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 ________.

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

Some Examples: Example #1: Example #2: Example #3: Example #4: Don’t forget to cross reduce if possible ONLY when multiplying!

Examples: Example #5: Example #6: Example #7: Don’t forget to cross reduce if possible ONLY when multiplying!