Lesson
9 A Mix of Addition and Subtraction
A Mix of Addition and Subtraction
What are the strategies for integer addition
and subtraction?
We have discussed the different methods we can use to solve integer
addition and subtraction. One thing we have learned to do is change
subtraction to “add the opposite.” This helps us with difficult situations,
such as “minus a negative.” We learned to use number lines to help us
with these problems.
There are two main questions we need to ask ourselves when we have a
mix of addition and subtraction problems.
• What is the rule? If it’s addition, we move to the next step. If it’s
subtraction, we “add the opposite.”
• Are we going in the right direction? This is where the number
line is helpful. As long as we remember what direction we are
going, we have a good chance of solving the problem successfully.
582 Unit 8 • Lesson 9
Lesson 9
Let’s look at a series of problems that are very similar. In fact, they
only differ in signs and operations. These problems show us how to
apply the rules for integer addition and subtraction. They also show
how important number lines and directional arrows are in solving
these problems.
4+ 3
4 + −3
−4 + 3
−4 + −3
S ​addition
4− 3
4 − −3
−4 − 3
−4 − −3
S ​subtraction
These problems all look very similar, but they differ in some very
important ways. We will use number lines to demonstrate. Example 1
presents a series of problems that show the important differences in
the operations.
Example 1
Use number lines to think about adding and subtracting integers.
Problem: 4 + 3 = 7
It is addition, and we move in a positive direction.
0
1
2
3
4
5
6
7
Unit 8 • Lesson 9 583
Lesson 9
Problem: 4 + −3 = 1
It is still addition, but this time we move in a positive direction and then
a negative direction.
0
1
2
3
4
5
6
7
Problem: −4 + 3 = −1
It is still addition, but this time we move in a negative direction and then
a positive direction.
−4
−3
−2
−1
0
1
2
3
Problem: −4 + −3 = −7
It is still addition, but this time we move only in a negative direction.
−7
−6
−5
−4
−3
−2
−1
0
1
2
Problem: 4 − 3 = 1
Now we are looking at subtraction. We change it to add the opposite. This is the same
as 4 + −3.
Rewrite as: 4 + −3 = 1
0
584 Unit 8 • Lesson 9
1
2
3
4
5
6
7
Lesson 9
Problem: 4 − −3 = 7
Because it is subtraction, we change it to add the opposite. This is the same as 4 + 3.
Rewrite as: 4 + 3 = 7
0
1
2
3
4
5
6
7
Problem: −4 − 3 = −7
Because it is subtraction, we change it to add the opposite. This is the same
as −4 + −3.
Rewrite as: −4 + −3 = −7
−7
−6
−5
−4
−3
−2
−1
0
1
2
Problem: −4 − −3 = −1
Since it is subtraction, we change it to add the opposite.
This is the same as −4 + 3.
Rewrite as: −4 + 3 = −1
It is still addition, but this time we move in a negative direction and then a positive
direction.
−4
−3
−2
−1
0
1
2
3
Keeping the rules straight and knowing which direction we are moving
on the number line will help us solve these problems, especially when
there is a mix of problems including both addition and subtraction.
Unit 8 • Lesson 9 585
Lesson 9
The Red & Black Game
Playing the Red & Black Game will help us understand these rules better.
We use black cards to represent positive integers and red cards to represent
negative integers.
The directions are in your Interactive Text.
Apply Skills
Turn to Interactive Text,
page 300.
586 Unit 8 • Lesson 9
Reinforce Understanding
Use the mBook Study Guide
to review lesson concepts.
Lesson 9
Homework
Activity 1
Solve the addition and subtraction problems with positive and negative
numbers. For the subtraction problems, remember to add the opposite.
1. 2 − −3 ​
2. −5 + −1 ​
3. −8 − 2 ​
4. −9 − −13 ​
5. −2 + −1
6. 10 − 7 ​
7. −3 + −2 ​
8. −9 − −9 ​
9. 3 + −4 ​
10. 10 − 6 ​
Activity 2
Look at the five cards dealt in each problem and tell what the final score
would be. Remember that the ace is 1 and the king and queen are 10.
1.
fwDRy
2.
cKtui
3.
BFUXp
Copyright 2010 by Cambium Learning Sopris West®. All rights reserved. Permission is granted to reproduce this page for student use.
Unit 8 • Lesson 9 587
Lesson 9
Homework
Activity 3
Look at the five cards dealt in each problem and tell what the final score
would be if you are subtracting.
1.

2.
OzM
3.
FgqHP
Activity 4 • Distributed Practice
Solve.
1. Convert 7.2% to a decimal number. ​
2
2. Write 4 as a decimal number. ​
7
1,000
3. Write 0.007 as a fraction. ​
4. 4.85 − 2.69 ​
1
2
11
5. 4 + 3 ​
12
1
1
6. 8 2 − 4 4 ​
1
4
7. 16.2 ÷ 0.2 ​
8.
588 4
5
÷ 14 ​
Unit 8 • Lesson 9
1
5
Copyright 2010 by Cambium Learning Sopris West®. All rights reserved. Permission is granted to reproduce this page for student use.