Adding and Subtracting Fractions

Let’s look at a model of adding fractions.Example:

21

41 First we need a fraction bar

representation of each addend.

We will stack these so that the shading of the second starts where the shading of the first ends.

To find the answer we need to change the second to the same number of sections that the first has.

Find the total of the shaded area.4

33 sections out of whole

441

ExampleFind

41

87

Remember:•Find fraction bars to represent both addends with the same number of sections•Stack these•Read answer

81

89 1

Let’s look at subtraction…Example

We are going to look at a take away model.85

211

First build only the first term.

Exchange these bars for an equivalent model using eighths.

Now we need to imagine taking 5/8 away and find what will be left.

87

Once your fractions have a common denominator, you will add or subtract the numerators and keep the denominators the same.

5

2

2

1

Our models show us that when adding and subtracting fractions, we need a common denominator.

10

9

10

4

10

5

Example #1

Example #25

4

3

1

152

1

15

17

15

12

15

5

Example #3

8

3

4

3

6

1

2471

24

31

24

9

24

22

24

9

24

18

24

4

Example #4

5

2

6

5

30

13

30

12

30

25

Example #54

1

9

5

12

11

18

11

36

22

36

9

36

13

36

9

36

20

36

33

Example #6Felicia is making cookies for her brother’s

birthday party. Her recipe calls for ¾ cups of brown sugar. She only has ⅓ cup left in the bag. How much brown sugar will she need to borrow from her neighbor to make the cookies?

3

1

4

3

12

512

4

12

9