Multiplying & Dividing Fractions

Multiply

• First, multiply the two numerators of the fractions.
• Then, multiply the two denominators of the fractions.
• Then, simplify the resulting fraction.

Example:

3/5  X  7/8 = ?

• Multiply the numerators ( 3 X 7 = 21)
• Next, multiply the denominators( 5 X 8 = 40)

3/5 X 7/8 = 21/40

This fraction is already simplified.

Did you notice? If you multiply two proper fractions, the answer is always another proper fraction, that is, a number less than 1.

Divide

• First, invert the divisor (the second fraction) – this means turn the fraction upside down. 23/8 becomes 8/23.
• Then, multiply the two fractions following the steps from above.
• Simplify and convert to a mixed number

Example:

3/5 ÷ 3/8 = ?

• Invert the divisor ( 3/8 becomes 8/3)

Now multiply the two fractions:

3/5 X 8/3

• Multiply the numerators ( 3 X 8 = 24)
• Next, multiply the denominators( 5 X 3= 15)

3/5 X 8/3 = 24/15

• Simplify

24/15 = 8/5

• Convert to a mixed number.

8/5 = 1  3/5

Did you notice? If you divide a fraction by a smaller fraction, the answer is always greater than 1.