# 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

## Recent Articles

1. ### Average age word problem

Aug 09, 16 01:40 PM

Average age of Dipu and Apu is 22 years. Average age of Dipu and Tipu is 24 years. Age of Dipu is 21 years. What are the ages of Apu, and tipu ? Let