Add and Subtract Mixed Numbers with Unlike Denominators

Students add and subtract mixed numbers where fractional parts have unlike denominators. They convert fractional parts to a common denominator, add or subtract whole numbers and fractions separately, and regroup when necessary (e.g., borrowing when subtracting).

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

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3 2/3 + 1 1/6 =

How it is taught

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Unlike mixed numbers need matching fraction parts before you subtract.

If the top fraction is too small, regroup one whole.

Read it: Wholes and pieces, one cut

5 1/3 − 2 1/2: cut both into sixths, so 5 2/6 − 2 3/6. 2 sixths cannot give 3, so open one whole: 4 8/6 − 2 3/6 = 2 5/6.

Cut both fractions into the same pieces.
Taking away: if the top pieces are too few, open one whole into pieces.
Adding: if the pieces make a whole or more, gather a whole. Then add or take away wholes and pieces.

Pieces of different sizes cannot be counted together, so the fractions are cut alike first.

Opening a whole does not change the amount: 5 2/6 and 4 8/6 are the same.

A whole's worth of pieces is one more whole: 13/10 is 1 whole and 3/10.

Rename the fractions with a common denominator, regroup a whole if you need to, then add or subtract the wholes and the fractions.

Taking 2 sixths from 3 sixths backward: 5 2/6 − 2 3/6 = 3 1/6.

The top has only 2 sixths, so open a whole first: 4 8/6 − 2 3/6 = 2 5/6.

4 1/2 − 1 4/5 = ___ — 2 7/10. Cut both into tenths: 4 5/10 − 1 8/10. Open a whole: 3 15/10 − 1 8/10 = 2 7/10.

2 1/3 + 1 1/4

Today we'll add mixed numbers when the bottoms are different. Let's try two and one-third plus one and one-fourth.

Here's our problem. The whole numbers are easy, but the fractions have different denominators — three and four.

First, find a common denominator. The smallest number that both three and four divide into is twelve.

Grade 5 · Combining mixed numbers with different bottoms

One-third is the same as four-twelfths. Multiply top and bottom by four.

One-fourth is the same as three-twelfths. Multiply top and bottom by three.

Now both fractions share the same bottom. Our problem becomes two and four-twelfths plus one and three-twelfths.

Add the fractions: four-twelfths plus three-twelfths is seven-twelfths.

Now add the whole numbers: two plus one is three.

Put them together. Two and one-third plus one and one-fourth is three and seven-twelfths!

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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Standard

CCSS.5.NF.A.1

Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions

Grade 5

Quoted from the Common Core State Standards.

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What a star here means

A star here is the top of a twenty-rung ladder, in four blocks of equal length — three of facts and one of the skill used in a real question — where a right answer climbs one rung and a wrong one drops back to the start of the block, never below it. The star is kept for good. How we grade

All of Grade 5

This is one rung of 81 in Grade 5 mathematics, in the order they build on each other.

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