Scaling Recipes & Ratios — Proportions (Grades 5–6)
Scaling keeps a ratio the same while making everything bigger (or smaller) by the same factor — like doubling a recipe.
Understanding scaling recipes & ratios — proportions
The trick is to find the scale factor first, then multiply every ingredient by it. If a recipe serves 4 people and you need it for 12, the scale factor is 12 ÷ 4 = 3, so every ingredient gets multiplied by 3.
Key Idea
The reason this works: a ratio only stays the same if both sides grow by the same factor. Multiply one ingredient by 3 and the rest by something else, and the recipe is ruined. "Same factor on every part" is the whole idea of a proportion.
Seeing it in action
Worked example
A recipe for 4 people uses 3 eggs. How many eggs for 12 people?
Scale factor: 12 ÷ 4 = 3.
Eggs: 3 × 3 = 9 eggs.
4 to 12 is ×3, so every ingredient is ×3.
Worked example 2
A 2:5 mix is scaled so the "2" becomes 6. What does the "5" become?
Scale factor: 6 ÷ 2 = 3. So 5 × 3 = 15. The mix is now 6:15 (same ratio as 2:5).
A common mistake, and the fix
Adding to both parts instead of multiplying them.
A recipe with 2 cups of flour to 3 cups of milk, scaled by adding 2 to each, becomes 4 : 5, a different mix; doubling gives 4 : 6, the same ratio. Scale every part by the same factor.
Try a few
A recipe for 2 makes 8 cookies. How many for 6?
factor 3.
Scale 3:4 so the 3 becomes 12.
factor 4.
A factor of 2.5 turns 4 cups into how many?
Try it in Numeris.
A short lesson, then practice with feedback on every answer.
Put the reasoning on paper.
Try six fraction, angle, perimeter and area questions with explained answers, for grades 4–6.
Free printable · 3 pagesText version (screen-reader friendly): Draw it. Explain it. Math sample
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