1. Adding and Subtracting Integers
Lesson 1.1.2

2. Adding and Subtracting Integers
Lesson
1.1.2
Adding and Subtracting Integers
California Standard:
Number Sense 2.3
Solve addition, subtraction, multiplication, and division problems, including those arising in concrete situations, that use positive and negative integers and combinations of these operations.
What it means for you:
You’ll learn to add positive and negative numbers to integers.
Key words:
positive
negative
integer

3. Adding and Subtracting Integers
Lesson
1.1.2
Adding and Subtracting Integers
You’ve met positive and negative numbers, and you know how to arrange them on the number line. 1 2 3 4 –1 –2 –3 –4
This Lesson covers addition and subtraction of integers, including negative numbers.

4. Adding and Subtracting Integers
Lesson
1.1.2
Adding and Subtracting Integers
Adding a Positive Moves Right on the Number Line
In the last Lesson, you saw that numbers on the number line are greater the farther to the right they are. 1 2 3 4 –1 –2 –3 –4
greater
smaller
When you add a positive integer to any number, you’re making it greater, so you move to the right.
To add a positive integer, move that number of positions to the right on the number line.
It doesn’t make any difference whether the original number is positive or negative — you always move to the right.

5. Adding and Subtracting Integers
Lesson
1.1.2
Adding and Subtracting Integers
Example 1
Using the number line, add 9 to –4.
Solution +1 +2 +3 +4 +5 +6 +7 +8 +9 1 2 3 4 –1 –2 –3 –4 5 –5 6 7
Counting 9 spaces to the right of –4 on the number line shows that the answer is 5.
Solution follows…

6. Adding and Subtracting Integers
Lesson
1.1.2
Adding and Subtracting Integers
Adding a Negative Moves Left on the Number Line
When you add a negative integer, move that number of positions to the left on the number line.
When you’re adding a negative number, it doesn’t matter whether you’re adding it to a positive or negative number — you always move to the left.

7. Adding and Subtracting Integers
Lesson
1.1.2
Adding and Subtracting Integers
Example 2
Using the number line, add –6 to 5.
Solution 6 5 4 3 2 1 1 2 3 4 –1 –2 –3 –4 5 –5 6 7
Counting 6 spaces to the left of 5 on the number line shows that the answer is –1.
Solution follows…

8. Adding and Subtracting Integers
Lesson
1.1.2
Adding and Subtracting Integers
Example 3
Using the number line, add –5 to –1.
Solution 5 4 3 2 1 –1 1 2 3 –2 –3 –4 –5 4 –6 5 6
Counting 5 spaces to the left of –1 on the number line shows that the answer is –6.
Solution follows…

9. Adding and Subtracting Integers
Lesson
1.1.2
Adding and Subtracting Integers
Guided Practice
Answer the following Exercises without using a calculator. Use a number line to help. 8 9 10 11 12 7 6 5 4 13 14 15 +1 +2 +3
2. –2 + 2
3. –8 + 4
= 10 1 2 3 4 –1 –2 –3 –4 5 6 7 +1 +2
= 0 –6 –5 –4 –3 –2 –7 –8 –9
–10 –1 1 +1 +2 +3 +4
= –4 1 2 3 4 –1 –2 –3 –4 5 6 7 +1 +2 +3
= 4
Solution follows…

10. Adding and Subtracting Integers
Lesson
1.1.2
Adding and Subtracting Integers
Guided Practice
Answer the following Exercises without using a calculator. Use a number line to help.
–78
–77
–76
–75
–74
–79
–80
–81
–82
–73
–72
–71 +1 +2 +3 +4 +5 +6 +7 +8
5. –81 + 8
6. –9 + 11
(–2)
(–10)
= –73 –5 –4 –3 –2 –1 –6 –7 –8 –9 1 2 +1 +2 +3 +4 +5 +6 +7 +8 +9
+10
+11
= 2 6 7 8 9 10 5 4 3 2 11 12 13 1
= 7 28 29 30 31 32 27 26 25 24 33 34 35 2 1 4 3 6 5 8 7 10 9
= 25
Solution follows…

11. Adding and Subtracting Integers
Lesson
1.1.2
Adding and Subtracting Integers
Guided Practice
Answer the following Exercises without using a calculator. Use a number line to help. –6 –5 –4 –3 –2 –7 –8 –9
–10 –1 1
9. –5 + (–1)
(–5)
(–10)
12. –15 + (–7)
= –6 –3 –2 –1 1 –4 –5 –6 –7 2 3 4 5
= –5 29 30 31 32 33 28 27 26 25 34 35 36 2 1 4 3 5 7 6 9 8 10
= 26
–20
–19
–18
–17
–16
–21
–22
–23
–24
–15
–14
–13 2 1 4 3 5 7 6
= –22
Solution follows…

12. Adding and Subtracting Integers
Lesson
1.1.2
Adding and Subtracting Integers
Subtracting a Positive is Like Adding a Negative
You already know that to add a negative integer, you move that number of positions to the left on the number line.
The method for subtracting a positive integer is exactly the same.

13. Adding and Subtracting Integers
Lesson
1.1.2
Adding and Subtracting Integers
Example 4
Using the number line, calculate 8 – 2.
Solution 2 1 4 5 6 7 8 3 2 1 9 10
The 2 tells you that you need to move 2 steps, and the “–” sign tells you that you need to move left.
So the answer is 6.
Solution follows…

14. Adding and Subtracting Integers
Lesson
1.1.2
Adding and Subtracting Integers
Guided Practice
Answer the following Exercises without using a calculator. Use a number line to help.
13. 7 – 3
14. –1 – 10
15. 8 – 8 3 4 5 6 7 2 1 –1 8 9 10
= 4 –8 –7 –6 –5 –4 –9
–10
–11
–12 –3 –2 –1 2 1 4 3 5 7 6 9 8 10
= –11 3 4 5 6 7 2 1 –1 8 9 10
= 0
Solution follows…

15. Adding and Subtracting Integers
Lesson
1.1.2
Adding and Subtracting Integers
Guided Practice
Answer the following Exercises without using a calculator. Use a number line to help.
16. 3 – 8
17. –2 – 9
18. 1 – 10 –2 –1 1 2 –3 –4 –5 –6 3 4 5 7 6 8
= –5 –8 –7 –6 –5 –4 –9
–10
–11
–12 –3 –2 –1 2 1 4 3 5 7 6 9 8
= –11 –6 –5 –4 –3 –2 –7 –8 –9
–10 –1 1 2 4 3 5 7 6 9 8 10
= –9
Solution follows…

16. Adding and Subtracting Integers
Lesson
1.1.2
Adding and Subtracting Integers
Subtracting a Negative Is Like Adding a Positive
You’ve already seen that adding a negative means you move left on the number line. So subtracting a negative must mean you move right on the number line.
Another way of saying this is that subtracting a negative is the same as adding a positive.

17. Adding and Subtracting Integers
Lesson
1.1.2
Adding and Subtracting Integers
Example 5
Calculate 8 – (–3).
Solution
8 – (–3)
This – sign tells you to go left on the number line…
…but this – sign reverses the direction again. 7 8 9 10 11 12 +1 +2 +3
You end up moving 3 steps right on the number line. So you can just write 8 – (–3) as = 11.
Solution follows…

18. Adding and Subtracting Integers
Lesson
1.1.2
Adding and Subtracting Integers
Guided Practice
Write Exercises 19–24 as additions, then find the solutions.
– (–9)
– (–10)
21. –9 – (–15)
22. 4 – (–4)
23. –4 – (–8)
24. –26 – (–17)
= 23
= 33
– = 6
4 + 4 = 8
–4 + 8 = 4
– = –9
Solution follows…

19. Adding and Subtracting Integers
Lesson
1.1.2
Adding and Subtracting Integers
Independent Practice
1. The water level of a lake in early April was 3 inches above normal.
The water level had dropped to –4 inches below normal by early May.
What integer can be added to 3 to get the water level, in inches, in early May? –7
Write each of Exercises 2–5 as an addition problem.
2. 4 – – 8
4. –1 – – 5
4 + (–3)
7 + (–8)
–1 + (–26)
4 + (–5)
Solution follows…

20. Adding and Subtracting Integers
Lesson
1.1.2
Adding and Subtracting Integers
Independent Practice
Write each of Exercises 6–9 as a subtraction problem.
(–9) (–3)
(–1) (–348)
5 – 9
1 – 3
2 – 1
433 – 348
Find the answer to each of Exercises 10–13.
(–15) – 9
– (–3)
–11 9 29 18
Solution follows…

21. Adding and Subtracting Integers
Lesson
1.1.2
Adding and Subtracting Integers
Round Up
Adding to and subtracting from integers is a matter of deciding which direction to move, then moving the correct distance.
When you’re deciding whether to go left or right you only need to think about whether you’re adding a positive or negative number — it doesn’t matter what you’re adding it to.