1. Dividing of Fractions
7 Math Unit 2 Week 5
May 26, 2019

2. 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.
Think: How many halves are in 1 ½ ?
1½ ÷ ½ = 3
You could watch 3 episodes.

3. Baking Cookies
You have 1 cups of sugar. It takes cup to make 1 batch of cookies. How many batches of cookies can you make?
How many cups of sugar are left?
How many batches of cookies could be made with the sugar that’s left? 3 3

4. 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 ÷ =
dividend divisor
(start) (what groups look like)
How many groups of 6 items are there?
So, 18 ÷ 6 = 3

5. 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…

6. 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?”

7. Dividing a Whole Number by a Fraction1 2 3 4 5 6 7 11 10 12 9 8
If you start with 3, you will have 12 groups of 1/4 .
So, 3 ÷ ¼ = 12.
Can you see how you could manipulate the fractions to get an answer of 12?

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

9. 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

10. 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. 

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

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

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

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

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

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

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

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

19. Dividing Fractions – An Example3 2 = ÷ 4 9
Since both are fractions, now you can Keep (1st fraction), Change (the operation to multiplication), and Flip (2nd Fraction)…

20. Now, Multiply and Simplify3 3 3 9 27 8 x = 8) 4 2 8 27 24 3

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

22. Dividing Fractions – Another Example1 2 = 2 ÷ 3 8
Convert to improper fraction

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

24. Now, Multiply and Simplify2 7 8 56 9 6 x = 6) 3 2 6 56 54 2 2 1 ÷ 9 = 9 2 6 ÷ 2 3

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

26. Dividing Fractions – More Examples

27. 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

28. Let’s Practice!
You have ½ of a pizza and you want to share it equally between 2 people. How much of the pizza does each person get?
You are making cupcakes for your friend’s birthday. You use ¼ cup of sugar for each batch. How many batches can you make if you have a can of sugar that holds 6 cups?
The serving size for the oatmeal that Jack likes to eat for breakfast is ¾ cup. How many servings are there in a box that holds 13 cups?