Understand the idea.
Ingredients are linked amounts
A recipe links ingredient amounts to a number of servings. Find the scale factor by dividing the required servings by the original servings, then multiply every ingredient by that factor. This keeps the mixture's proportions unchanged.
The factor need not be a whole number. Changing from four servings to six uses , meaning one original batch plus half a batch. Keep each ingredient's own unit as its amount is scaled.
Scaling down and checking practicality
Scaling down uses the same reasoning: half as many servings needs half of every ingredient. Check whether the amounts are practical to measure; a proportional answer can be mathematically correct while requiring thought about an indivisible ingredient.
For a mixture, distinguish the ingredient ratio from the total. Concentrate:water contains five parts altogether. Ingredient proportions do not determine cooking time: temperature, container shape and depth may require a separate practical decision.
See the method in action.
Scale up by a fractional factor
A recipe for 4 people uses 300 g pasta and 200 mL sauce. Find the amounts for 6 people.
Worked solution
- 1
Find the serving scale factor.
Six people require one and a half times the four-person recipe.
- 2
Scale the pasta.
The pasta amount is multiplied by the serving factor.
- 3
Scale the sauce.
Using the same factor keeps the sauce-to-pasta proportion unchanged.
450 g pasta and 300 mL sauce.
Make a fixed volume of drink
Concentrate:water is . Make 2.5 L of drink.
Worked solution
- 1
Count the mixture's total parts.
One concentrate part and four water parts together form the drink.
- 2
Find the volume of one part.
The full two-and-a-half litres must be shared among all five parts.
- 3
Calculate each ingredient.
Each ratio entry multiplies the same half-litre part.
- 4
Check the volume and proportion.
The amounts meet both the required total and the stated ingredient ratio.
0.5 L concentrate and 2 L water.
Try it yourself.
Check your understanding
A recipe for 3 people needs 180 g rice. Find the rice for 5 people.
Show answer & reasoning
300 g.
One serving requires grams of rice. Five equal servings therefore require grams, assuming the serving size stays the same.
Keep practising
6 worksheet questions · 15 marks
Read the questions online
- A recipe for 2 people uses 100 g flour. Find the amount for 6 people.2 marks
- Soup for 8 people needs 1.2 L stock. Find the stock for 4 people.2 marks
- Blue:white paint is . How much white goes with 400 mL blue?2 marks
- A recipe for 5 people uses 250 g rice and 150 g peas. Find both amounts for 8 people.3 marks
- Concentrate:water is . How much concentrate is in 1.8 L of drink?3 marks
- A cook doubles every ingredient in a cake. Must the baking time double? Explain.3 marks
Read the worked solutions
Equivalent correct methods earn the corresponding marks. Include units where asked.
- A recipe for 2 people uses 100 g flour. Find the amount for 6 people.2 marks
Six is three times two, so multiply 100 g by 3.
300 g. - Soup for 8 people needs 1.2 L stock. Find the stock for 4 people.2 marks
Four is half of eight; halve 1.2 L.
0.6 L. - Blue:white paint is . How much white goes with 400 mL blue?2 marks
Two parts are 400 mL, so one is 200 mL.
Three parts are 600 mL.
600 mL. - A recipe for 5 people uses 250 g rice and 150 g peas. Find both amounts for 8 people.3 marks
Multiply both amounts by .
; .
400 g rice and 240 g peas. - Concentrate:water is . How much concentrate is in 1.8 L of drink?3 marks
Six parts make 1.8 L.
Concentrate is one part: L.
0.3 L, or 300 mL. - A cook doubles every ingredient in a cake. Must the baking time double? Explain.3 marks
Ingredient amounts can scale with servings.
Baking time also depends on the tin, depth and oven. The same assumption need not hold.
No.
Curriculum reference & lesson scope
Australian Curriculum v9 / SA Curriculum Mathematics
Year 7 ratio comparisons and practical proportional models, including units, part-to-whole meaning and assumptions.
Official curriculum source ↗