Multiplying mixed numbers!

Multiplying mixed numbers is what you will learn here with some easy to follow examples.
Multiplying mixed numbers
If you did not understand the example above, keep reading. 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.

More examples about multiplying mixed numbers


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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