Multiplying mixed numbers!
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A mixed number, also called mixed fraction, 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 proper fraction.
In our example, the whole number is 9.
The proper 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.
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
Step 4. Finally, simplify the improper fraction you found in step 3 if needed.
Now, you are ready to multiply mixed numbers with a couple of good examples.
Examples about 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
|
Rewrite each mixed number as an improper fraction 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
and it is already in simplest form
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
and it is already in simplest form
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
|
Sometimes, teachers or textbooks may ask you to write your answer as a mixed number. So feel free to rewrite 143/12 as a mixed number
|
13
6
|
×
11
2
|
=
13 × 11
6 × 2
|
=
143
12
|
Sometimes, teachers or textbooks may ask you to write your answer as a mixed number. So feel free to rewrite 143/12 as a mixed number
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