DIVISION OF

FRACTIONS

IMPORTANT: We always want to remember that dividing is asking “how many of that fit into this?“.  In 10 ÷ 5, we are really asking “how many 5′s fit into 10?”  This is the same question we ask when dividing fractions: “how many of the second fraction fit into the first?”

I have 6 cookies. I put two (2) cookies in a bag. How many bags do I need?

Problem:

Pictorial Representation I say I write I can write as

2

1

x1

1

1

22

1

2or

x1

2

1

24

1

4or2

1

6 ÷ 2 = 3

= 2 bags with half a cookie each

1 ÷

2 ÷ =4 bags with half a cookie each

A serving is cookie. How

many servings can I make from 2

cookies?

2

1

I say: How many cookies am I going to cut into halves?

Representation:

Cut by =

1 432

I write: 2 ÷ = 42

1

1. A serving is cookie. How many servings can I

make from 1 cookie?2

1

2. A serving is cookie. How many servings can I

make from 3 cookies?2

1

3. A serving is cookie. How many servings can I

make from cookie?2

1

4

3

3. A serving is cookie. How many servings can I

make from cookie?2

1

8

7

TASK 2

Tony cuts a meter piece of wood and

divides it into 3 pieces. How long is each piece

of wood?

2

1

meter2

1

m6

1 m6

1m6

1

How many halves are

there in six – fourths?

Let’s say that we wanted to find (2/5) ÷ (1/8).  Convention tells us to “flip the 1/8 and multiply across”.  But can we show this with pictures?

This picture below represents 2/5.

Out of the 5 rows we have 2 orange ones.

Now to address “divide by 1/8″ we want to divide the entire area into 8 vertical columns (8ths)….

… and take 1 of these columns (because we want 1/8)….

The darker line surrounds 1 out of the 8 vertical columns we had drawn in the previous step.  This area – 1×5 or 5 – will be our answer’s denominator.  But what will the answer’s numerator be?

In the above picture, the “extra” orange boxes have been colored green to show that they are outside the bounded area.  We now have to figure out how many sets of 5 (from area 1×5) we have. 

We have 3 sets of 5 and 1 left over, or 3 and 1/5.  This answer’s improper fraction is16/5, which is the number of colored boxes over the total number of boxes within the bounded 1×5 region.

Closing Activity

Make an illustration to find each quotient. Express your answer in lowest terms.

3

21. ÷

4

1= _______

7

52. ÷

12

1= _______

13

43. ÷

13

2= _______

22

54. ÷

11

5= _______

5

25. ÷

18

5= _______

13

26. ÷

5

1= _______

4

37. ÷

7

5= _______

12

18. ÷

13

2= _______

13

29. ÷

12

5= _______

2

110. ÷

4

3= _______

Doing and Undoing

Dividend Divisor

6

12

Divide by 2

1

5

2

6

2

7

1

5

3

Supply the missing number in the [ ] to make the sentence correct.

1. [ ] ÷5

32 =

5

422. ÷

5

22 = [ ] ÷

3. [ ] ÷12

12 =

4. =

12

14 ÷

5

45

7

38

7

33 ÷

12

51

2

12 ÷

4

32 [ ] ÷

7

35

3. [ ] ÷5

41 =

12

13 ÷

5

21