Multiplying and Dividing Fractions

1. Multiplying and Dividing Fractions 7th Grade Math August, 2012

2. 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!!!

3. MULTIPLYING FRACTIONS ANDMIXED NUMBERS!

4. Discovery Education Videos Multiply Fractions Multiply Mixed Numbers

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

6. 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).

7. 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.

8. 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.

9. 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

10. Examples: • Example #5: • ¾ • 7/8 • Example #6: • 5 1/3 • 9 ½ • Example #7: • 6(1 2/5)

11. 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)

12. Practice Problems – • Glencoe Textbook • Page 255 - #1-6 • Partners

13. Dividing Fractions and Mixed Numbers

14. Discovery Education Videos Dividing Fractions 2 minute – 4 minute mark Dividing Fractions Example

15. 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 ________.

16. 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

17. 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)

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

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

20. Practice Problems – “Practice Section” of your notebook • Glencoe Textbook • Page 267 - #1-8 • Partners

21. “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.

22. 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.