# Multiplying fractions

Multiply the numerators, multiply the denominators, and simplify if necessary.

## How does multiplying fractions work?

The following topics are discussed with examples.
- Multiplying a fraction by a fraction
- Multiplying a fraction by a cardinal number
- Multiplying fractions with cancellation
- Multiplying with multiple cancellations

On this page you will find examples and exercices. For an extensive practice go to one of the 5-step plans.

### 5-step plans

Number of questions:

Time per question::

Tip: use tab to go to the next field

### Example 1

#### Multiplying a fraction by a fraction

Numerator multiplied by numerator, denominator multiplied by denominator, and simplify if necessary.

Sum 1. 12 x 12 = 1 x 1 = 12 x 2 = 4 = 14

Sum 2. 58 x 34 = 5 x 3 = 158 x 4 = 32 = 1532

### Example 2

#### Multiplying a fraction by a cardinal number

In this example we explain the sum 8 x 14.

You can also write the 8 as a fraction, namely 81.

Now you can multiply the fractions as in example 1.

81 x 14 = 84 = 2

### Example 3

#### Multiplying fractions with cancellation

Cancellation means dividing the numerator and denominator by the greatest common factor (GCF) crosswise.
We first solve the following sum:

14 x 47 =
This can be done in two ways. As in example 1 or with cancellation. In this example we show the second option.

1) 14 x 47 =

First we look for the greatest common factor of the numerator of the first fraction and the denominator of the second fraction. The numerator is 1 and the denominator is 7. The greatest common factor is 1 because the numerator can only be divided by 1. Both numbers remain the same.
Now we look for the GCF of the denominator of the first fraction and the numerator of the second fraction. Both numbers are 4. That makes the GCF easy to find because both numbers can be divided by 4.
We then get 4 : 4 = 1 The sum now looks like:

14 x 47 = 11 x 17 =

This is much easier to solve.

11 x 17 = 17

2)  150 x 25 4 =

1 and 4 can't be simplified any further.
Now we'll look at 25 and 50.
25 can be divided by 1, 5, and 25
50 can be divided by 1, 2, 5, 10, 25, and 50
The greatest common factor is 25.
25 : 25 = 1 and 50 : 25 = 2
We get the following sum:

150 x 254 = 12 x 14 = 18

### Example 4

#### Multiplication with multiple cancellations

In example 3 only one number was crossed out, but in this example both numbers can be simplified crosswise.

430 x 1028 =

First we'll look for the greatest common factor (GCF) of 4 and 28.
4 can be divided by 1, 2, and 4. ​
28 can be divided by 1, 2, 4, 7, and 14
The GCF is 4. We then get 4 : 4 = 1 and 28 : 4 = 7.

Now we'll look for the GCF of 30 and 10.
30 can be divided by 1, 2, 3, 5, 6, 10, 15, and 30
10 can be divided by 1, 2, 5, and 10
The GCF is 10. We then get 30 : 10 = 3 and 10 : 10 = 1.

The sum now becomes:

430 x 1028 = 13 x 17 =121