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
x1
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
x1
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÷
43 =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 (2nd
Fraction)…
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:
