Scaling by fractions and simple rates · seed 1 · A4, ink-friendly. The answer key prints on its own page for grown-ups.

Scaling with fractions and rates

Mathematics · Multiplication & Division · ages 9-10
Name ______________________   Date ____________

  1. A shop sells 3 kg of oranges for 12 pounds. At the same rate, what does 5 kg cost in pounds?

    Answer: ______________

  2. A recipe for 4 people needs 200 g of flour. How many grams of flour are needed for 6 people?

    Answer: ______________

  3. A recipe for 4 people needs 200 g of flour. How much flour is needed for 8 people?

    • 208 g
    • 400 g
    • 100 g

  4. 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

  5. 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

  6. A rectangle is 8 cm long and 6 cm wide. Both sides are scaled by a factor of 1/2. What are the new dimensions?

    • 4 cm by 3 cm
    • 6 cm by 4 cm
    • 4 cm by 6 cm
    • 16 cm by 12 cm

  7. A recipe for 4 people needs 600 ml of stock. How much stock is needed for 6 people?

    • 900 ml
    • 800 ml
    • 1200 ml
    • 750 ml

  8. A recipe for 4 people needs 200 g of flour. How much flour is needed for 6 people?

    • 250 g
    • 300 g
    • 350 g

  9. 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 should have subtracted instead
    • He forgot to double the sugar too
    • He added instead of using the ratio between people and flour

  10. Paint costs £15 for 3 litres. Using the same idea as the flour and cheese, how many pounds for 5 litres?

    Answer: ______________

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Answer key

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

Scaling with fractions and rates W1-mt_ZOJ6EbdPOb-s1

  1. 20 · One kilogram costs 12 divided by 3, which is 4 pounds, and 5 kg costs 5 times 4 pounds, which is 20 pounds.
  2. 300 · Each person needs 200 divided by 4, which is 50 g, and 6 people need 6 times 50 g, which is 300 g.
  3. 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.
  4. 6 cm · Scaling by 1/2 means multiplying by 1/2, so 12 cm becomes 6 cm.
  5. 4 cm · Every side is multiplied by 1/2, so 8 cm becomes 4 cm.
  6. 4 cm by 3 cm · Half of 8 cm is 4 cm and half of 6 cm is 3 cm, so the scaled rectangle is 4 cm by 3 cm.
  7. 900 ml · One person needs 600 divided by 4, which is 150 ml, and 6 people need 6 times 150 ml, which is 900 ml.
  8. 300 g · 4 people need 200 g, so 1 person needs 50 g. 6 people need 6 times 50 g, which is 300 g.
  9. 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.
  10. 25 · £15 divided by 3 litres is £5 per litre. £5 times 5 litres is £25.
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