Adding fractions with unlike denominators

Objective

Add two proper fractions with different denominators by finding a common denominator, then simplify if needed.

Worked example

1/2 + 1/3

1. Halves and thirds are different sizes. Find a common denominator: 2 and 3 both divide 6.
2. 1/2 = 3/6 because 1×3=3 and 2×3=6.
3. 1/3 = 2/6 because 1×2=2 and 3×2=6.
4. 3/6 + 2/6 = 5/6. Already simplified.

Check: 0.5 + 0.333… = 0.833… and 5÷6 ≈ 0.833. Same value.

Misconception

Adding tops and bottoms (1/2 + 1/3 = 2/5) treats “2 and 3” as if they were already the same piece. 2/5 = 0.4, which is smaller than 1/2. Adding a positive amount to 1/2 must make the result larger, so 2/5 cannot be correct.

Practice

1. 3/4 + 1/6
2. 2/5 + 3/10
3. 1/4 + 1/8
4. 2/3 + 1/9
5. 5/6 + 1/4

Adaptations

• Support: give the common denominator; students only rewrite and add.
• Challenge: item 5 is an improper result — convert to a mixed number.
• Language: say “same-size pieces” instead of “common denominator” first.

Answer key

1. 3/4 + 1/6 = 9/12 + 2/12 = 11/12
2. 2/5 + 3/10 = 4/10 + 3/10 = 7/10
3. 1/4 + 1/8 = 2/8 + 1/8 = 3/8
4. 2/3 + 1/9 = 6/9 + 1/9 = 7/9
5. 5/6 + 1/4 = 10/12 + 3/12 = 13/12 = 1 1/12

Decimal checks: 0.75+0.166…=0.916… (11/12); 0.4+0.3=0.7; 0.25+0.125=0.375; 0.666…+0.111…=0.777…; 0.833…+0.25=1.083… (13/12).

Plain Chalk lesson pack · Updated 13 September 2026. Adapt the pace and level of support for your class.