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Multiplying fractions

Multiply numerators and denominators, then simplify.

Practice + answer key · 2 pages

Worksheet settings12 questions · 2 columns · A4
Denominator range

Each input fraction denominator uses these bounds, with a nonzero proper numerator.

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Multiplying fractionsMultiplying fractions. Practice. Calculate and simplify: 2/6 × 5/6. Calculate and simplify: 2/3 × 4/5. Calculate and simplify: 3/6 × 4/10. Calculate and simplify: 4/5 × 1/2. Calculate and simplify: 1/9 × 2/6. Calculate and simplify: 1/8 × 1/2. Calculate and simplify: 1/3 × 3/7. Calculate and simplify: 1/7 × 4/10. Calculate and simplify: 6/8 × 1/3. Calculate and simplify: 2/9 × 6/8. Calculate and simplify: 7/8 × 2/9. Calculate and simplify: 3/4 × 5/9.Name __________________________Date _______________Multiplying fractionsMultiply each pair and write the answer in simplest form.Worked exampleCalculate 2/3 × 3/4. → 1/2Multiply the numerators: 2 × 3 = 6.1.Calculate and simplify: 2/6 ×5/6.2.Calculate and simplify: 2/3 ×4/5.3.Calculate and simplify: 3/6 ×4/10.4.Calculate and simplify: 4/5 ×1/2.5.Calculate and simplify: 1/9 ×2/6.6.Calculate and simplify: 1/8 ×1/2.7.Calculate and simplify: 1/3 ×3/7.8.Calculate and simplify: 1/7 ×4/10.9.Calculate and simplify: 6/8 ×1/3.10.Calculate and simplify: 2/9 ×6/8.11.Calculate and simplify: 7/8 ×2/9.12.Calculate and simplify: 3/4 ×5/9.MathSprig · mathsprig.site · support@mathsprig.sitePage 1 of 1mathsprig-1 · mathsprig-v1 · 38b2bf5a
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Practice + answer key · 2 pages

Fractions

What you’ll practice

Multiply two proper fractions and write the product in simplest form.

Unlike addition, fraction multiplication does not need matching denominators. Multiply straight across, then look for a common factor to simplify the product.

How this skill works

Multiplying a/b by c/d gives (a × c)/(b × d). The denominators do not need to match because multiplication is not a count of equal fractional units.

A common factor can be canceled before multiplying, or the complete product can be simplified afterward. Both methods preserve the same exact value.

Worked example

Calculate 2/3 × 3/4.
  1. Multiply the numerators: 2 × 3 = 6.
  2. Multiply the denominators: 3 × 4 = 12.
  3. 6/12 simplifies to 1/2.

Answer: 1/2

Teaching notes

  • Keep numerator products above denominator products.
  • Look for cross-canceling factors if the products become large.
Practice questions
  1. Calculate and simplify: 2/6 × 5/6.
  2. Calculate and simplify: 2/3 × 4/5.
  3. Calculate and simplify: 3/6 × 4/10.
  4. Calculate and simplify: 4/5 × 1/2.
  5. Calculate and simplify: 1/9 × 2/6.
  6. Calculate and simplify: 1/8 × 1/2.
  7. Calculate and simplify: 1/3 × 3/7.
  8. Calculate and simplify: 1/7 × 4/10.
  9. Calculate and simplify: 6/8 × 1/3.
  10. Calculate and simplify: 2/9 × 6/8.
  11. Calculate and simplify: 7/8 × 2/9.
  12. Calculate and simplify: 3/4 × 5/9.
Answers and steps
  1. 5/18
    1. Multiply numerators and denominators: (2 × 5)/(6 × 6) = 10/36.
    2. The greatest common factor of 10 and 36 is 2. Divide both by 2: 10/36 = 5/18.
  2. 8/15
    1. Multiply numerators and denominators: (2 × 4)/(3 × 5) = 8/15.
    2. The greatest common factor of 8 and 15 is 1. Divide both by 1: 8/15 = 8/15.
  3. 1/5
    1. Multiply numerators and denominators: (3 × 4)/(6 × 10) = 12/60.
    2. The greatest common factor of 12 and 60 is 12. Divide both by 12: 12/60 = 1/5.
  4. 2/5
    1. Multiply numerators and denominators: (4 × 1)/(5 × 2) = 4/10.
    2. The greatest common factor of 4 and 10 is 2. Divide both by 2: 4/10 = 2/5.
  5. 1/27
    1. Multiply numerators and denominators: (1 × 2)/(9 × 6) = 2/54.
    2. The greatest common factor of 2 and 54 is 2. Divide both by 2: 2/54 = 1/27.
  6. 1/16
    1. Multiply numerators and denominators: (1 × 1)/(8 × 2) = 1/16.
    2. The greatest common factor of 1 and 16 is 1. Divide both by 1: 1/16 = 1/16.
  7. 1/7
    1. Multiply numerators and denominators: (1 × 3)/(3 × 7) = 3/21.
    2. The greatest common factor of 3 and 21 is 3. Divide both by 3: 3/21 = 1/7.
  8. 2/35
    1. Multiply numerators and denominators: (1 × 4)/(7 × 10) = 4/70.
    2. The greatest common factor of 4 and 70 is 2. Divide both by 2: 4/70 = 2/35.
  9. 1/4
    1. Multiply numerators and denominators: (6 × 1)/(8 × 3) = 6/24.
    2. The greatest common factor of 6 and 24 is 6. Divide both by 6: 6/24 = 1/4.
  10. 1/6
    1. Multiply numerators and denominators: (2 × 6)/(9 × 8) = 12/72.
    2. The greatest common factor of 12 and 72 is 12. Divide both by 12: 12/72 = 1/6.
  11. 7/36
    1. Multiply numerators and denominators: (7 × 2)/(8 × 9) = 14/72.
    2. The greatest common factor of 14 and 72 is 2. Divide both by 2: 14/72 = 7/36.
  12. 5/12
    1. Multiply numerators and denominators: (3 × 5)/(4 × 9) = 15/36.
    2. The greatest common factor of 15 and 36 is 3. Divide both by 3: 15/36 = 5/12.