Adding and Subtracting Fractions: A Step-by-Step Guide for Grades 5–6

Adding and subtracting fractions comes down to one rule: you can only add or subtract pieces of the same size. The denominator tells you the size of the pieces, so the denominators have to match before you do anything else.

Same denominators

If the denominators already match, add or subtract the numerators and keep the denominator: 3/8 + 2/8 = 5/8. Then simplify if you can: 2/8 + 2/8 = 4/8 = 1/2.

Different denominators: four steps

• Find a common denominator. The least common multiple of the denominators is easiest. For 1/4 + 1/6, multiples of 4 are 4, 8, 12… and multiples of 6 are 6, 12… so use 12.
• Rewrite each fraction. Multiply the top and bottom by the same number: 1/4 = 3/12 and 1/6 = 2/12.
• Add or subtract the numerators. 3/12 + 2/12 = 5/12.
• Simplify. 5/12 is already in lowest terms.

Worked example (subtraction)

5/6 − 1/4: the least common denominator is 12. 5/6 = 10/12 and 1/4 = 3/12, so 10/12 − 3/12 = 7/12.

Mixed numbers

Either convert to improper fractions first (2 1/3 = 7/3), or add the whole numbers and fractions separately. Converting is safer for subtraction: 3 1/4 − 1 2/3 becomes 13/4 − 5/3 = 39/12 − 20/12 = 19/12 = 1 7/12.

The three most common mistakes

• Adding the denominators. 1/2 + 1/3 is not 2/5. A quick sanity check: 1/2 + 1/3 must be more than 1/2, and 2/5 is less than 1/2.
• Changing only the denominator. Whatever you multiply the bottom by, you must multiply the top by too.
• Forgetting to simplify. 6/8 is correct but unfinished; most teachers want 3/4.

Practice tip: ask students to estimate first ("is the answer more or less than 1?"). Estimating catches most denominator mistakes before they're marked wrong.