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# Mixed Numbers: Division

Dividing gets a little tricker when we deal with mixed numbers. Thankfully, there are simple tricks we can use to make this process a total breeze. Let's put some of these tricks to good use and start dividing our first mixed numbers:

## What is a mixed number?

First, let's review the definition of a mixed number:

• A mixed number contains both a whole number and a fraction.

Examples of mixed numbers include 4 and $\frac{5}{8}$ , 6 and $\frac{3}{7}$ , 1 and $\frac{1}{2}$ , and so on.

## How do we divide mixed numbers?

In order to divide mixed numbers, we need to first rewrite them as improper fractions.

As you might recall, an improper fraction is a fraction that has a numerator greater than its denominator. Remember, the numerator is the top number in a fraction, while the denominator is the bottom number.

For example, we would rewrite 1 and one $\frac{1}{2}$ as the improper fraction $\frac{3}{2}$ . It means exactly the same thing, but we have written it in a more convenient way for the next step.

After we have rewritten the mixed number as an improper fraction, all we need to do is multiply the number by the reciprocal of the improper fraction. Remember the reciprocal is the number formed when we flip the reciprocal and the denominator. In other words, we flip the improper fraction we have just created upside-down.

## Practicing dividing improper fractions

Let's try a few practice exercises:

2 and $\frac{1}{6}$ divided by 1 and $\frac{1}{5}$

First, we turn the mixed numbers into improper fractions:

$\frac{13}{6}$ divided by $\frac{5}{6}$

Now we multiply by the reciprocal of $\frac{6}{5}$ , which is $\frac{5}{6}$ :

$\frac{13}{5}×\frac{5}{6}=\frac{65}{36}$

The final step is to simplify this and write it as a mixed number:

$1\frac{29}{36}$

Let's try another practice exercise:

$7\frac{1}{2}÷2\frac{1}{20}$

Rewrite as improper fractions:

$\frac{15}{2}÷\frac{21}{10}$

Next, multiply by the reciprocal:

$\frac{15}{2}×\frac{10}{21}$

Note that we can simplify these numbers at this point:

$\frac{5}{1}×\frac{5}{7}$

$=\frac{25}{7}$

$=3\frac{4}{7}$

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