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Add Fractions with Unlike Denominators

Students add two or more fractions with unlike denominators by first replacing them with equivalent fractions sharing a common denominator, then adding the numerators and simplifying the result.

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Add Fractions with Unlike Denominators

Grade 5 · Adding and Subtracting Fractions with Unlike Denominators · question 1 of 3

0 of 20

20 rungs. A star at the top.

1/2 + = 23/18

How it is taught

0:00 of 3:16

Unlike denominators cannot be added until they match.

Rewrite as equivalent fractions, then add the tops.

Read it: Make one cut, then count

1/5 and 3/10 are cut differently: one bar in fifths, one in tenths. Cut each fifth into 2 and 1/5 is 2/10. Now the pieces line up: 2/10 + 3/10 = 5/10, which is 1/2.

  1. Find a cut both bottom numbers go into: 5 and 10 both go into 10.
  2. Write each fraction in that cut: 1/5 is 2/10, and 3/10 stays 3/10.
  3. Add or take away the top numbers and keep the cut: 2/10 + 3/10 = 5/10, which is 1/2.

Pieces of different sizes cannot be counted together, so both bars are cut into the same pieces first.

Cutting a piece into smaller pieces does not change the amount: 1/5 and 2/10 shade the same part of a bar.

The least common denominator is the smallest cut both go into, so its pieces are the biggest that line up.

To add or subtract fractions with different denominators, write both in a common denominator, then add or subtract the numerators.

Adding the tops and the bottoms: 1/5 + 3/10 = 4/15.

4/15 is less than 3/10 alone, because fifteenths are smaller pieces. Cut both into tenths: 2/10 + 3/10 = 5/10, which is 1/2.

1/6 + 5/12 = ___ — 7/12. Cut both bars into 12: 1/6 is 2/12 and 5/12 stays 5/12. Together that is 7/12.

1/2 + 1/3

Let's add one-half and one-third. The pieces are different sizes, so we can't just add them yet.

See? A half-piece and a third-piece don't match up. We need same-sized pieces first.

We need a common denominator — a bottom number that works for both. Six works, because two and three both fit into six.

One-half is the same as three-sixths. We multiply top and bottom by three.

One-third is the same as two-sixths. We multiply top and bottom by two.

Now our problem looks like three-sixths plus two-sixths.

Same-sized pieces! Add the numerators: three plus two is five.

Keep the denominator the same — still sixths.

12 + 13 = ?1213Common denominator: 6362612 × 33 = 3613 × 22 = 2636+26=56ANSWER56five-sixths
Grade 5 · Find a common denominator, then add

One-half plus one-third equals five-sixths. Great work!

What you see

While they climb, your page writes one true line to ask about tonight, and a short note each Sunday.

MayaGrade 3 · Mathematics
Did you know?

A chessboard has 64 squares — share them out between the 8 rows and each row holds exactly 8.

Today’s goal
1 star — one skill mastered, every rung of its ladder climbed
Climbing now
Divide within 100

An example student.

MayaGrade 3 · Mathematics

Maya earned 2 stars this week — Interpret multiplication as equal groups, which took 6 answers over 3 days before its star landed 3 days ago and Multiply by 6, 7, 8 and 9. Next up: Divide within 100.

An example week.

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