Scale recipes and quantities up or down using the unitary method or a scale factor. It is on Foundation and Higher, aimed at grade 3. Free questions with answers are on this page. Worked examples show each line before you try the questions.
Recipes, maps and similar 'this much for that many' questions are unitary method: find one, then find many. If 8 pancakes need 300 ml of milk, one pancake needs 37.5 ml, so 12 pancakes need 450 ml. You can also scale by a multiplier (12÷8=1.5, so ×1.5 everything).
When two ingredients are tied together, keep them in step. If you only have 200 ml of milk, the limiting ingredient sets the scale — other amounts come down with it. Round down if you cannot make a fraction of a pancake (unless the question is just about the ingredient).
The unitary method (find one, then scale) and the scale-factor method (how many times bigger) are the same idea. For a recipe that does not scale to a whole number of eggs, you still scale the other ingredients — do not round until the question says so.
Objectives
Find the amount for one, then multiply.
The ratio stays the same when both quantities scale.
Scale every ingredient by the same multiplier.
Key points
Find the amount for one person or one item, then multiply (unitary method).
Find a scale factor by dividing the new number by the old number.
Scale every ingredient by the same factor.
Work out the largest amount you can make from limited ingredients.
Worked examples
Example 1
4 cakes need 200 g of flour. How many grams does 1 cake need?
2 marks
One cake needs 200 ÷ 4 = 50 g.
1 cake needs 1 × 50 = 50 g.
The flour needed is 50 g.
Answer: 50 g
Common slips
Slip: One cake needs 200 × 4 = 800 g. To find one cake, divide the flour by the number of cakes.
Slip: 1 cake needs 1 + 50 = 51 g. Multiply the flour for one cake by the number of cakes. Adding mixes up cakes and grams.
Slip: The flour needed is 200 g. That is the flour for 4 cakes, not for 1.
Example 2
4 cakes need 200 g of flour. How many grams do 2 cakes need?
2 marks
One cake needs 200 ÷ 4 = 50 g.
2 cakes need 2 × 50 = 100 g.
The flour needed is 100 g.
Answer: 100 g
Common slips
Slip: One cake needs 200 × 4 = 800 g. To find one cake, divide the flour by the number of cakes.
Slip: 2 cakes need 2 + 50 = 52 g. Multiply the flour for one cake by the number of cakes. Adding mixes up cakes and grams.
Slip: The flour needed is 200 g. That is the flour for 4 cakes, not for 2.
Example 3
4 cakes need 200 g of flour. How many grams do 3 cakes need?
3 marks
One cake needs 200 ÷ 4 = 50 g.
3 cakes need 3 × 50 = 150 g.
The flour needed is 150 g.
Answer: 150 g
Common slips
Slip: One cake needs 200 × 4 = 800 g. To find one cake, divide the flour by the number of cakes.
Slip: 3 cakes need 3 + 50 = 53 g. Multiply the flour for one cake by the number of cakes. Adding mixes up cakes and grams.
Slip: The flour needed is 200 g. That is the flour for 4 cakes, not for 3.
Questions and answers
GCSE Maths proportion questions and answers. Try each one, then open the answer. Easy questions come first.
Question 1 Easy2 marks
2 cakes need 100 g of flour. How many grams do 6 cakes need?
Show answer
Answer: 300
The number of cakes is multiplied by 3.
Multiply the flour by the same scale factor.
M1 — The number of cakes is multiplied by 3.
A1 — Answer 300
Question 2 Easy2 marks
4 cakes need 200 g of flour. How many grams does one cake need?
Show answer
Answer: 50
Divide by the number of cakes.
That is the amount for one cake.
M1 — Divide by the number of cakes.
A1 — Answer 50
Question 3 Medium2 marks
2 kg of rice cost £6. What price do 5 kg cost?
Show answer
Answer: 15
Find the price of 1 kg.
Multiply that price by 5.
M1 — Find the price of 1 kg.
A1 — Answer 15
Question 4 Medium2 marks
4 portions use 200 g. How many grams do 6 portions use?
Show answer
Answer: 300
Find the amount for one portion.
Multiply that by 6.
M1 — Find the amount for one portion.
A1 — Answer 300
Question 5 Hard2 marks
You have 500 g of flour and 180 g of sugar. One cake needs 100 g of flour and 60 g of sugar. How many cakes can you make?
Show answer
Answer: 3
Flour is enough for one number of cakes and sugar for another.
You can make only as many as the smaller of those two numbers.
M1 — Flour is enough for one number of cakes and sugar for another.
A1 — Answer 3
Question 6 Hard2 marks
Pack A is 400 g for £4 and pack B is 900 g for £6. Which pack is the better value? Answer A or B.
Show answer
Answer: B
Compare the price of the same mass.
The lower price per gram is the better value.
M1 — Compare the price of the same mass.
A1 — Answer B
Question 7 Exam-style3 marks
You have 600 g of flour and 240 g of sugar. One cake needs 100 g of flour and 60 g of sugar. How many cakes can you make?
Show answer
Answer: 4
Flour is enough for one number of cakes and sugar for another.
You can make only as many as the smaller of those two numbers.
M1 — Flour is enough for one number of cakes and sugar for another.
M1 — You can make only as many as the smaller of those two numbers.
A1 — Answer 4
Common mistakes
Most lost marks on this topic are one slip.
Adding the extra cakes onto the flour in grams.
Scale by multiplying, not by adding the difference of the counts.
Finding one unit and forgetting to multiply by the new number.
The unit is a step, not the final answer, unless you were asked for one.
Scaling only one ingredient.
Every ingredient uses the same multiplier.
Spot the slip
If 2 cakes need 100 g of flour, 1 cake needs
50 g
200 g
100 g
Show the slip
50 g One cake is half of two cakes.
Exam tips
This topic can appear on a calculator or a non-calculator paper. Show enough working for a method mark.
If the question says “show that”, the result is given. The marks are for the steps that reach it.
The method is the same on AQA-style and Edexcel-style papers.
Write the scale factor or 'for 1 person' amount clearly — that line is the method mark.
In limited-ingredient questions, show a calculation for every ingredient, then state which one limits you.
Printable worksheet
The same questions are in a PDF you can print. Answers start on a later page.