Dividing of Fractions
by Carol Edelstein
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.
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
(start)
6 =
divisor
(what groups look like)
So, 18 ÷ 6 = 3
How
many
groups of
6 items are
there?
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
2
½ ÷ ¾ = /3
Ok. Let’s look at how we can solve these problems…
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?”
Dividing a Whole Number
by a Fraction
1
2
3
4
5
6
9
10
7
8
11
12
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?
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?
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
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. 
Dividing a Fraction by a
Fraction
Basically, in order to divide fractions we
will have to multiply.
1
2
÷
1
4
=
1 x 4
2
1
Dividing a Fraction by a
Fraction
From this point, the problem can be solved in
the way that you did for multiplying
fractions.
2
1 x 4 =2 = 2
2
1 1
1
How to Divide Fractions
•
Step 1 – Convert whole numbers and
mixed numbers to improper fractions.
This example is from a prior slide.
1
3
3÷ 4 = 1
÷
1
4
How to Divide Fractions
•
Step 2 – Keep your first fraction.
3
1
÷
1 = 3
4
1
How to Divide Fractions
•
Step 3 – Change the operation to
multiplication.
3
1
÷
1 = 3
4
1
x
How to Divide Fractions
•
Step 4 – Flip the second fraction.
3
1
÷
1 = 3
1
4
x
4
1
How to Divide Fractions
•
Step 5 – Multiply the numerators,
then multiple the denominators.
3
1
x
4 = 12
1
1
How to Divide Fractions
•
Step 6 – Simplify (if possible).
3
1
x
4 = 12 =12
1
1
Dividing Fractions –
An Example
3
4
÷
2 =
9
Since both are fractions, now you can Keep (1st fraction), Change
(the operation to multiplication), and Flip (2nd Fraction)…
Now, Multiply and Simplify
3
38
3 x 9 = 27
4
2 8 8)27
24
3
Dividing Fractions
So,
3
4
÷
2 = 3
3
8
9
Dividing Fractions –
Another Example
1
2
3
÷
2 =
8
Convert to improper fraction
Dividing Fractions
7
3
÷
2 = 7
8 3
Keep
Change
Flip
x
8
2
Now, Multiply and Simplify
2
96
7 x 8 = 56
3
2 6 6)56
54
2
÷2 = 1
9 6 ÷2 9 3
2
Dividing Fractions
So,
1
2 3
÷
2 = 1
9
3
8
Dividing Fractions –
More Examples
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
2
½ ÷ ¾ = /3
Great job!