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Dividing fractions

Divide fractions by multiplying by the reciprocal.

Practice + answer key · 2 pages

Worksheet settings12 questions · 2 columns · A4
Denominator range

Both denominators fall within this range. Each numerator is at least 1 and smaller than its denominator.

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Dividing fractionsDividing fractions. Practice. Calculate and simplify: 1/5 ÷ 7/9. Calculate and simplify: 2/3 ÷ 2/5. Calculate and simplify: 2/4 ÷ 5/7. Calculate and simplify: 1/8 ÷ 3/8. Calculate and simplify: 1/3 ÷ 3/9. Calculate and simplify: 2/3 ÷ 1/8. Calculate and simplify: 3/7 ÷ 5/10. Calculate and simplify: 5/9 ÷ 1/3. Calculate and simplify: 2/5 ÷ 1/4. Calculate and simplify: 2/3 ÷ 3/5. Calculate and simplify: 3/10 ÷ 8/10. Calculate and simplify: 6/7 ÷ 5/9.Name __________________________Date _______________Dividing fractionsDivide each pair and write the answer in simplest form.Worked exampleCalculate 2/3 ÷ 4/5. → 5/6Replace division by multiplication by 5/4.1.Calculate and simplify: 1/5 ÷7/9.2.Calculate and simplify: 2/3 ÷2/5.3.Calculate and simplify: 2/4 ÷5/7.4.Calculate and simplify: 1/8 ÷3/8.5.Calculate and simplify: 1/3 ÷3/9.6.Calculate and simplify: 2/3 ÷1/8.7.Calculate and simplify: 3/7 ÷5/10.8.Calculate and simplify: 5/9 ÷1/3.9.Calculate and simplify: 2/5 ÷1/4.10.Calculate and simplify: 2/3 ÷3/5.11.Calculate and simplify: 3/10 ÷8/10.12.Calculate and simplify: 6/7 ÷5/9.MathSprig · mathsprig.site · support@mathsprig.sitePage 1 of 1mathsprig-1 · mathsprig-v1 · 0f655d17
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Practice + answer key · 2 pages

Fractions

What you’ll practice

Calculate exact quotients of nonzero fractions and simplify the result.

Keep the first fraction as it is. Turn the second fraction upside down, multiply, then simplify. The result may be greater than one even when both starting fractions are smaller than one.

How this skill works

To divide by a nonzero fraction, multiply by its reciprocal. Only the second fraction, the divisor, is inverted.

A quotient may be greater than one even when both input fractions are proper. Keep an improper fraction when that is the simplified exact result.

Worked example

Calculate 2/3 ÷ 4/5.
  1. Replace division by multiplication by 5/4.
  2. 2/3 × 5/4 = 10/12.
  3. Divide numerator and denominator by 2 to get 5/6.

Answer: 5/6

Teaching notes

  • Identify the divisor before taking a reciprocal.
  • Multiply the answer by the divisor to check the original dividend.
Practice questions
  1. Calculate and simplify: 1/5 ÷ 7/9.
  2. Calculate and simplify: 2/3 ÷ 2/5.
  3. Calculate and simplify: 2/4 ÷ 5/7.
  4. Calculate and simplify: 1/8 ÷ 3/8.
  5. Calculate and simplify: 1/3 ÷ 3/9.
  6. Calculate and simplify: 2/3 ÷ 1/8.
  7. Calculate and simplify: 3/7 ÷ 5/10.
  8. Calculate and simplify: 5/9 ÷ 1/3.
  9. Calculate and simplify: 2/5 ÷ 1/4.
  10. Calculate and simplify: 2/3 ÷ 3/5.
  11. Calculate and simplify: 3/10 ÷ 8/10.
  12. Calculate and simplify: 6/7 ÷ 5/9.
Answers and steps
  1. 9/35
    1. Multiply by the reciprocal of the second fraction: 1/5 × 9/7 = 9/35.
    2. The greatest common factor of 9 and 35 is 1. Divide both by 1: 9/35 = 9/35.
  2. 5/3
    1. Multiply by the reciprocal of the second fraction: 2/3 × 5/2 = 10/6.
    2. The greatest common factor of 10 and 6 is 2. Divide both by 2: 10/6 = 5/3.
  3. 7/10
    1. Multiply by the reciprocal of the second fraction: 2/4 × 7/5 = 14/20.
    2. The greatest common factor of 14 and 20 is 2. Divide both by 2: 14/20 = 7/10.
  4. 1/3
    1. Multiply by the reciprocal of the second fraction: 1/8 × 8/3 = 8/24.
    2. The greatest common factor of 8 and 24 is 8. Divide both by 8: 8/24 = 1/3.
  5. 1
    1. Multiply by the reciprocal of the second fraction: 1/3 × 9/3 = 9/9.
    2. The greatest common factor of 9 and 9 is 9. Divide both by 9: 9/9 = 1.
  6. 16/3
    1. Multiply by the reciprocal of the second fraction: 2/3 × 8/1 = 16/3.
    2. The greatest common factor of 16 and 3 is 1. Divide both by 1: 16/3 = 16/3.
  7. 6/7
    1. Multiply by the reciprocal of the second fraction: 3/7 × 10/5 = 30/35.
    2. The greatest common factor of 30 and 35 is 5. Divide both by 5: 30/35 = 6/7.
  8. 5/3
    1. Multiply by the reciprocal of the second fraction: 5/9 × 3/1 = 15/9.
    2. The greatest common factor of 15 and 9 is 3. Divide both by 3: 15/9 = 5/3.
  9. 8/5
    1. Multiply by the reciprocal of the second fraction: 2/5 × 4/1 = 8/5.
    2. The greatest common factor of 8 and 5 is 1. Divide both by 1: 8/5 = 8/5.
  10. 10/9
    1. Multiply by the reciprocal of the second fraction: 2/3 × 5/3 = 10/9.
    2. The greatest common factor of 10 and 9 is 1. Divide both by 1: 10/9 = 10/9.
  11. 3/8
    1. Multiply by the reciprocal of the second fraction: 3/10 × 10/8 = 30/80.
    2. The greatest common factor of 30 and 80 is 10. Divide both by 10: 30/80 = 3/8.
  12. 54/35
    1. Multiply by the reciprocal of the second fraction: 6/7 × 9/5 = 54/35.
    2. The greatest common factor of 54 and 35 is 1. Divide both by 1: 54/35 = 54/35.