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

Simplifying Fractions

Mathematics · Fractions · ages 10-11
Name ______________________   Date ____________

  1. What number should you divide the numerator and denominator by to simplify a fraction?

    • Their HCF (highest common factor)
    • Any two numbers
    • Their difference

  2. Which of these fractions is already in its simplest form?

    • 8/12
    • 5/8
    • 9/15
    • 14/21

  3. Which fraction is equal to 3/5 but has a denominator of 15?

    • 6/15
    • 10/15
    • 5/15
    • 9/15

  4. Which fraction is the simplified form of 8/12?

    • 4/6
    • 2/3
    • 1/2

  5. Jay wants to add 2/3 and 5/8. What common denominator should he use?

    • 11
    • 16
    • 24

  6. The smallest common denominator for 3/5 and 2/7 is 35.

    Circle one:   True   False

  7. Rewrite 2/5 and 3/8 so they share a common denominator. Which pair is correct?

    • 16/40 and 15/40
    • 10/40 and 15/40
    • 16/40 and 12/40
    • 8/40 and 15/40

  8. Simplify 27/45 to its simplest form.

    • 9/15
    • 2/3
    • 3/5
    • 5/9

  9. Mia simplified 10/15 by dividing only the denominator by 5, getting 10/3. What mistake did she make?

    • She did not divide the numerator by 5 too
    • She used the wrong HCF
    • 10/3 is not allowed as a fraction

  10. The HCF of 14 and 21 is 7. Divide both numbers by 7 to simplify 14/21, then add the new numerator and new denominator together. What is the sum?

    Answer: ______________

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Answer key

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

Simplifying Fractions W1-mt_b7T-CjOYUR-s1

  1. Their HCF (highest common factor) · The HCF is the biggest number that divides evenly into both parts, so dividing by it gets you to simplest form in one step.
  2. 5/8 · 5 and 8 share no common factor except 1, so 5/8 cannot be simplified. The others all simplify.
  3. 9/15 · 15 is 5 times 3, so multiply the top by 3 too: 3 x 3 = 9, giving 9/15.
  4. 2/3 · 8 and 12 share a common factor of 4. Dividing both by 4 gives 2/3, which is already in simplest form.
  5. 24 · 24 is a multiple of both 3 and 8, so it works as a common denominator for 2/3 and 5/8.
  6. True · The multiples of 5 and 7 first meet at 35.
  7. 16/40 and 15/40 · Both denominators 5 and 8 divide into 40, giving 16/40 and 15/40.
  8. 3/5 · The HCF of 27 and 45 is 9, so 27/45 = 3/5.
  9. She did not divide the numerator by 5 too · Dividing only one part of a fraction changes its value. Both numbers need to be divided by 5 to get the correct answer, 2/3.
  10. 5 · Dividing 14 and 21 by their HCF, 7, gives 2 and 3. Adding those together makes 5.
Worksheet · LightMySky