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 PracticeWhen 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

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?”

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

Dividing a Whole Number by a Fraction

Can you see how you could manipulate the fractions to get an answer of 12?

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?

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

x12

41

Basically, in order to divide fractions we will have to multiply.

12

14

÷ =

Dividing a Fraction by a Fraction

x12

41

From this point, the problem can be solved in the way that you did for multiplying fractions.

12=

21

= 2

How to Divide Fractions

• Step 1 – Convert whole numbers and mixed numbers to improper fractions.

÷4

31

1÷43 =1

This example is from a prior slide.

How to Divide Fractions

• Step 2 – Keep your first fraction.

÷4

31

1 = 31

How to Divide Fractions

• Step 3 – Change the operation to multiplication.

÷4

31

1 = 31 x

How to Divide Fractions

• Step 4 – Flip the second fraction.

÷

431

1 = 31 x

14

How to Divide Fractions

• Step 5 – Multiply the numerators, then multiple the denominators.

x 131

4 = 121

How to Divide Fractions

• Step 6 – Simplify (if possible).

x 131

4 = 121 =12

Dividing Fractions – An Example

29

34 =÷

Since both are fractions, now you can Keep (1st fraction), Change (the operation to multiplication), and Flip (2nd Fraction)…

Now, Multiply and Simplify

92

34 = 27

8 8)273x

243

38

Dividing Fractions

29

34 =÷ 3 3

8

So,

Dividing Fractions – Another Example

28

13

=÷2Convert to improper fraction

28

73 =÷ 8

273 x

KeepChange

Flip

Dividing Fractions

Now, Multiply and Simplify

82

73 = 56

6 6)569x

542

26

9 26

÷ 22

=9 13÷

Dividing Fractions

28 =÷ 9 1

3

So, 132

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!