Dividing Fractions

1. Division
of
Fractions

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.
1½ ÷ ½ = 3
You could watch 3 episodes.

3. 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

4. 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…

5. 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?”

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

7. 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?

8. 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

9. 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. 

10. 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
÷
=

11. 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

12. 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.

13. How to Divide Fractions
• Step 2 – Keep your first fraction (dividend).
÷
4
3
1
1
=
3
1

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

15. How to Divide Fractions
• Step 4 – Take the reciprocal of the
divisor.
÷
4
3
1
1
=
3
1
x
1
4

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

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

18. 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)…

19. Now, Multiply and Simplify
9
2
3
4
=
27
88)27
3
x
24
3
3
8

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

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

22. 2
8
7
3
=÷
8
2
7
3
x
Keep
Change
Flip
Dividing Fractions

23. Now, Multiply and Simplify
8
2
7
3
=
56
66)56
9
x
54
2
2
6
9
2
6
÷2
2
=9
1
3÷

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

25. Dividing Fractions –
More Examples

26. 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

27. Edelstein, Carol Retrieved from http://www.google.com.ph/url?
sa=t&rct=j&q=&esrc=s&source=web&cd=1&cad=rja&ved=0CCgQFjAA&
url=http%3A%2F%2Fwww.understandmath4life.com%2FDocuments
%2FFractions%2520-%2520Dividing
%2520Fractions.ppt&ei=tylLUvOYDMXIiAfcjYDIDw&usg=AFQjCNHShyeL
0fTWc8DJCkeNsUFIgaVgaA&bvm=bv.53371865,d.aGc
Reference: