# Illustrative Mathematics Grade 7, Unit 5, Lesson 5: Representing Subtraction

Learning Targets:

• I can explain the relationship between addition and subtraction of rational numbers.
• I can use a number line to subtract positive and negative numbers.

Related Pages
Illustrative Math

#### Lesson 5: Representing Subtraction

Let’s subtract signed numbers.

Illustrative Math Unit 7.5, Lesson 5 (printable worksheets)

#### Lesson 5 Summary

The following diagram shows how to use a number line to subtract positive and negative numbers.

#### Lesson 5.1 Equivalent Equations

For the equations in the second and third columns, write two more equations using the same numbers that express the same relationship in a different way. If you get stuck, consider looking at the examples in the first column.

#### Lesson 5.2 Subtraction with Number Lines

1. Here is an unfinished number line diagram that represents a sum of 8.
a. How long should the other arrow be?
b. For an equation that goes with this diagram, Mai writes 3 + ? = 8.
Tyler writes 8 - 3 = ?. Do you agree with either of them?
c. What is the unknown number? How do you know?
2. Here are two more unfinished diagrams that represent sums.
For each diagram:
a. What equation would Mai write if she used the same reasoning as before?
b. What equation would Tyler write if he used the same reasoning as before?
c. How long should the other arrow be?
d. What number would complete each equation? Be prepared to explain your reasoning.
3. Draw a number line diagram for (-8) - (-3) = ? What is the unknown number? How do you know?

1. Match each diagram to one of these expressions:
2. Which expressions in the first question have the same value? What do you notice?
3. Complete each of these tables. What do you notice?

#### Are you ready for more?

It is possible to make a new number system using only the numbers 0, 1, 2, and 3. We will write the symbols for adding and subtracting in this system like this: 2 ⊕ 1 = 3 and 2 ⊖ 1 = 1. The table shows some of the sums.

#### Lesson 5 Practice Problems

1. Write each subtraction equation as an addition equation.
a. a - 9 = 6
b. p - 20 = -30
c. z - (-12) = 15
d. x - (-7) = -10
2. Find each difference. If you get stuck, consider drawing a number line diagram.
a. 9 - 4
b. 4 - 9
c. 9 - (-4)
d. -9 - (-4)
e. -9 - 4
f. 4 - (-9)
g. -4 - (-9)
h. -4 - 9
3. A restaurant bill is \$59 and you pay \$72. What percentage gratuity did you pay?
4. Find the solution to each equation mentally.
a. 30 + a = 40
b. 500 + b = 200
c. -1 + c = -2
d. d + 3,567 = 0
5. One kilogram is 2.2 pounds. Complete the tables. What is the interpretation of the constant of proportionality in each case?

The Open Up Resources math curriculum is free to download from the Open Up Resources website and is also available from Illustrative Mathematics.

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