1 Dividing Fractions… And what it means

2 Rules for Multiplying Fractions: *Review* 1) Change mixed numbers into improper fractions. 2) Cancel if possible. 3) Multiply the numerators. 4) Multiply the denominators.

3 What does it mean to multiply a fraction? For example, we want to multiply: 3 x 2/7 That equals: 2/7 + 2/7 + 2/7 What’s the answer? 6/7

4 Word problem review with fraction multiplication: How do you write the equation for the question… What is ¾ of 20? Try it on your paper and show me…. ¾ x 20 = 15

5 Try this… How do you write what ½ of 7/8 ths is in an equation? Write it on your paper and show me when you’re done please. ½ x 7/8 = 7/16

6 It is important that you understand multiplying fractions, before we begin dividing them…. Are you READY?

7 Dividing Fractions: W hat are we really doing when we divide fractions? Whole number example: How many 2-foot sections are there in something that is 10 feet long? We write: 10 ÷ 2 = 5 feet Fraction example: How many ½-foot sections are there in something that is 1 ¾ feet long? We write: 1 ¾ ÷ ½= hmmm…

8 Stop and take a Look ! The answer is: 3 ½

9 Here’s another way we divide fractions… Whole number example: If 2 jump ropes are 10 meters long, how long is one jump rope? We write: 10 ÷ 2 = 5 meters Fraction example: If ½ of a jump rope is 1 ¾ meters, what is the length of the whole rope? We write: 1 ¾ ÷ ½ =hmm…

10 Let’s take another Look! The answer is: 3 ½

11 Be aware… We cannot visualize all division by fraction problems, therefore it is necessary to know how to use the mathematical process.

12 Your turn… Can you think of some word problems that would require division by fractions? Think about it, then using scrap paper, create a visual for your word problem. You have 4 minutes.

13 Dividing Fractions: The Process 1) Change mixed numbers into improper fractions. 2) Invert and multiply. (You may choose to cancel before multiplying.) 3) Reduce your answer (if possible).

14 Teacher Example: 15/3 ÷ 2/9= We can prove that it’s correct too! Answer: 45/2

15 Another Teacher Example: 3 1/5 ÷ 1 2/8 = Then, We’ll prove that it’s correct! Answer: 64/25

16 Understanding the rules

17 Rule #1: Change mixed numbers into improper fractions. Which problem would you prefer to solve? This one: 3 ¾ ÷ 2 1/3 Or this one: 15/4 ÷ 7/3

18 Rule #2: Invert and Multiply Why invert and multiply? This is actually a short cut that helps us get to the answer more quickly. Dividing by a number is equivalent to multiplying by its reciprocal. After all, dividing by 1 is much easier than dividing by 3/8! Example: 6/7 ÷ 3/8 = ______ Answer: 16/7

19 Rule #3: Reduce Your Answer Reducing before multiplying helps simplify the equation early on, so that there is less work later.

20 Let’s try a few together: 1)5/8 ÷ 7/8 = 2)3/5 ÷ 2 = 3)15 ÷ 2 ½ =

21 Now you are ready to try some problems on your own!

22 Closing What are the 3 steps in dividing fractions?