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.

Adding and Subtracting Fractions With the Same Denominator1

Seeing Addition or Subtraction in the Representation of a Fraction

When you represent a fraction, you can sometimes see a fraction sum or difference right in the model.

For example, this picture shows that 58 = 2

8 + 38 .

You can also see that 88 − 5

8 = 38 because the model shows that you have to add

38 to the coloured sections ( 5

8 ) to get the whole ( 88 ).

In this picture, you can see that 48 = 2

5 + 25 and that 5

5 − 45 = 1

5 .

Adding Fractions With the Same Denominator

You can think of a fraction as copies of a unit based on the denominator. For example, 3

5 is 3 units of 15 .

When you add fractions with the same denominator, it is helpful to think this way.

For example, you might think of 310 + 4

10 like this: 3 tenths + 4 tenths is 7 tenths, just as 3 bananas + 4 bananas is 7 bananas or 3 nickels + 4 nickels is 7 nickels.

In a picture, you can see that if you fill 3 of the tenths with white counters and 4 with shaded counters, you have filled 7 of the tenths with counters.

310 + 4

10 = 710

0

15

25

45

55

15

15

15

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

1 Adding and Subtracting Fractions With the Same Denominator (continued)

Subtracting Fractions With the Same Denominator

When you subtract fractions with the same denominator, it might also be helpful to think of the fraction in terms of a unit based on the denominator.

For example, you might think of 65 − 6

1 like this: 5 sixths − 1 sixth is 4 sixths, just as 5 bananas − 1 banana is 4 bananas or 5 nickels − 1 nickel is 4 nickels.

In a picture, you can see that if 5 of 6 sections are filled with counters and you remove 1 of the counters, 4 of the 6 sections are still filled.

65 − 6

1 = 64

Or you could think of 65 − 6

1 as what to add to 1 sixth to get to 5 sixths. It’s 4 sixths.

65 − 6

1 = 64

Definitions

denominator: the number below the bar in a fraction, which tells the number of equal parts in the whole; for example, the denominator of 3

4 is 4, which means that the whole is divided into 4 equal parts

numerator: the number above the bar in a fraction, which tells the number of equal parts that the fraction describes; for example, the numerator of 3

4 is 3, which means that 3 out of 4 equal parts are being described