Multiplying and Dividing Fractions

A Quick Review: KEY POINT when multiplying or dividing

fractions:

☼☼ Change a mixed number into an improper fraction,

Still simplify your answer.

More on Multiplying Fractions:

The word “of” in a problem usually means multiply!

Here is an example: There are 8 cars in Michael’s toy collection. 1/2 of

the cars are red. How many red cars does Michael have?

This problem is asking “What is 1/2 of 8?” A way to answer it is to put a multiplication sign in place of “of.” You

then get 1/2 x 8 or 8 x ½ (remember that multiplication is commutative).

Multiplication Continued: What operation will I use for 2/3 of 15?

It means 2/3 x 15 It could mean anything. It is helpful if you think of a

situation such as: Mike ate 2/3 of 15 cookies. Susie took 2/3 of her 15 marbles to school. The dog ran 2/3 of its 15 laps around the yard.

Multiplying Fractions:

Just multiply straight across. Multiply numerators together. Then, multiply denominators together.

A Few Examples: Example #1: 2/3 X 4/5

Answer: 8/15

Example #2: 9/2 X 3/7 Answer: 27/14=1 13/27

Example #3: 2 1/6 X 3/2 Answer: 39/12=3 3/12=3 ¼

Example #4: 5 X 2/7 Answer: 10/7=1 3/7

Examples:

Example #5: ¾ • 7/8

Example #6: 5 1/3 • 9 ½

Example #7: 6(1 2/5)

Make Life Easier!! Cross Reduce

When multiplying, you can simplify your factors by “cross reducing”.

Examples: 6/35 • 5/24

2/15 • 3/18

1/8 (4/5)

What in the World is a “Reciprocal”?

When two fractions are multiplied together and their product is 1.

AKA “inverting” or “flipping” a number Examples:

The reciprocal of ½ is _______. The reciprocal of 1 ¾ is _______. The reciprocal of 8 is ________.

123

32

Rules for Dividing Fractions

STEP 1: Keep the first fraction the same STEP 2: Change the "÷" sign to "x" STEP 3: Invert the second fraction

(Use its reciprocal)

STEP 4: Multiply. STEP 5: Simplify, if needed. Example:

¼ ÷ ½ changes to

12

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Some Examples:

Example #1:

Example #2:

Example #3:

Example #4:

65

43

42

38

31

5

32

241

6

Don’t forget to cross reduce if possible

ONLY when multiplying!

Examples:

Example #5:

Example #6:

Example #7:

21

43

21

85

32

21

4

Don’t forget to cross reduce if possible ONLY when

multiplying!