# Multiplying mixed numbers!

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

A mixed number 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 fraction

In our example, the whole number is 9

The fraction is
3 / 4

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

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

Example #1:

 2 1 / 6 ×   4 3 / 2
Example #1:

 2 1 / 6 ×   4 3 / 2

Convert each mixed number 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

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

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

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

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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