This document provides instruction on multiplying and dividing fractions. It begins with a review of key points, such as changing mixed numbers to improper fractions and simplifying answers. It then discusses multiplying fractions by multiplying numerators and denominators across. Several examples of multiplying fractions are shown. The document also covers dividing fractions using the keep, change, reciprocal method and provides examples. It concludes with an activity involving multiplying and dividing fractions using cards and dominoes.

1. Multiplying and Dividing
Fractions
7th Grade Math
August, 2013

2. A Quick Review:
 KEY POINT when multiplying or dividing
fractions:
Change a mixed number into
an improper fraction,
 Still simplify your answer.

3. More on Multiplying Fractions:
 “of” means multiply!
 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).

4. Multiplying Fractions:
 Multiplying fractions is easier than adding or
subtraction because you don’t need to find
common denominators. YAY!!!!!!
 Just multiply straight across.
 Multiply numerators
 Then, multiply denominators

5. A Few Examples:
 Example #1: 2/3 X 4/5
 Answer: 8/15
 Example #2: 9/2 X 3/7
 Answer: 27/14=1 13/14
 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
 Example #5: 5 1/3 • 9 ½
 Answer: 50 2/3

6. 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)

7. What in the World is a
“Reciprocal”?
 Reciprocal:
 When two fractions are multiplied 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 ________.
1
2
3
3
2



8. Algorithm: Dividing Fractions
 Remember these three words:
 KEEP, CHANGE, RECIPROCAL
 KEEP First fraction
 CHANGE Division to multiplication
 RECIPROCAL of last fraction
 Multiply and Simplify

9. Some Examples:
 Example #1:
 Example #2:
 Example #3:
 Example #4:
6
5
4
3

4
2
3
8

3
1
5 
3
2
2
4
1
6 
Don’t forget
to cross
reduce if
possible
ONLY when
multiplying!

10. “Card and Domino Multiplication/Division”
 Each partner draws one (1) card and one (1)
domino
 Card = whole number
 Domino = fraction
 Multiply your two numbers (individually)
 Divide your two numbers (individually)
 Compare your answers. If you both have the
same answer, give your team a point for each
problem. Highest points (with work shown) wins
candy!