Scaling recipes and mixtures | Year 7

01 / LEARN

The idea, step by step

Ingredients are linked amounts

For a recipe serving four people, double every ingredient to serve eight people. Doubling the flour but leaving the liquid unchanged makes a different mixture. Find the scale factor by dividing the servings wanted by the original servings. Apply it consistently, including to quantities that use different units.

Scaling down and checking practicality

Half as many servings requires half of every ingredient. Sometimes this creates awkward amounts, such as half an egg, so practical choices need thought. Ingredient scaling alone does not show how long to cook: tin shape, depth and the oven can affect time. State which quantities your proportional model actually links.

A common trap

Treating the water entry in $1 : 4$ as the whole drink.

Instead: The ratio compares concentrate with water. One litre concentrate plus four litres water makes five litres of drink.

02 / WORKED EXAMPLES

See the thinking

Example 1

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.

The factor is $6 / 4 = 1.5$ .
Pasta becomes $300 (1.5) = 450$ g.
Sauce becomes $200 (1.5) = 300$ mL.

450 g pasta and 300 mL sauce.

Example 2

Make a fixed volume of drink

Concentrate:water is $1 : 4$ . Make 2.5 L of drink.

There are five parts in total.
One part is $2.5 / 5 = 0.5$ L.
Use one part concentrate and four parts water.

0.5 L concentrate and 2 L water.

Check your understanding

A recipe for 3 people needs 180 g rice. Find the rice for 5 people.

Show answer

300 g.

One person needs $180 / 3 = 60$ g; five need $5 (60) = 300$ g.

03 / WORKSHEET

Your turn

6 questions · 15 marks · Work at your own pace.

Worksheet PDF Worked solutions

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 $2 : 3$ . 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 $1 : 5$ . 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 $2 : 3$ . 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 $8 / 5$ .
$250 (8 / 5) = 400$ ; $150 (8 / 5) = 240$ .
400 g rice and 240 g peas.
Concentrate:water is $1 : 5$ . How much concentrate is in 1.8 L of drink?
3 marks
Six parts make 1.8 L.
Concentrate is one part: $1.8 / 6 = 0.3$ 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.

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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 ↗

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