Division of Fractions

Created by: Leslie Fenton

The Division Principle

8 ÷ 4 = 2Dividen

d

Divisor

Quotient

Dividend

: The amount you want to divide up: The number you divide by

Quotient : The answer after you divide one number by another

The Division Principle

8 ÷ 4 = 2Dividen

d

Divisor

Quotient

21 3 4 5 6 7 8

Total number to be divided

Number of groups is the quotient.

1 2

Num

ber i

n ea

ch

grou

p is th

e

divi

sor.

The Division of Fractions Principle

• IT IS THE SAME !! 2 ÷ 1/2 = 4

2

1

Tota

l num

ber t

o be

divi

ded

The number in each group is ½ so each group needs to be cut in half.

The number of groups is the quotient.

1 2

3 4

Another problem Dividing Fractions

2 ÷ 1/3 =

2

1

Tota

l num

ber t

o be

divi

ded

Need to cut each group into thirds.

Number of total groups

6?

Is there anything you notice about dividing by a fraction that is different from dividing with whole numbers?

1/31/3

1/3

1/31/3

1/3

1 2

3

4 5

6

You already know this…If it takes 2 cups of cheese for half a pizza,

How much cheese will it take for a whole pizza?

Think about it……

Cups of cheese 2 ?

pizza ½ 1

x 2

x 2

Cups of cheese 2 4

pizza ½ 1

2 1

24

Look for a pattern in the following problems.

Divide this

2 1

36

Cups of cheese 2 ?

pizza 1/3 1

x 3

x 3

Cups of cheese 2 6

pizza 1/3 1

Look for the pattern.

Divide this

1 1

55

Cups of cheese 1 ?

pizza 1/5 1

x 5

x 5

Cups of cheese 1 5

pizza 1/5 1

Do you see a pattern?

The pattern lies with what we multiply by to get the solutions.

x 3

x 3

Cups of cheese 2 6pizza 1/3 1

x 2

x 2

Cups of cheese 2 4pizza ½ 1

x 5

x 5

Cups of cheese 1 5pizza 1/5 1

How is the number we multiply by related to the fraction we are dividing by?

The number we multiply by is the RECIPROCAL of the fraction we are dividing by.

Reciprocal

a number that you multiply by so the result equals 1.

The easiest way to find the reciprocal of a fraction is to just flip the fraction over.

1/2 X 2 = 1

1/4 X 4 = 11/3 X 3 = 12/5 X 5/2 = 1

Determine the algorithm

• What are the “rules” for dividing fractions?

– Take the reciprocal of the fraction you are dividing by

– And multiply

A look at some simple problems

2 1

2

2 1

3

11

5

2 2

5

2 1

5

Complete the problems on your whiteboard.Show your work

Step Up a Notch w/ more problemsComplete the problems on your whiteboard.

Show your work

2 2

3

6 3

4

3 3

4

1 1/4 1

2

Stumper Problems

2

3

1

3

Show What You Know

• 6-7 Skills Practice: Dividing Fractions & Mixed Numbers– Show all steps by stacking– Write in simplest form– Square off your answer– Do 2/5 of the problems (assignment has 50 problems)

– Above 80 – your done– 79 or lower – review division strategies