Grade 7 • Adding and Subtracting Fractions © 2020 Rubicon Publishing Inc. 1

Dear parent or guardian: This is a summary of the key ideas your child is learning in mathematics. You can use this summary as background as you support your child’s work.

Formal Addition and Subtraction of Fractions4Using a Rule to Add Fractions

• You can add fractions by creating equivalent fractions with the same denominator. The same denominator is often called a common denominator.

• When you use a grid and counters to model adding fractions with different denominators, the model shows a common denominator. For example, to model 1

3 + 38 , you can make a 3-by-8 grid, which has 24 cells.

You can model 13 by filling in 1 of the 3 rows. So, you are renaming 1

3 as 824.

You can model 38

by filling in 3 of the 8 columns. So, you are renaming 38

as 924

. When you move the counters so that each cell has only one counter, you can see that 8

24 + 9

24 = 17

24.

• To choose a common denominator without a model, you can multiply the two given denominators. For example, for 1

3 + 38 , you could multiply 3 by 8 to get a common denominator

of 24.

So, 1

3 + 38 is the same as 8

24 + 924, which is 17

24.

13

8=

× 8

× 8

2438

9=

× 3

× 3

24

Grade 7 • Adding and Subtracting Fractions © 2020 Rubicon Publishing Inc. 2

4 Formal Addition and Subtraction of Fractions (continued)

Using a Rule to Add Fractions (continued)

• Sometimes you can find a common denominator without multiplying. For example, for 3

4 + 58 , you can rename 3

4 as 68 .

You can show the equivalent fractions with fraction strips. Now that you have a common denominator, you can add more easily: 68 + 5

8 = 118 .

• You can also use a number line to show the common denominator as well as the addition. For example, you can show 3

8 + 23 in terms of 24ths on a number line.

You can see that 38 =

924 and that 2

3 = 1624.

So, you can add 1624

to 924

on the 24ths line.

⅛ ⅛ ⅛ ⅛ ⅛ ⅛

¼ ¼ ¼

0 138

0 1

1

23

924

1624

0 1 124

1624+

Grade 7 • Adding and Subtracting Fractions © 2020 Rubicon Publishing Inc. 3

4 Formal Addition and Subtraction of Fractions (continued)

Using a Rule to Subtract Fractions

• You can subtract fractions by creating equivalent fractions with the same denominator.

• When you use a grid and counters to model subtracting fractions with different denominators, the model shows a common denominator. For example, to model 4

5 − 13 , you can make a 5-by-3 grid, which has 15 cells.

You can model 45 by filling in 4 of the 5 rows. So, you are renaming 4

5 as 1215.

You can model 13 by filling in 1 of the 3 columns. So, you are renaming 1

3 as 515 .

Since both fractions have the same denominator now, you can subtract more easily: 1215 − 5

15 = 715 .

• To find a common denominator without a model, you can multiply the two given denominators. For example, for 4

5 − 13 , you could multiply 5 by 3 to get a common denominator

of 15. So, 4

5 − 13 is the same as 12

15 − 515 , which is 7

15 .

45

12=

× 3

× 3

1513

5=

× 5

× 5

15

Grade 7 • Adding and Subtracting Fractions © 2020 Rubicon Publishing Inc. 4

4 Formal Addition and Subtraction of Fractions (continued)

Using a Rule to Subtract Fractions (continued)

• Sometimes you can find a common denominator without multiplying. For example, for 6

5 − 45 , you could use 12 as the common denominator.

You can show the equivalent fractions with fraction strips.

65 is the same as 10

12 : 34 is the same as 9

12 : 1012 − 9

12 = 112

• You can use a number line to show the common denominator as well as the subtraction. For example, you can show 6

5 − 34 in terms of 12ths on a number line.

You can see that 65 = 10

12 and that 34

= 912 .

So, you can subtract 912

from 1012

on the 12ths line.

1 1 2 1 1 2 1 1 2 1 1 2 1 1 2 1 1 2 1 1 2 1 1 2 1 1 2 1 1 2

⅙ ⅙ ⅙ ⅙ ⅙

1 1 2 1 1 2 1 1 2 1 1 2 1 1 2 1 1 2 1 1 2 1 1 2 1 1 2

¼ ¼ ¼

0 156

0 134

112

1012

912

10

112−

Grade 7 • Adding and Subtracting Fractions © 2020 Rubicon Publishing Inc. 5

4 Formal Addition and Subtraction of Fractions (continued)

Notes

It is important to remember that it’s not that you can’t add fractions with different denominators; it’s just that it’s not easy to visualize the exact answer without using a model.

For example, you can add 35 + 4

7 by thinking of the number 35, determining 35

of it (as 21) and 47 of it (as 20), and then add the two numbers to get 41. Then you

have to remember the unit is 35ths, so it’s 4135. You have actually created equivalent

fractions, but you might not even realize it.

Definitions

common denominator: a denominator shared by two or more fractions

equivalent fractions: fractions that name the same part of the same whole or are in the same position on a number line; for example, 2

3 and 64 are equivalent

fractions