All skills Math

Learn Index · Fractions, Decimals, and Percentages Grade 3–5

Adding and subtracting fractions

Combining fractions by using a common denominator.

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Adding like fractions

Like fractions have the same denominator, so the parts are the same size. Just add (or subtract) the numerators and keep the denominator.

  • 2/7 + 3/7 = 5/7
  • 5/8 − 2/8 = 3/8

Think of it like apples: 2 sevenths + 3 sevenths = 5 sevenths. The "sevenths" don’t change, just as "apples" wouldn’t.

Never add the denominators

A common mistake is 1/2 + 1/2 = 2/4. But 2/4 is only a half! Two halves make one whole: 1/2 + 1/2 = 2/2 = 1.

Adding unlike fractions

Unlike fractions have different denominators. You can’t add thirds and quarters directly, any more than you can add apples and oranges and call them "apples". First rename them with a common denominator.

Steps:

  1. Find the least common denominator (LCD): the smallest number both denominators divide into.
  2. Rewrite each fraction as an equivalent fraction with that denominator.
  3. Add or subtract the numerators.
  4. Simplify if possible.

Example: 1/3 + 1/4

  • LCD of 3 and 4 is 12.
  • 1/3 = 4/12; 1/4 = 3/12.
  • 4/12 + 3/12 = 7/12.

Example: 5/6 − 1/4

  • LCD of 6 and 4 is 12.
  • 5/6 = 10/12; 1/4 = 3/12.
  • 10/12 − 3/12 = 7/12.

Answers bigger than 1

Example: 3/4 + 2/3

  • 9/12 + 8/12 = 17/12 = 1 5/12.

Mixed numbers

Add the whole numbers, then the fractions.

Example: 2 1/2 + 1 1/3

  • Wholes: 2 + 1 = 3.
  • Fractions: 1/2 + 1/3 = 3/6 + 2/6 = 5/6.
  • Answer: 3 5/6.

For subtraction, you may need to borrow 1 whole:

Example: 4 1/4 − 1 3/4

  • 1/4 is less than 3/4, so borrow: 4 1/4 = 3 5/4.
  • 3 5/4 − 1 3/4 = 2 2/4 = 2 1/2.

Worked examples

Example 1: 3/10 + 4/10 = 7/10

Example 2: 1/2 + 3/8 → 4/8 + 3/8 = 7/8

Example 3: 7/9 − 1/3 → 7/9 − 3/9 = 4/9

Common mistakes

  • Adding the denominators: 1/3 + 1/4 ≠ 2/7.
  • Changing the denominator without changing the numerator.
  • Forgetting to simplify: 4/8 should be 1/2.
  • Not borrowing correctly when subtracting mixed numbers.

Try it yourself

  1. 2/9 + 5/9
  2. 1/2 + 1/5
  3. 3/4 − 1/6
  4. 1 2/3 + 2 1/6
  5. 5 1/3 − 2 2/3

Answers: 1) 7/9 2) 7/10 3) 7/12 4) 3 5/6 5) 2 2/3

Quick recap

  • Like fractions: add or subtract numerators; keep the denominator.
  • Unlike fractions: find a common denominator first.
  • Simplify and convert improper answers to mixed numbers.