Multiplying and Dividing Fractions

7th Grade MathAugust, 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 ANDMIXED 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

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)

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.

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

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: Example #1:

Example #2:

Example #3:

Example #4:

65

43

42

38

315

322

416

Don’t forget to cross reduce if possible

ONLY when multiplying!

Examples:

Example #5:

Example #6:

Example #7:

21

43

21

85

32

214

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.htm

laccessed 11/25/03

http://mathforum.org/library/drmath/view/58170.htmlaccessed 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.