Ratio Notation · seed 1 · A4, ink-friendly. The answer key prints on its own page for grown-ups.

Ratio Notation: Comparing Two Amounts

Mathematics · Ratio & Proportion · ages 11-12
Name ______________________   Date ____________

  1. Share £30 in the ratio 4:1. How many pounds is the smaller share?

    Answer: ______________

  2. Write the ratio 14:21 in its simplest form.

    • 2:3
    • 7:3
    • 3:2
    • 1:2

  3. A 4:3 split means shares of 4/7 and 3/7 of the whole. True or false?

    Circle one:   True   False

  4. In the ratio 3:2, how many equal parts are there in total?

    • 3
    • 5
    • 2

  5. Simplify the ratio 2/3:1/6.

    • 4:1
    • 2:1
    • 1:4
    • 1:2

  6. Write the ratio 1.5:3 in simplest form.

    • 3:6
    • 1:2
    • 15:3

  7. Write the ratio 0.6:1.8 in its simplest whole-number form.

    • 6:18
    • 2:6
    • 1:3
    • 3:9

  8. A classroom has 18 boys and 12 girls. Write the ratio of boys to girls in simplest form.

    Boys18Girls12
    • 3:2
    • 18:12
    • 2:3

  9. A student simplifies the ratio 20:15 by dividing only the first number by 5, getting 4:15. What is wrong with this?

    • 20:15 cannot be simplified any further
    • 4:15 is already the simplest form
    • Both numbers must be divided by the same factor, giving 4:3

  10. A trail mix recipe combines nuts and raisins in the ratio 3:2. If you make 20 cups of trail mix in total, how many cups are nuts?

    Nuts3Raisins2

    Answer: ______________

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Answer key

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

Ratio Notation: Comparing Two Amounts W1-mt_XWSGuFW7It-s1

  1. 6 · 4 + 1 = 5 parts of £6 each: the small share is 1 x 6 = £6.
  2. 2:3 · Divide both sides by 7: 14:21 = 2:3.
  3. True · 4 parts and 3 parts make 7, so the shares are 4/7 and 3/7.
  4. 5 · Add the two numbers in the ratio: 3 + 2 = 5 total parts.
  5. 4:1 · Multiply by 6 to clear fractions (4:1), already simplest.
  6. 1:2 · Multiply both numbers by 2 to clear the decimal: 1.5 times 2 is 3, and 3 times 2 is 6. Then divide by 3 to simplify 3:6 down to 1:2.
  7. 1:3 · Multiply by 10 to clear decimals (6:18), then divide by 6: 1:3.
  8. 3:2 · Divide both numbers by their greatest common factor, 6: 18 divided by 6 is 3, and 12 divided by 6 is 2, giving 3:2.
  9. Both numbers must be divided by the same factor, giving 4:3 · To simplify a ratio, divide every number in it by the same common factor. Dividing just one side changes the relationship between the amounts.
  10. 12 · The ratio has 3 + 2 = 5 total parts. Each part is 20 divided by 5, which is 4 cups, and nuts make up 3 parts, so 3 times 4 is 12 cups.
Worksheet · LightMySky