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Adding and subtracting unlike denominators

Find a common denominator before adding or subtracting.

Practice + answer key · 2 pages

Worksheet settings10 questions · 2 columns · A4
Original denominators

Both original denominators stay in the range and must differ. The common denominator may be larger.

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Adding and subtracting unlike denominatorsAdding and subtracting unlike denominators. Practice. Calculate and simplify: 2/3 + 1/2. Calculate and simplify: 5/7 − 1/2. Calculate and simplify: 6/8 + 3/5. Calculate and simplify: 3/6 − 2/5. Calculate and simplify: 3/4 + 3/8. Calculate and simplify: 3/5 − 2/4. Calculate and simplify: 3/4 + 4/5. Calculate and simplify: 3/6 − 1/2. Calculate and simplify: 1/2 + 4/8. Calculate and simplify: 6/7 − 3/5.Name __________________________Date _______________Adding and subtracting unlike denominatorsFind a common denominator, calculate, and simplify.Worked exampleCalculate 1/3 + 1/6. → 1/2The least common denominator of 3 and 6 is 6.1.Calculate and simplify: 2/3 +1/2.2.Calculate and simplify: 5/7 −1/2.3.Calculate and simplify: 6/8 +3/5.4.Calculate and simplify: 3/6 −2/5.5.Calculate and simplify: 3/4 +3/8.6.Calculate and simplify: 3/5 −2/4.7.Calculate and simplify: 3/4 +4/5.8.Calculate and simplify: 3/6 −1/2.9.Calculate and simplify: 1/2 +4/8.10.Calculate and simplify: 6/7 −3/5.MathSprig · mathsprig.site · support@mathsprig.sitePage 1 of 1mathsprig-1 · mathsprig-v1 · 0cf7e435
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Practice + answer key · 2 pages

Fractions

What you’ll practice

Use a common denominator to add or subtract positive fractions with different denominators.

Thirds and sixths are different-sized parts. Rewrite both fractions in the same unit first, then add or subtract their numerators and simplify the result.

How this skill works

Different denominators mean the fractions count different-sized parts. Rewrite them with a common denominator before combining their numerators.

The least common multiple is a convenient denominator. Multiplying each numerator by the same factor as its denominator preserves the original value.

Worked example

Calculate 1/3 + 1/6.
  1. The least common denominator of 3 and 6 is 6.
  2. 1/3 = 2/6, so 2/6 + 1/6 = 3/6.
  3. Simplify 3/6 to 1/2.

Answer: 1/2

Teaching notes

  • Record the multiplier used for each denominator and numerator.
  • Keep the converted denominator unchanged while combining numerators.
Practice questions
  1. Calculate and simplify: 2/3 + 1/2.
  2. Calculate and simplify: 5/7 − 1/2.
  3. Calculate and simplify: 6/8 + 3/5.
  4. Calculate and simplify: 3/6 − 2/5.
  5. Calculate and simplify: 3/4 + 3/8.
  6. Calculate and simplify: 3/5 − 2/4.
  7. Calculate and simplify: 3/4 + 4/5.
  8. Calculate and simplify: 3/6 − 1/2.
  9. Calculate and simplify: 1/2 + 4/8.
  10. Calculate and simplify: 6/7 − 3/5.
Answers and steps
  1. 7/6
    1. Use the least common denominator 6: 2/3 = 4/6, and 1/2 = 3/6.
    2. Keep the common denominator 6 and add the numerators: 4 + 3 = 7.
    3. The greatest common factor of 7 and 6 is 1. Divide both by 1: 7/6 = 7/6.
  2. 3/14
    1. Use the least common denominator 14: 5/7 = 10/14, and 1/2 = 7/14.
    2. Keep the common denominator 14 and subtract the numerators: 10 − 7 = 3.
    3. The greatest common factor of 3 and 14 is 1. Divide both by 1: 3/14 = 3/14.
  3. 27/20
    1. Use the least common denominator 40: 6/8 = 30/40, and 3/5 = 24/40.
    2. Keep the common denominator 40 and add the numerators: 30 + 24 = 54.
    3. The greatest common factor of 54 and 40 is 2. Divide both by 2: 54/40 = 27/20.
  4. 1/10
    1. Use the least common denominator 30: 3/6 = 15/30, and 2/5 = 12/30.
    2. Keep the common denominator 30 and subtract the numerators: 15 − 12 = 3.
    3. The greatest common factor of 3 and 30 is 3. Divide both by 3: 3/30 = 1/10.
  5. 9/8
    1. Use the least common denominator 8: 3/4 = 6/8, and 3/8 = 3/8.
    2. Keep the common denominator 8 and add the numerators: 6 + 3 = 9.
    3. The greatest common factor of 9 and 8 is 1. Divide both by 1: 9/8 = 9/8.
  6. 1/10
    1. Use the least common denominator 20: 3/5 = 12/20, and 2/4 = 10/20.
    2. Keep the common denominator 20 and subtract the numerators: 12 − 10 = 2.
    3. The greatest common factor of 2 and 20 is 2. Divide both by 2: 2/20 = 1/10.
  7. 31/20
    1. Use the least common denominator 20: 3/4 = 15/20, and 4/5 = 16/20.
    2. Keep the common denominator 20 and add the numerators: 15 + 16 = 31.
    3. The greatest common factor of 31 and 20 is 1. Divide both by 1: 31/20 = 31/20.
  8. 0
    1. Use the least common denominator 6: 3/6 = 3/6, and 1/2 = 3/6.
    2. Keep the common denominator 6 and subtract the numerators: 3 − 3 = 0.
    3. The greatest common factor of 0 and 6 is 6. Divide both by 6: 0/6 = 0.
  9. 1
    1. Use the least common denominator 8: 1/2 = 4/8, and 4/8 = 4/8.
    2. Keep the common denominator 8 and add the numerators: 4 + 4 = 8.
    3. The greatest common factor of 8 and 8 is 8. Divide both by 8: 8/8 = 1.
  10. 9/35
    1. Use the least common denominator 35: 6/7 = 30/35, and 3/5 = 21/35.
    2. Keep the common denominator 35 and subtract the numerators: 30 − 21 = 9.
    3. The greatest common factor of 9 and 35 is 1. Divide both by 1: 9/35 = 9/35.