Scaling a recipe
Scaling a recipe means adjusting every ingredient by the same scale factor, so the finished dish keeps the same taste and texture while serving a different number of people.
The scale factor is always found the same way:
Scale factornew servings ÷ original servings
Scaling a recipe up
Worked Example 1
A recipe for 4 people uses 200g flour, 100g sugar, and 2 eggs. Scale the recipe to serve 10 people.
1
Find the scale factor: 10 ÷ 4 = 2.5
2
Multiply every ingredient by 2.5: flour = 200 × 2.5 = 500g, sugar = 100 × 2.5 = 250g, eggs = 2 × 2.5 = 5
Answer500g flour, 250g sugar, 5 eggs
Each ingredient in the scaled-up card is exactly 2.5 times the original — the scale factor never changes between ingredients.
Scaling a recipe down
Worked Example 2
A recipe for 8 people uses 320g rice. Scale the recipe down to serve 5 people.
1
Find the scale factor: 5 ÷ 8 = 0.625
2
Multiply the rice by the scale factor: 320 × 0.625 = 200
Answer200g rice
Finding the scale factor from a known ingredient
Worked Example 3
A recipe for 6 people uses 120g butter. A caterer has 300g butter and wants to use all of it, following the same ratio. How many people can be served?
1
Find the scale factor from the known ingredient: 300 ÷ 120 = 2.5
2
Multiply the original number of people by the scale factor: 6 × 2.5 = 15
Answer15 people
Rounding whole-item ingredients
Some ingredients — eggs, chicken breasts, whole lemons — can't be split into fractions. When scaling gives a decimal answer for one of these, you must round up to the next whole number, since rounding down would leave you without enough ingredient.
Practice questions
Work through each question before checking the answers.
Foundation (Grade 3–5)
Q1A recipe for 4 people uses 200g pasta. Scale it up to serve 8 people.Foundation
Q2A recipe for 6 people uses 3 eggs. How many eggs are needed for 12 people?Foundation
Q3A recipe for 10 people uses 500ml stock. Scale it down to serve 5 people.Foundation
Q4A cake recipe for 8 people uses 240g sugar. How much sugar is needed for 4 people?Foundation
Q5A recipe for 5 people uses 150g rice. Find the amount of rice needed for 15 people.Foundation
Higher (Grade 5–7)
Q6A recipe for 4 people uses 220g flour. Scale the recipe to serve 6 people.Higher
Q7A recipe for 12 people uses 480g chocolate. Scale it down to serve 9 people.Higher
Q8A soup recipe for 5 people uses 750ml stock. How much stock is needed to serve 8 people?Higher
Q9A recipe for 6 people uses 75g butter. A chef has 150g butter and wants to use all of it, following the same ratio. How many people can be served?Higher
Q10A recipe for 8 people uses 2.4kg potatoes. Scale it to serve 5 people.Higher
Higher — Hard (Grade 8–9)
Q11A recipe for 4 people uses 180g flour and 90g sugar. A scaled version uses 315g sugar. Find the number of people it serves, and the amount of flour needed.Grade 8–9
Q12A recipe for 5 people requires 275g rice. Find the amount of rice required to serve 22 people, in kilograms.Grade 8–9
Q13A pancake recipe uses 2 eggs for 4 people. Find the minimum number of whole eggs needed to serve 7 people, explaining why you must round up rather than down.Grade 8–9
Q14A recipe for 6 people uses 200g flour, 300ml milk, and 2 eggs. Scale the recipe to serve 9 people, finding all three quantities.Grade 8–9
Q15A recipe for 4 people costs £6.00 in ingredients. Assuming the cost is directly proportional to the number of servings, find the cost of making the recipe for 18 people.Grade 8–9
Answers
Foundation (Q1–Q5)
Q1400g
Q26 eggs
Q3250ml
Q4120g
Q5450g
Higher (Q6–Q10)
Q6330g(scale factor 1.5, 220 × 1.5)
Q7360g(scale factor 0.75, 480 × 0.75)
Q81200ml(scale factor 1.6, 750 × 1.6)
Q912 people(scale factor 2, 6 × 2)
Q101.5kg(scale factor 0.625, 2.4 × 0.625)
Higher — Hard (Q11–Q15)
Q1114 people, 630g flour(scale factor 315 ÷ 90 = 3.5, people = 4 × 3.5, flour = 180 × 3.5)
Q121.21kg(scale factor 4.4, 275 × 4.4 = 1210g)
Q134 eggs(scale factor 1.75, 2 × 1.75 = 3.5, rounded up to 4 since 3 eggs would be too few)
Q14300g flour, 450ml milk, 3 eggs(scale factor 1.5)
Q15£27.00(scale factor 4.5, £6.00 × 4.5)
Common mistakes
Common Mistake 1
Adding instead of multiplying
Scaling a recipe up by "6 more people" does not mean adding a fixed amount to each ingredient — every ingredient must be multiplied by the same scale factor.
Common Mistake 2
Only scaling some of the ingredients
Every single ingredient in the recipe must be scaled by the same factor — forgetting one ingredient (especially a small one like salt or baking powder) throws off the whole recipe.
Common Mistake 3
Rounding whole-item ingredients down
If scaling gives 3.5 eggs, rounding down to 3 leaves the recipe short — always round whole, indivisible items up to the next whole number.
Common Mistake 4
Finding the scale factor the wrong way round
The scale factor is always new servings ÷ original servings — dividing the other way round gives the reciprocal and scales the recipe in the wrong direction.
Exam tips
💡 Exam Tip 1
Always find the scale factor first
Write "scale factor = new servings ÷ original servings" as a clear first line of working — this secures method marks even if a later multiplication slips.
💡 Exam Tip 2
Apply the same factor to every ingredient
List every ingredient and multiply each one by the scale factor in turn — don't skip any, even ones that seem too small to matter.
💡 Exam Tip 3
Explain your rounding for whole items
When a question asks about eggs, fruit, or other whole items, state clearly that you're rounding up and briefly explain why — this is often worth a method mark on its own.
💡 Exam Tip 4
Double-check by working backwards
After scaling, divide your new ingredient amount by the scale factor — it should give back the original amount. This is a fast way to catch arithmetic errors.
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