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Adding and subtracting like denominators

Add and subtract fractions with the same denominator.

Practice + answer key · 2 pages

Worksheet settings12 questions · 2 columns · A4
Common denominator range

Each question selects one denominator from the range and uses it for both fractions.

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Adding and subtracting like denominatorsAdding and subtracting like denominators. Practice. Calculate and simplify: 11/12 + 9/12. Calculate and simplify: 10/12 − 9/12. Calculate and simplify: 6/8 + 7/8. Calculate and simplify: 5/9 − 5/9. Calculate and simplify: 3/7 + 2/7. Calculate and simplify: 7/9 − 5/9. Calculate and simplify: 2/3 + 1/3. Calculate and simplify: 1/3 − 1/3. Calculate and simplify: 4/8 + 6/8. Calculate and simplify: 2/4 − 1/4. Calculate and simplify: 5/7 + 2/7. Calculate and simplify: 2/3 − 1/3.Name __________________________Date _______________Adding and subtracting like denominatorsCalculate each expression and write the result in simplest form.Worked exampleCalculate 3/8 + 1/8. → 1/2Both fractions count eighths, so add the numerators: 3 + 1 = 4.1.Calculate and simplify: 11/12 +9/12.2.Calculate and simplify: 10/12 −9/12.3.Calculate and simplify: 6/8 +7/8.4.Calculate and simplify: 5/9 −5/9.5.Calculate and simplify: 3/7 +2/7.6.Calculate and simplify: 7/9 −5/9.7.Calculate and simplify: 2/3 +1/3.8.Calculate and simplify: 1/3 −1/3.9.Calculate and simplify: 4/8 +6/8.10.Calculate and simplify: 2/4 −1/4.11.Calculate and simplify: 5/7 +2/7.12.Calculate and simplify: 2/3 −1/3.MathSprig · mathsprig.site · support@mathsprig.sitePage 1 of 1mathsprig-1 · mathsprig-v1 · 4bf4b06b
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Practice + answer key · 2 pages

Fractions

What you’ll practice

Calculate sums and nonnegative differences of fractions with a common denominator.

The parts are already the same size, so add or subtract the numerators and keep the denominator. Simplify your answer when you have finished.

How this skill works

With equal denominators, the fractional units already match. Add or subtract the numerators to count how many of those units remain.

The denominator does not get added or subtracted. Reduce the result afterward; a sum can be an improper fraction and a difference can be zero.

Worked example

Calculate 3/8 + 1/8.
  1. Both fractions count eighths, so add the numerators: 3 + 1 = 4.
  2. The sum is 4/8.
  3. Divide numerator and denominator by 4 to get 1/2.

Answer: 1/2

Teaching notes

  • Name the fractional unit to remember why the denominator stays fixed.
  • Check for a common factor after combining the numerators.
Practice questions
  1. Calculate and simplify: 11/12 + 9/12.
  2. Calculate and simplify: 10/12 − 9/12.
  3. Calculate and simplify: 6/8 + 7/8.
  4. Calculate and simplify: 5/9 − 5/9.
  5. Calculate and simplify: 3/7 + 2/7.
  6. Calculate and simplify: 7/9 − 5/9.
  7. Calculate and simplify: 2/3 + 1/3.
  8. Calculate and simplify: 1/3 − 1/3.
  9. Calculate and simplify: 4/8 + 6/8.
  10. Calculate and simplify: 2/4 − 1/4.
  11. Calculate and simplify: 5/7 + 2/7.
  12. Calculate and simplify: 2/3 − 1/3.
Answers and steps
  1. 5/3
    1. Keep the common denominator 12 and add the numerators: 11 + 9 = 20.
    2. The greatest common factor of 20 and 12 is 4. Divide both by 4: 20/12 = 5/3.
  2. 1/12
    1. Keep the common denominator 12 and subtract the numerators: 10 − 9 = 1.
    2. The greatest common factor of 1 and 12 is 1. Divide both by 1: 1/12 = 1/12.
  3. 13/8
    1. Keep the common denominator 8 and add the numerators: 6 + 7 = 13.
    2. The greatest common factor of 13 and 8 is 1. Divide both by 1: 13/8 = 13/8.
  4. 0
    1. Keep the common denominator 9 and subtract the numerators: 5 − 5 = 0.
    2. The greatest common factor of 0 and 9 is 9. Divide both by 9: 0/9 = 0.
  5. 5/7
    1. Keep the common denominator 7 and add the numerators: 3 + 2 = 5.
    2. The greatest common factor of 5 and 7 is 1. Divide both by 1: 5/7 = 5/7.
  6. 2/9
    1. Keep the common denominator 9 and subtract the numerators: 7 − 5 = 2.
    2. The greatest common factor of 2 and 9 is 1. Divide both by 1: 2/9 = 2/9.
  7. 1
    1. Keep the common denominator 3 and add the numerators: 2 + 1 = 3.
    2. The greatest common factor of 3 and 3 is 3. Divide both by 3: 3/3 = 1.
  8. 0
    1. Keep the common denominator 3 and subtract the numerators: 1 − 1 = 0.
    2. The greatest common factor of 0 and 3 is 3. Divide both by 3: 0/3 = 0.
  9. 5/4
    1. Keep the common denominator 8 and add the numerators: 4 + 6 = 10.
    2. The greatest common factor of 10 and 8 is 2. Divide both by 2: 10/8 = 5/4.
  10. 1/4
    1. Keep the common denominator 4 and subtract the numerators: 2 − 1 = 1.
    2. The greatest common factor of 1 and 4 is 1. Divide both by 1: 1/4 = 1/4.
  11. 1
    1. Keep the common denominator 7 and add the numerators: 5 + 2 = 7.
    2. The greatest common factor of 7 and 7 is 7. Divide both by 7: 7/7 = 1.
  12. 1/3
    1. Keep the common denominator 3 and subtract the numerators: 2 − 1 = 1.
    2. The greatest common factor of 1 and 3 is 1. Divide both by 1: 1/3 = 1/3.