Add Mixed Numbers with Like Denominators

Students add mixed numbers that share the same denominator by adding the whole number parts and fractional parts separately, then regrouping when the fractional sum is an improper fraction. They use models and equations.

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Grade 4 · Adding and Subtracting Mixed Numbers · question 1 of 3

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20 rungs. A star at the top.

Mix 1 1/5 cups with 2 3/5 cups. How many cups is that?

How it is taught

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A mixed number has a whole and a fraction.

Add the wholes, then add the like fractions.

Keep the same bottom when the fractions add.

Read it: Whole bars and pieces

1 2/3 + 1 2/3: the pieces come to 4/3, so 3 of them make 1 more whole bar, and the sum is 3 1/3. Taking away, a whole bar opens into 3 pieces when the pieces are too few.

Work with the pieces first: put them together, or take them away.
Pieces that make 3/3 become 1 more whole bar; too few pieces open 1 whole bar.
Then the whole bars, and count what you have: wholes, then pieces.

3/3 is 1 whole, so 3 pieces of 1/3 are as much as a whole bar.

The fraction part of a mixed number is less than 1 whole, so 4/3 still holds a whole bar.

Opening a whole bar into 3 pieces does not change how much there is, only how it is cut.

Add or take away the pieces, then the whole bars, making or opening a whole bar when the pieces need it.

Leaving the pieces as 4/3 and writing 2 4/3.

4/3 is more than 1 whole: 3/3 of it is 1 more whole bar. So 1 2/3 + 1 2/3 is 3 1/3.

2 4/6 + 2 3/6 = ___ — 5 1/6. The pieces come to 7/6, so 6 of them gather into 1 more whole: 5 1/6.

2 3/5 + 1 4/5

Let's add two mixed numbers: two and three-fifths plus one and four-fifths.

We add the whole parts and the fraction parts separately.

First, add the whole numbers. Two plus one equals three.

Next, add the fractions. Three-fifths plus four-fifths.

Add the numerators: three plus four is seven. The denominator stays five. So we get seven-fifths.

But seven-fifths is more than one whole! Five-fifths fills one whole, with two-fifths left over.

Grade 4 · Adding mixed numbers with regrouping

So we regroup seven-fifths as one whole and two-fifths.

Now add that extra one to our three wholes: three plus one is four. We have four wholes and two-fifths.

So two and three-fifths plus one and four-fifths equals four and two-fifths!

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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