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 ÷ 6 = How
dividend divisor many
(start) (what groups look like)
groups of
6 items are
there?
So, 18 ÷ 6 = 3
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…
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 9 10
5 6
3 4 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 ÷
1 1 x 4
=
2 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 2
1 x 4 = =2
1 2 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 = 3
1 4 1
How to Divide Fractions
• Step 3 – Change the operation to
multiplication.
3 ÷ 1 = 3 x
1 4 1
How to Divide Fractions
• Step 4 – Flip the second fraction.
3 ÷ 1 = 3 x 4
1 4 1 1
How to Divide Fractions
• Step 5 – Multiply the numerators,
then multiple the denominators.
3 x
4 = 12
1 1 1
How to Divide Fractions
• Step 6 – Simplify (if possible).
3 x
4 = 12 =12
1 1 1
Dividing Fractions –
An Example
3 ÷ 2 =
4 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
3 x 9 = 27 38
4 2 8 8)27
24
3
Dividing Fractions
So,
3 ÷ 2 = 3
4 9 38
Dividing Fractions –
Another Example
2 1 ÷ 2 =
3 8
Convert to improper fraction
Dividing Fractions
7 ÷
2 = 7 x
8
3 8 3 2
Keep
Change
Flip
Now, Multiply and Simplify
2
7 x 8 = 56 96
3 2 6 6)56
2 ÷2 =9 1 54
9 6 ÷2 3 2
Dividing Fractions
So,
1
2 3 ÷ 2 = 1
8 93
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
½÷¾= 2/3
Great job!