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

Using inverse operations

Mathematics · Multiplication & Division · ages 11-12
Name ______________________   Date ____________

  1. Multiplication and division are inverse operations. If 6 × 9 = 54, which calculation checks the answer?

    • 54 ÷ 54
    • 54 ÷ 9
    • 9 ÷ 54

  2. Tom thinks x = 7 solves 6x = 42. Which calculation checks this using the inverse operation?

    • 42 x 6 = 7
    • 7 / 6 = 42
    • 42 / 6 = 7
    • 6 / 42 = 7

  3. Work out 23 - 9.

    Answer: ______________

  4. Addition and subtraction are inverse operations. If 23 + 14 = 37, which calculation checks the answer?

    • 37 - 14
    • 37 + 14
    • 14 - 23

  5. What is the square root of 81?

    • 8
    • 7
    • 6
    • 9

  6. Which pair of operations undo each other?

    • Squaring and square-rooting
    • Squaring and doubling
    • Square-rooting and halving
    • Cubing and square-rooting

  7. Work out 96 / 6.

    Answer: ______________

  8. Tom finds that 9² = 81. Which calculation is the correct inverse check?

    • 81 - 9
    • √81
    • 9 × 9

  9. Leo checks '96 ÷ 8 = 12' by working out 12 - 8. What is his mistake?

    • He used the right inverse but picked the wrong numbers
    • There is no mistake
    • He used subtraction instead of multiplication, the true inverse of division

  10. A square has area 144 square centimetres. What is the length of one side in centimetres?

    Answer: ______________

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Answer key

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

Using inverse operations W1-mt_VUQNveSYjQ-s1

  1. 54 ÷ 9 · Dividing 54 by 9 undoes the multiplication and returns 6.
  2. 42 / 6 = 7 · Division undoes multiplication, and 42 / 6 = 7, which matches Tom's value.
  3. 14 · 23 - 9 = 14, and the inverse check 14 + 9 = 23 confirms it.
  4. 37 - 14 · Subtracting 14 back from 37 undoes the addition and returns 23.
  5. 9 · 9 x 9 = 81, so the square root of 81 is 9.
  6. Squaring and square-rooting · Squaring 9 gives 81, and √81 returns 9, so the operations undo each other.
  7. 16 · 96 / 6 = 16, and the inverse check 16 x 6 = 96 confirms it.
  8. √81 · Squaring's inverse is square-rooting, so √81 checks that 9² = 81, giving back 9.
  9. He used subtraction instead of multiplication, the true inverse of division · Division's inverse is multiplication, so Leo should work out 12 × 8, not 12 - 8.
  10. 12 · The side length is the square root of 144, and 12 x 12 = 144.
Worksheet · LightMySky