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Simplifying fractions

Write fractions in simplest form by dividing top and bottom together.

Practice + answer key · 2 pages

Worksheet settings12 questions · 2 columns · A4
Original denominators

Bounds apply before simplification. Only denominators that permit a reducible proper fraction are used.

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Simplifying fractionsSimplifying fractions. Practice. Write 12/15 in simplest form. Write 8/20 in simplest form. Write 3/6 in simplest form. Write 3/21 in simplest form. Write 9/18 in simplest form. Write 9/24 in simplest form. Write 3/9 in simplest form. Write 6/10 in simplest form. Write 9/18 in simplest form. Write 8/24 in simplest form. Write 14/21 in simplest form. Write 4/8 in simplest form.Name __________________________Date _______________Simplifying fractionsWrite every fraction in simplest form.Worked exampleSimplify 18/24. → 3/4The greatest common factor of 18 and 24 is 6.1.Write 12/15 in simplest form.2.Write 8/20 in simplest form.3.Write 3/6 in simplest form.4.Write 3/21 in simplest form.5.Write 9/18 in simplest form.6.Write 9/24 in simplest form.7.Write 3/9 in simplest form.8.Write 6/10 in simplest form.9.Write 9/18 in simplest form.10.Write 8/24 in simplest form.11.Write 14/21 in simplest form.12.Write 4/8 in simplest form.MathSprig · mathsprig.site · support@mathsprig.sitePage 1 of 1mathsprig-1 · mathsprig-v1 · 5df03206
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Practice + answer key · 2 pages

Fractions

What you’ll practice

Use the greatest common factor to express a proper fraction in simplest form.

Look for a factor shared by the numerator and denominator. Divide both by that factor, and keep going until their only common factor is 1.

How this skill works

Divide the numerator and denominator by a shared factor to preserve the value. Dividing by their greatest common factor completes the reduction in one step.

An equivalent answer can still be unfinished. For example, 6/8 = 3/4 is simplest, but reducing 12/16 only to 6/8 leaves another common factor.

Worked example

Simplify 18/24.
  1. The greatest common factor of 18 and 24 is 6.
  2. 18 ÷ 6 = 3 and 24 ÷ 6 = 4.
  3. 3 and 4 share no factor greater than 1, so 3/4 is simplest.

Answer: 3/4

Teaching notes

  • Divide top and bottom by the same number.
  • Check that the final numerator and denominator are relatively prime.
Practice questions
  1. Write 12/15 in simplest form.
  2. Write 8/20 in simplest form.
  3. Write 3/6 in simplest form.
  4. Write 3/21 in simplest form.
  5. Write 9/18 in simplest form.
  6. Write 9/24 in simplest form.
  7. Write 3/9 in simplest form.
  8. Write 6/10 in simplest form.
  9. Write 9/18 in simplest form.
  10. Write 8/24 in simplest form.
  11. Write 14/21 in simplest form.
  12. Write 4/8 in simplest form.
Answers and steps
  1. 4/5
    1. The greatest common factor of 12 and 15 is 3. Divide both by 3: 12/15 = 4/5.
  2. 2/5
    1. The greatest common factor of 8 and 20 is 4. Divide both by 4: 8/20 = 2/5.
  3. 1/2
    1. The greatest common factor of 3 and 6 is 3. Divide both by 3: 3/6 = 1/2.
  4. 1/7
    1. The greatest common factor of 3 and 21 is 3. Divide both by 3: 3/21 = 1/7.
  5. 1/2
    1. The greatest common factor of 9 and 18 is 9. Divide both by 9: 9/18 = 1/2.
  6. 3/8
    1. The greatest common factor of 9 and 24 is 3. Divide both by 3: 9/24 = 3/8.
  7. 1/3
    1. The greatest common factor of 3 and 9 is 3. Divide both by 3: 3/9 = 1/3.
  8. 3/5
    1. The greatest common factor of 6 and 10 is 2. Divide both by 2: 6/10 = 3/5.
  9. 1/2
    1. The greatest common factor of 9 and 18 is 9. Divide both by 9: 9/18 = 1/2.
  10. 1/3
    1. The greatest common factor of 8 and 24 is 8. Divide both by 8: 8/24 = 1/3.
  11. 2/3
    1. The greatest common factor of 14 and 21 is 7. Divide both by 7: 14/21 = 2/3.
  12. 1/2
    1. The greatest common factor of 4 and 8 is 4. Divide both by 4: 4/8 = 1/2.