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

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)


Step 3. Your numerator is the answer of step 2. Your denominator stays the same.

The fraction is  
37 / 4

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

Examples about multiplying mixed numbers

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

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)


Step 3. Your numerator is the answer of step 2. Your denominator stays the same.

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)

Step 3. Your numerator is the answer of step 2. Your denominator stays the same.

The fraction is  
11 / 2

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
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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