 3 bananas to make 5 servings. How many bananas are needed to make 15 servings?
Edexcel
A recipe uses 400g of pasta for 4 people. How much pasta is required for 7 people?
AQA
Exam-style questions based on the AQA GCSE Mathematics specification, emphasising scaling up and down in real-life contexts.
AQA
A bread recipe requires 500g of flour to make 10 rolls. How much flour is needed to make 16 rolls?
AQA
A recipe uses 2.5 litres of juice to serve 20 people. How much juice is needed for 8 people?
AQA
A sauce recipe requires 3 tablespoons of oil for 6 portions. How much oil is needed for 15 portions?
AQA
A recipe uses 180g of butter to bake 9 biscuits. How much butter is needed to bake 15 biscuits?
AQA
Explain how to scale a recipe correctly when increasing or decreasing the number of servings.
OCR
Exam-style questions aligned with OCR GCSE Mathematics, focusing on proportional reasoning, unit conversions, and multi-step problems.
OCR
A recipe uses 250g of flour and 150g of sugar to make 10 muffins. Calculate the quantities required to make 18 muffins.
OCR
A recipe for 4 people requires 0.6 litres of milk. How much milk is needed for 15 people?
OCR
A recipe needs 3 eggs to serve 8 people. How many eggs are required to serve 20 people?
OCR
A drink mixture uses 2 litres of water and 500ml of syrup for 10 servings. Find the quantities needed for 25 servings.
OCR
A recipe for 12 cookies requires 300g of chocolate. How much chocolate is needed for 30 cookies?
Exam Checklist
Step 1
Find the old number of servings and the new number of servings.
Step 2
Work out the scale factor.
Step 3
Multiply every ingredient by the same factor.
Step 4
Check whether the answer makes sense for a bigger or smaller recipe.
Most common exam mistakes
Factor mistake
Using the wrong fraction for the scale factor.
Operation mistake
Adding instead of multiplying.
Incomplete answer
Changing one ingredient but forgetting the others.
Direction mistake
Making values bigger when the recipe should be smaller, or vice versa.
Common Mistakes
These are common mistakes students make when scaling recipes in GCSE Maths.
Using the wrong scale factor
Incorrect
A student chooses an incorrect multiplier for the new quantity.
Correct
Find the scale factor by comparing the new amount to the original. For example, doubling a recipe uses a scale factor of 2.
Changing only one ingredient
Incorrect
A student adjusts one value but leaves others unchanged.
Correct
All ingredients must be scaled by the same factor to keep the proportions correct.
Adding instead of multiplying
Incorrect
A student adds a fixed amount instead of scaling proportionally.
Correct
Scaling uses multiplication, not addition. Multiply each quantity by the scale factor.
Confusing scaling up and scaling down
Incorrect
A student uses a number greater than 1 when reducing a recipe.
Correct
Scaling up uses a factor greater than 1, while scaling down uses a factor between 0 and 1.
Handling fractions incorrectly
Incorrect
A student makes errors when working with fractional quantities.
Correct
Simplify fractions carefully and convert between mixed numbers and improper fractions when needed.
Try It Yourself
Practise scaling recipes using proportional reasoning.
Foundation
Foundation Practice
Scale recipes up and down using simple multiplication and division.
A recipe uses 300 ml of milk for 3 people. How much milk is needed for 6 people?
Double the number of people.
6 is double 3 → 300 × 2 = 600 ml.
A recipe uses 500 g of sugar for 10 cakes. How much is needed for 5 cakes?
Half the recipe.
5 is half of 10 → 500 ÷ 2 = 250 g.
A recipe uses 4 eggs for 8 people. How many eggs are needed for 4 people?
Half the number of people.
4 is half of 8 → 4 ÷ 2 = 2 eggs.
A recipe for 2 people uses 100 g of butter. How much is needed for 6 people?
Multiply by 3.
6 ÷ 2 = 3 → 100 × 3 = 300 g.
A recipe for 5 people uses 250 g of flour. How much is needed for 10 people?
Double the recipe.
10 is double 5 → 250 × 2 = 500 g.
A student doubles the number of people but forgets to change the ingredients. What is wrong?
Scaling must match.
If people double, ingredients must also double.
A recipe uses 600 ml of water for 12 people. How much is needed for 6 people?
Half the number of people.
6 is half of 12 → 600 ÷ 2 = 300 ml.
A recipe for 4 people uses 80 g of sugar. How much is needed for 1 person?
Divide by 4.
80 ÷ 4 = 20 g per person.
A recipe uses 3 eggs for 6 people. How many eggs are needed for 12 people?
Double the recipe.
12 is double 6 → 3 × 2 = 6 eggs.
Higher
Higher Practice
Solve multi-step scaling problems including fractions and non-integer scaling.
A recipe for 6 people uses 300 g of flour. How much is needed for 9 people?
Find scale factor.
9 ÷ 6 = 1.5 → 300 × 1.5 = 450 g.
A recipe for 4 people uses 200 ml of milk. How much is needed for 7 people?
Find per person first.
200 ÷ 4 = 50 per person → 50 × 7 = 350 ml.
A recipe uses 500 g of flour for 10 people. You only have 300 g. For how many people can you make the recipe?
Find fraction of recipe.
300/500 = 0.6 → 10 × 0.6 = 6 people.
A recipe for 8 people uses 4 eggs. How many eggs are needed for 14 people?
Find eggs per person.
4 ÷ 8 = 0.5 per person → 0.5 × 14 = 7 eggs.
A recipe for 5 people uses 250 g of sugar. How much is needed for 3 people?
Find per person.
250 ÷ 5 = 50 per person → 50 × 3 = 150 g.
A recipe for 12 people uses 600 ml of milk. How much is needed for 5 people?
Find per person first.
600 ÷ 12 = 50 → 50 × 5 = 250 ml.
A student multiplies all ingredients by 2 when increasing from 4 people to 6 people. What is wrong?
Check the ratio 6 : 4.
Scale factor = 6 ÷ 4 = 1.5, not 2.
A recipe for 3 people uses 180 g of flour. How much is needed for 10 people?
Find per person.
180 ÷ 3 = 60 → 60 × 10 = 600 g.
A recipe for 4 people uses 2 eggs. Which expression gives eggs needed for n people?
Find eggs per person.
2 ÷ 4 = 0.5 per person → n/2 eggs.
A recipe for 6 people uses 300 g of sugar. How much is needed for 2 people?
Find per person.
300 ÷ 6 = 50 → 50 × 2 = 100 g.
Games
Practise this topic with interactive games.
Games coming soon.