Keith loves snakes. Last summer, he found a

In this concept, you will learn how to divide mixed numbers.

### Dividing Mixed Numbers

You can divide a mixed number by another mixed number. This means that you are looking for how many groups and parts of groups can be made from another whole and part. This seems complicated, but if you follow a few simple steps, you can figure it out.

These are the rules for dividing a mixed number by a fraction.

- Convert the mixed number to an improper fraction.
- Change the division to its inverse, multiplication, and multiply by the reciprocal of the divisor.
- Multiply and simplify to find the quotient.

Here is a division problem.

The first step to dividing a mixed number by another mixed number is to convert both mixed numbers to improper fractions.

Next, rewrite the problem with the improper fractions.

Then, change the operation to multiplication and multiply by the reciprocal.

Next, multiply the fractions and simplify the answer.

### Examples

#### Example 1

Earlier, you were given a problem about Keith and the garter snake.

Keith wrote a division problem to find out how many

First, convert both mixed numbers to improper fractions.

Then, change the operation to multiplication and multiply by th reciprocal.

Next, multiply the fractions and simplify the answer. You can cross simplify before multiplying the fractions.

It would take 6 garter snakes to equal the length of the one anaconda in Keith's book.

#### Example 2

Divide the mixed number:

First, convert both mixed numbers to improper fractions.

Rewrite the problem with the improper fractions.

Then, change the operation to multiplication and multiply by the reciprocal.

Next, multiply the fractions and simplify the answer.

The quotient is

.#### Example 3

Divide the mixed number:

First, convert both mixed numbers to improper fractions.

Then, change the operation to multiplication and multiply by the reciprocal.

Next, multiply the fractions and simplify the answer.

The quotient is

#### Example 4

Divide the mixed number:

First, convert both mixed numbers to improper fractions.

Then, change the operation to multiplication and multiply by the reciprocal.

Next, multiply the fractions and simplify the answer.

The quotient is

#### Example 5

Divide the mixed number:

First, convert both mixed numbers to improper fractions.

Then, change the operation to multiplication and multiply by the reciprocal.

Next, multiply the fractions and simplify the answer.

The quotient is

### Review

Divide the mixed number. Answer in simplest form.

212÷113=−−−− 114÷313=−−−− 116÷112=−−−− 412÷112=−−−− 512÷112=−−−− 314÷113=−−−− 412÷512=−−−− 612÷214=−−−− 513÷212=−−−− 312÷312=−−−− 623÷112=−−−− 825÷113=−−−− - \begin{align*}12 \frac{1}{2} \div 2 \frac{1}{4} = \underline{\;\;\;\;\;\;\;\;}\end{align*}
- \begin{align*}6 \frac{5}{6} \div 2 \frac{1}{2} = \underline{\;\;\;\;\;\;\;\;}\end{align*}
- \begin{align*}8 \frac{3}{4} \div 2 \frac{1}{2} = \underline{\;\;\;\;\;\;\;\;}\end{align*}

### Review (Answers)

To see the Review answers, open this PDF file and look for section 7.12.