# Multiplying mixed numbers!

Multiplying mixed numbers is what you will learn here with some easy to follow examples.

A mixed number, also called mixed fraction, is any number that has the following format:

9
3 / 4

The reason it is called mixed is because it is a mixture of a whole number and a proper fraction.

In our example, the whole number is 9.

The proper fraction is
3 / 4

## Converting a mixed number into an improper fraction.

It is extremely important to convert a mixed number into an improper fraction before doing the multiplication.

We show you next how to convert a mixed number into an improper fraction using the mixed number above.

Step 1. Multiply the whole number by the denominator of the fraction: (9 × 4 = 36)

Step 2. Add the result of step 1 to the numerator of the fraction: (36 + 3 = 37)

The fraction is
37 / 4

Step 4. Finally, simplify the improper fraction you found in step 3 if needed.

Now, you are ready to multiply mixed numbers with a couple of good examples.

## Examples about multiplying mixed numbers

If you did not understand the examples in the figure above, just keep reading.

Example #1:

 2 1 / 6 ×   4 3 / 2
Example #1:

 2 1 / 6 ×   4 3 / 2

Rewrite each mixed number as an improper fraction by following the steps outlined above.

Here is how for 2
1 / 6

Step 1. Multiply the whole number by the denominator of the fraction: (2 × 6 = 12)

Step 2. Add the result of step 1 to the numerator of the fraction: (12 + 1 = 13)

The fraction is
13 / 6
and it is already in simplest form

Here is how for 4
3 / 2

Step 1. Multiply the whole number by the denominator of the fraction: (4 × 2 = 8)

Step 2. Add the result of step 1 to the numerator of the fraction: (8 + 3 = 11)

The fraction is
11 / 2
and it is already in simplest form

Now just multiply the fractions. Do this by multiplying the numerators together and the denominators together.

 13 / 6 ×   11 / 2 =   13 × 11 / 6 × 2 =   143 / 12

Sometimes, teachers or textbooks may ask you to write your answer as a mixed number. So feel free to rewrite 143/12 as a mixed number

 13 / 6 ×   11 / 2 =   13 × 11 / 6 × 2 =   143 / 12

Sometimes, teachers or textbooks may ask you to write your answer as a mixed number. So feel free to rewrite 143/12 as a mixed number

Example #2:

 7 5 / 5 ×   4 3 / 3

Convert the mixed numbers

 7 5 / 5 =   7 × 5 + 5 / 5 =   40 / 5

 4 3 / 3 =   4 × 3 + 3 / 3 =   15 / 3

 40 / 5 ×   15 / 3 =   40 × 15 / 5 × 3 =   600 / 15

and
600 / 15
= 40

Example #2:

 7 5 / 5 ×   4 3 / 3

Convert the mixed numbers

 7 5 / 5 =   7 × 5 + 5 / 5 =   40 / 5

 4 3 / 3 =   4 × 3 + 3 / 3 =   15 / 3

 40 / 5 ×   15 / 3 =   40 × 15 / 5 × 3 =   600 / 15

and
600 / 15
= 40

Sometimes, multiplying mixed numbers is a piece of cake with some good observations. If you had noticed that 40 divided by 5 is 8 and 15 divided by 3 is 5.

You can just multiply 8 and 5 to get 40.

Looking at the example #2 again.

Noticed that 5 divided by 5 is 1 and 3 divided by 3 is 1.

Remember that between a whole number and a fraction, there is always a + sign.

The problem just becomes 7 + 1 × 4 + 1 = 8 × 5 = 40

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