Download Multiplying and Dividing Fractions

Multiplying and Dividing
Fractions
7th Grade Math
August, 2012
Lesson Overview:


This lesson will serve as a REVIEW of
multiplying and dividing fractions.
If you struggle with this concept, please
pay close attention and let’s master this
stuff!!!
MULTIPLYING FRACTIONS AND
MIXED NUMBERS!
Discovery Education Videos
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:

Multiplying fractions is easier than adding or
subtraction because you don’t need to find
common denominators. YAY!!!!!!

Just multiply straight across.


Multiply numerators together.
Then, multiply denominators together.
A Few Examples:

Example #1: 2/3 X 4/5


Example #2: 9/2 X 3/7


Answer: 27/14=1 13/27
Example #3: 2 1/6 X 3/2


Answer: 8/15
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)
Practice Problems –

Glencoe Textbook


Page 255 - #1-6
Partners
Dividing Fractions and Mixed Numbers
Discovery Education Videos
2 minute – 4 minute mark
What in the World is a
“Reciprocal”?

When two fractions are multiplied together
and their product is 1. 2 3
3



2
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



Keep the first fraction the same
STEP 2: Change the "÷" sign to "x"
STEP 3: Invert the second fraction
STEP 1:




(Use its reciprocal)
STEP 4: Multiply.
STEP 5: Simplify, if needed.
Example:

¼ ÷ ½ changes to
1 2

4 1
Algorithm: Dividing Fractions

Remember these three words:
 KEEP, CHANGE, RECIPROCAL

First fraction remains the same (KEEP)
Division symbol is changed to multiplication (CHANGE)
Last fraction is changed to its reciprocal (RECIPROCAL)
Then, Multiply and simplify your answer (Don’t forget to cross
reduce if possible)



Some Examples:




5
Example #1: 3

4
6
8
2
Example #2:

3 4
Example #3: 5  1
3
1
2
Example #4: 6 4  2 3
Don’t forget
to cross
reduce if
possible
ONLY when
multiplying!
Examples:
Example #5:
3 1

4
2
Example #6:
5 1

8 2
Example #7:
1
2
4 
2
3
Don’t forget
to cross
reduce if
possible
ONLY
when
multiplying!
Practice Problems – “Practice
Section” of your notebook

Glencoe Textbook


Page 267 - #1-8
Partners
“Card and Domino
Multiplication”

Each partner draws one (1) card and
one (1) domino




Card = whole number
Domino = fraction
Multiply your two numbers together
(individually)
Then, compare your answers.
Sources:




http://www.helpwithfractions.com/dividing-fractions.html
accessed 11/25/03
http://mathforum.org/library/drmath/view/58170.html
accessed 11/25/03
http://school.discovery.com/homeworkhelp/webmath/fractions.html
accessed 11/25/03
Van De Walle, J.A. (2001). Elementary and middle school
mathematics. New York: Longman.