Scaling with fractions and rates

Mathematics · Multiplication & Division · ages 9-10

Name ______________________ Date ____________

If 5 kg of grapes costs £15, then 1 kg costs £3.
Circle one: True False
A recipe for 4 people needs 200 g of flour. How much flour is needed for 8 people?
- 208 g
- 400 g
- 100 g
A shape is scaled by a factor of 1/2. A side was 12 cm. What is the new length?
- 24 cm
- 6 cm
- 9 cm
If 4 kg of cheese costs £12, how much does 5 kg cost? Type the amount in pounds.
Answer: ______________
A recipe for 4 people needs 200 g of flour. How much flour is needed for 6 people?
- 250 g
- 300 g
- 350 g
A rectangle is scaled by a factor of 1/2. Its length was 14 cm and its width was 8 cm. What is the new width?
- 4 cm
- 7 cm
- 16 cm
Paint costs £15 for 3 litres. Using the same idea as the flour and cheese, how many pounds for 5 litres?
Answer: ______________
Ben scales a recipe. It needs 200 g of flour for 4 people. He wants to make it for 6 people, so he says '200 g + 6 = 206 g'. What went wrong?
- He added instead of using the ratio between people and flour
- He should have subtracted instead
- He forgot to double the sugar too

Answer key

For grown-ups. Fold this page away before handing over the rest.

True · £15 shared over 5 kg is £3 for each kilogram.
400 g · 8 people is double 4 people, so you need double the flour: 400 g. Adding the extra people straight to the grams, or halving, gives the wrong amount.
6 cm · Scaling by 1/2 means multiplying by 1/2, so 12 cm becomes 6 cm.
15 · £12 divided by 4 kg is £3 per kg. £3 times 5 kg is £15.
300 g · 4 people need 200 g, so 1 person needs 50 g. 6 people need 6 times 50 g, which is 300 g.
4 cm · Every side is multiplied by 1/2, so 8 cm becomes 4 cm.
25 · £15 divided by 3 litres is £5 per litre. £5 times 5 litres is £25.
He added instead of using the ratio between people and flour · Scaling means multiplying by how the amount of people changes, not adding the extra people straight to the grams. 6 people need 300 g.