2. Dividing of Fractions by Carol Edelstein

3. Warm Up

4. Warm up What does it mean to divide?

5. Essential Question How can you divide a fraction by a fraction?

6. When would you divide fractions? One example is when you are trying to figure out how many episodes of your favorite ½ hour tv program you could watch in the 1 ½ hrs you have available. 1½ ÷ ½ = 3 You could watch 3 episodes.

7. General Division Practice When you are faced with the division problem 18 divided by 6, think “If I have 18 items and I make groups of 6, how many groups will I have?” 18 ÷ 6 = dividend divisor (start) (what groups look like) How many groups of 6 items are there? So, 18 ÷ 6 =3

8. Dividing Fractions – Conceptual Understanding Like when we divided decimals, when you divide two fractions that are between 0 and 1, the quotient is going to be larger than at least one of your fractions. ½ ÷ ½ = 1 ½ ÷ ¾ = 2 / 3 Ok. Let’s look at how we can solve these problems…

9. Dividing a Whole Number by a Fraction What is 3 ÷ ¼ ? Use your prior knowledge and the illustration above to figure it out. Think, “If I start with 3, how many groups that look like ¼ will I have?”

10. So, 3 ÷ ¼ = 12. If you start with 3, you will have 12 groups of 1/4. 12 34 56 711 10 12 9 8 Dividing a Whole Number by a Fraction Can you see how you could manipulate the fractions to get an answer of 12?

11. Dividing a Whole Number by a Fraction So, 5 ÷ 1 / 3 = 15. If you start with 5, you will have 15 groups of 1/3. What is 5 ÷ 1 / 3 ? Can you see how you could manipulate the fractions to get an answer of 15?

12. Dividing a Fraction by a Fraction What is 1 / 2 ÷ 1 / 4 ? How many groups of 1 / 4 could you fit in the half of the rectangle? 2

13. Dividing a Fraction by a Fraction For the problem 1 / 2 ÷ 1 / 4, how could you get an answer of 2 ? Can you see how you could manipulate the fractions to get an answer of 2? Isn’t ½ x 4 = 2? Remember that division is the opposite operation of multiplication, so we can do the following… MULTIPLY.

14. Dividing a Fraction by a Fraction x 1 2 4 1 Basically, in order to divide fractions we will have to multiply. 1 2 1 4 ÷ =

15. Dividing a Fraction by a Fraction x 1 2 4 1 From this point, the problem can be solved in the way that you did for multiplying fractions. 1 2 = 2 1 = 2

16. How to Divide Fractions Step 1 – Convert whole numbers and mixed numbers to improper fractions. ÷ 4 3 1 1 ÷ 4 3 = 1 This example is from a prior slide.

17. How to Divide Fractions Step 2 – Keep your first fraction. ÷ 4 3 1 1 = 3 1

18. How to Divide Fractions Step 3 – Change the operation to multiplication. ÷ 4 3 1 1 = 3 1 x

19. How to Divide Fractions Step 4 – Flip the second fraction. ÷ 4 3 1 1 = 3 1 x 1 4

20. How to Divide Fractions Step 5 – Multiply the numerators, then multiple the denominators. x 1 3 1 4 = 12 1

21. How to Divide Fractions Step 6 – Simplify (if possible). x 1 3 1 4 = 12 1 =

22. Dividing Fractions – An Example 2 9 3 4 = ÷ Since both are fractions, now you can Keep ( 1st fraction ), Change ( the operation to multiplication ), and Flip ( 2 nd Fraction )…

23. Now, Multiply and Simplify 9 2 3 4 = 27 8 8)8) 3 x 24 3 3 8

24. Dividing Fractions 2 9 3 4 = ÷ 3 3 8 So,

25. Dividing Fractions – Another Example 2 8 1 3 = ÷ 2 Convert to improper fraction

26. 2 8 7 3 = ÷ 8 2 7 3 x Keep Change Flip Dividing Fractions

27. Now, Multiply and Simplify 8 2 7 3 = 56 6 6)6) 9 x 54 2 2 6 9 2 6 ÷ 2 2 = 9 1 3 ÷

28. Dividing Fractions 2 8 = ÷ 9 1 3 So, 1 3 2

29. Dividing Fractions – More Examples

30. REVIEW: Dividing Fractions – Conceptual Understanding Remember, when you divide two fractions that are between 0 and 1, the quotient is going to be larger than at least one of your fractions. ½ ÷ ½ = 1 ½ ÷ ¾ = 2 / 3

31. Great job!