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:

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)

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

Example #1:

1 / 6

× 4

3 / 2

Example #1:

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 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:

5 / 5

× 4

3 / 3

Convert the mixed numbers

5 / 5

7 × 5 + 5 / 5

40 / 5

3 / 3

4 × 3 + 3 / 3

15 / 3

40 / 5

15 / 3

40 × 15 / 5 × 3

600 / 15

and

600 / 15

= 40

Example #2:

5 / 5

× 4

3 / 3

Convert the mixed numbers

5 / 5

7 × 5 + 5 / 5

40 / 5

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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Multiplying mixed numbers