multiplying and dividing fractions. a quick review: key point when multiplying or dividing...
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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
41
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!
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