Super Awesome Math

Add & Subtract Fractions Worksheets

Like and unlike denominators, and mixed numbers · Grades 4–6

Addition and subtraction of fractions written on a notebook grid, numerator over denominator, with a line of working under every problem. Start with like denominators, move to unlike denominators whose common denominator stays within the chosen limit, then to mixed numbers, where half the sums carry past a whole and half the differences borrow one. Answers are never negative and the answer key gives the simplest form, as a mixed number or an improper fraction.

Skills: adding fractions, subtracting fractions, common denominators, mixed numbers, simplest form. Format: printable, randomized on every load.

Sheets are randomized, free to print, and carry no answer key on purpose – why Super Awesome Math works this way.

How to do it

Fractions can only be added or subtracted once they are counted in the same units, so the whole job is turning unlike denominators into like ones before the numerators are touched.

  1. If the denominators already match, add or subtract the numerators and leave the denominator alone: 2/7 + 3/7 = 5/7.
  2. If they differ, find a common denominator – the least common multiple of the two will do. For thirds and quarters, that is twelfths.
  3. Rewrite each fraction with that denominator by multiplying top and bottom by the same number: 2/3 becomes 8/12, and 1/4 becomes 3/12.
  4. Now add or subtract the numerators: 8/12 + 3/12 = 11/12. The denominator does not change at this step.
  5. With mixed numbers, deal with the whole numbers and the fractions separately, then simplify the answer to lowest terms.

Where it goes wrong

  • Adding the denominators. 1/2 + 1/3 is not 2/5 – that answer is smaller than one of the fractions you started with.
  • Forgetting to convert the second fraction. Changing only 2/3 to 8/12 and leaving 1/4 as it is gives nonsense.
  • Leaving the answer unsimplified. 6/12 is correct but not finished.

Frequently asked questions
Why must the denominators match before adding?
A denominator names the size of the pieces, and pieces of different sizes cannot be counted together. One third and one quarter become four twelfths and three twelfths, and only then do the numerators add to seven twelfths. The unlike level keeps every common denominator within the limit, so that step never turns into a hunt.
What is a mixed number, and when should an answer be written as one?
A mixed number is a whole number and a fraction, such as 2 3/4. Many schools ask for answers above 1 in that form, while others, including most French, Spanish and Italian classrooms, keep the improper fraction 11/4. The Answers setting follows your language by default and can be switched either way.
Why is every answer expected in simplest form?
Simplifying at the end checks that the child can still see common factors after the arithmetic is done, and it gives every problem exactly one correct answer to mark against. 3/8 + 1/8 is 4/8, which the answer key writes as 1/2.

Settings
  • Level: like denominators, unlike denominators or mixed numbers
  • Operation: addition, subtraction or both
  • Denominators: up to 10, 12 or 20
  • Answers: a mixed number or an improper fraction
  • Columns: 2, 3 or 4 (12–24 problems)
  • Print an answer key

Example problems
  • 3/8 + 2/8 = □/□
  • 2/3 − 1/4 = □/□
  • 2 3/4 + 1 5/6 = □ □/□
  • 5 1/3 − 2 5/6 = □ □/□

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