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.
Understanding adding fractions with unlike denominators
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.
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.
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.
A common mistake, and the fix
Adding tops and bottoms straight across.
1/2 + 1/3 is not 2/5, which is less than 1/2 on its own. Rewrite with a common denominator first: 3/6 + 2/6 = 5/6.
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.
Try it in Numeris.
A short lesson, then practice with feedback on every answer.
Put the reasoning on paper.
Try six fraction, angle, perimeter and area questions with explained answers, for grades 4–6.
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