Adding Fractions with Unlike Denominators (Grades 4–5)
You can only add fractions when the pieces are the same size — that is, when the denominators match. When they don't, the first job is to give both fractions a common denominator: rewrite each as an equivalent fraction so the bottoms agree. Then add the tops as usual.
Understanding adding fractions with unlike denominators
You can only add fractions when the pieces are the same size — that is, when the denominators match. When they don't, the first job is to give both fractions a common denominator: rewrite each as an equivalent fraction so the bottoms agree. Then add the tops as usual.
To find a common denominator, find a number both bottoms divide into — the least common denominator is the smallest such number and keeps the math tidy (for 1/2 and 1/3, that's 6). Rewrite each fraction to that denominator using equivalent fractions, then add.
Key Idea
To find a common denominator, find a number both bottoms divide into — the least common denominator is the smallest such number and keeps the math tidy (for 1/2 and 1/3, that's 6). Rewrite each fraction to that denominator using equivalent fractions, then add.
Seeing it in action
Worked example
1/2 + 1/3 = ?
Common denominator of 2 and 3 is 6.
Rewrite: 1/2 = 3/6, 1/3 = 2/6.
Add tops: 3/6 + 2/6 = 5/6. (Visual: a bar in sixths, 3 shaded + 2 shaded = 5/6.)
Worked example 2
3/4 + 1/6 = ?
Least common denominator of 4 and 6 is 12.
Rewrite: 3/4 = 9/12, 1/6 = 2/12.
Add: 9/12 + 2/12 = 11/12.
Try a few
1/2 + 1/4
1/2 = 2/4.
2/3 + 1/6
2/3 = 4/6.
1/3 + 1/4
4/12 + 3/12.
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