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# Lesson 8: Multiplying Fractions.

### HOW TO MULTIPLY FRACTIONS

The good news is you do not need a common denominator when multiplying fractions.
To multiply two (or more) fractions you have to:

• Change all mixed fractions ( if any) to improper fractions.
• Multiply out the numerators.
• Multiply out the denominators.
• "Tidy up" the result - change the improper fraction to a
mixed fraction and simplify it if possible.

### MULTIPLYING SIMPLE FRACTIONS

#### Example

 Find 2 x 2 3 5

Solution:

 2 x 2 = 2 x 2 Multiply the numerators 3 5 3 x 5 Multiply the denominators
 = 4 15

#### Example

 Find 7 x 1 x 3 3 2 2

Solution:

 7 x 1 x 3 = 7 x 1 x 3 Multiply the numerators. 3 2 2 3 x 2 x 2 Multiply the denominators.

 = 21 = 1 9 Change the result to a mixed fraction. 12 12

 = 1 3 Simplify the result 4 (divide both sides of the fraction by 3).

Sometimes you can simplify before calculating the final result.
This can be done if any numerator and denominator have common factors.
REMEMBER
only top numbers can cancel bottom numbers.
In the example below you can cancel 14 and 7 (they have the common factor of 7),
but you cannot cancel 14 and 2, because they are both numerators.

#### Example

 Find 14 x 2 5 7

Solution:

 14 x 2 = 14 x 2 Multiply the numerators. 5 7 5 x 7 Multiply the denominators.

 = 2 x 2 = 4 Simplify before calculating the final result 5 x 1 5 (divide the top number 14 and the bottom number 7 by 7).

### MULTIPLYING MIXED FRACTIONS

#### Example

 Find 2 1 x 1 1 2 10

 2 1 x 1 1 = 5 x 11 Convert mixed fractions to 2 10 2 10 improper fractions.

 = 5 x 11 = 1 x 11 Simplify before multiplying 2 x 10 2 x 2 (divide 5 and 10 by 5)

 = 11 = 2 3 Change the result to a mixed fraction. 4 4

### MULTIPLYING FRACTION BY WHOLE NUMBERS

We can write any whole number as a fraction with a denominator of 1.

 For example, we can write 3 as 3 . Why? 1

#### Example

 Find 4 x 2 5

Solution:

 4 x 2 = 4 x 2 Write 2 as 2 5 5 1 1

 = 4 x 2 = 8 Multiply the numerators. 5 x 1 5 Multiply the denominators.

 = 1 3 Change the result to a mixed fraction. 5

#### Example

 Find 8 x 5 12

Solution:

 8 x 5 = 8 x 5 Write 8 as 8 12 1 12 1

 = 8 x 5 = 2 x 5 Simplify before multiplying 1 x 12 1 x 3 (divide 8 and 12 by 4)

 = 10 = 3 1 Change the result to a mixed fraction. 3 3

 Why 3 = 3 ? 1
 Do you remember that 3 means "3 divided by 1"? And 3 divided by 1 equals 3. 1

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