4.6 Add and subtract mixed numbers

Model addition of mixed numbers with a common denominator

So far, we’ve added and subtracted proper and improper fractions, but not mixed numbers. Let’s begin by thinking about addition of mixed numbers using money.

If Ron has $1$ dollar and $1$ quarter, he has $1\frac{1}{4}$ dollars.

If Don has $2$ dollars and $1$ quarter, he has $2\frac{1}{4}$ dollars.

What if Ron and Don put their money together? They would have $3$ dollars and $2$ quarters. They add the dollars and add the quarters. This makes $3\frac{2}{4}$ dollars. Because two quarters is half a dollar, they would have $3$ and a half dollars, or $3\frac{1}{2}$ dollars.

When you added the dollars and then added the quarters, you were adding the whole numbers and then adding the fractions.

We can use fraction circles to model this same example:

Start with $1\frac{1}{4}$ .	one whole and one $\frac{1}{4}$ pieces
Add $2\frac{1}{4}$ more.	two wholes and one $\frac{1}{4}$ pieces
The sum is:	three wholes and two $\frac{1}{4}$ 's

Model $2\frac{1}{3}+1\frac{2}{3}$ and give the sum.

Solution

We will use fraction circles, whole circles for the whole numbers and $\frac{1}{3}$ pieces for the fractions.

two wholes and one $\frac{1}{3}$
plus one whole and two $\frac{1}{3}$ s
sum is three wholes and three $\frac{1}{3}$ s

This is the same as $4$ wholes. So, $2\frac{1}{3}+1\frac{2}{3}=4.$

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Model $1\frac{3}{5}+2\frac{3}{5}$ and give the sum as a mixed number.

Solution

We will use fraction circles, whole circles for the whole numbers and $\frac{1}{5}$ pieces for the fractions.

one whole and three $\frac{1}{5}$ s
plus two wholes and three $\frac{1}{5}$ s.
sum is three wholes and six $\frac{1}{5}$ s

Adding the whole circles and fifth pieces, we got a sum of $3\frac{6}{5}.$ We can see that $\frac{6}{5}$ is equivalent to $1\frac{1}{5},$ so we add that to the $3$ to get $4\frac{1}{5}.$

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Add mixed numbers

Modeling with fraction circles helps illustrate the process for adding mixed numbers: We add the whole numbers and add the fractions, and then we simplify the result, if possible.

Add: $3\frac{4}{9}+2\frac{2}{9}.$

Solution

	$3\frac{4}{9}+2\frac{2}{9}$
Add the whole numbers.
Add the fractions.
Simplify the fraction.

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