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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 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. Lets 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

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?

Isnt 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

4

x

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

4

x

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

1

3

4

4

1

How to Divide Fractions

- Step 2 Keep your first fraction.

3

1

3

4

1

1

How to Divide Fractions

- Step 3 Change the operation to multiplication.

3

1

3

x

4

1

1

How to Divide Fractions

- Step 4 Flip the second fraction.

3

1

3

4

x

1

4

1

1

How to Divide Fractions

- Step 5 Multiply the numerators, then multiple

the denominators.

3

4

12

x

1

1

1

How to Divide Fractions

- Step 6 Simplify (if possible).

3

4

12

12

x

1

1

1

Dividing Fractions An Example

2

3

9

4

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

9

3

27

8

x

8)

2

4

8

27

24

3

Dividing Fractions

So,

2

3

9

4

Dividing Fractions Another Example

2

1

2

3

8

Convert to improper fraction

Dividing Fractions

2

8

7

x

8

2

3

Keep

Change

Flip

Now, Multiply and Simplify

2

8

7

56

9

6

x

6)

2

3

6

56

54

2

2

1

9

9

2

6

2

3

Dividing Fractions

So,

2

1

2

8

3

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!