The document is a lesson on adding and subtracting integers: 1. It provides examples of adding and subtracting integers and finding the sums and differences. 2. It explains that to subtract an integer, you add its additive inverse, such as 4 - 9 = 4 + (-9) = -5. 3. It contains practice problems evaluating integer expressions and solving real-world problems involving adding and subtracting integers.

1. Course 2, Lesson 3-3
Add.
1. −4 + 4
2. 8 + (−7)
3. 3 + (−5)
Write an addition expression to describe each situation. Then
find each sum and explain the meaning.
4. A bird flies up 50 feet and swoops back down 10 feet.
5. Teresa owes her brother $14. She finds $10 and gives it to him.
6. What is the value of x + y if x = −3 and y = −9?

2. Course 2, Lesson 3-3
ANSWERS
1. 0
2. 1
3. −8
4. 50 + (−10) = 40; the bird is 40 feet above where it started.
5. −14 + 10 = −4; Theresa still owes her brother $4.
6. –12

3. WHAT happens when you add,
subtract, multiply, and divide integers?
The Number System
Course 2, Lesson 3-3

4. Course 2, Lesson 3-3 Common Core State Standards © Copyright 2010. National Governors Association Center for Best Practices and Council of
Chief State School Officers. All rights reserved.
The Number System
• 7.NS.1
Apply and extend previous understandings of addition and
subtraction to add and subtract rational numbers; represent
addition and subtraction on a horizontal or vertical number line
diagram.
• 7.NS.1c
Understand subtraction of rational numbers as adding the additive
inverse, p – q = p + (–q). Show that the distance between two
rational numbers on the number line is the absolute value of their
difference, and apply this principle in real-world contexts.

5. The Number System
• 7.NS.1d
Apply properties of operations as strategies to add and subtract
rational numbers.
• 7.NS.3
Solve real-world and mathematical problems involving the four
operations with rational numbers.
Course 2, Lesson 3-3 Common Core State Standards © Copyright 2010. National Governors Association Center for Best Practices and Council of
Chief State School Officers. All rights reserved.

6. Course 2, Lesson 3-3 Common Core State Standards © Copyright 2010. National Governors Association Center for Best Practices and Council of
Chief State School Officers. All rights reserved.
The Number System
Mathematical Practices
1 Make sense of problems and persevere in solving them.
2 Reason abstractly and quantitatively.
3 Construct viable arguments and critique the reasoning of others.
4 Model with mathematics.
5 Use appropriate tools strategically.
6 Attend to precision.
7 Look for and make use of structure.

7. • To subtract integers
• To solve real-world problems
involving integers
Course 2, Lesson 3-3
The Number System

8. Course 2, Lesson 3-3
The Number System
Words To subtract an integer, add its additive inverse.
Symbols p − q = p + (−q)
Examples 4 − 9 = 4 + (−9) = −5 7 − (−10) = 7 +(10) = 17

9. 1
Need Another Example?
2
3
4
Step-by-Step Example
1. Find 8 – 13.
8 – 13 = 8 + (–13) To subtract 13, add –13.
Simplify.= –5
Check by adding –5 + 13 = 8
?
8 = 8

10. Answer
Need Another Example?
Find 2 – 15.
–13

11. 1
Need Another Example?
2
3
4
Step-by-Step Example
2. Find –10 – 7.
To subtract 7, add –7.
Simplify.
–10 – 7 = –10 + (–7)
= –17
Check by adding –17 + 7 = –10
–10 = –10
?

12. Answer
Need Another Example?
Find –13 – 8.
–21

13. 1
Need Another Example?
2
Step-by-Step Example
3. Find 1 – (–2).
1 – (–2) = 1 + 2 To subtract –2, add 2.
Simplify.= 3

14. Answer
Need Another Example?
Find 12 – (–6).
18

15. 1
Need Another Example?
2
Step-by-Step Example
4. Find –10 – (–7).
To subtract –7, add 7.
Simplify.
–10 – (–7) = –10 + 7
= –3

16. Answer
Need Another Example?
Find –21 – (–8).
–13

17. Need Another Example?
Step-by-Step Example
1
2
5. Evaluate x – y if x = –6 and y = –5.
Replace x with –6 and y with –5.
To subtract –5, add 5.
x – y = –6 – (–5)
= –6 + 5
3 Simplify.= –1

18. Answer
Need Another Example?
Evaluate g – h if g = –2 and h = –7.
5

19. Need Another Example?
Step-by-Step Example
1
2
6. Evaluate m – n if m = –15 and n = 8.
Replace m with –15 and n with 8.
To subtract 8, add –8.
m – n = –15 – 8
= –15 + (–8)
3 Simplify.= –23

20. Answer
Need Another Example?
Evaluate a – b if a = –10 and b = 4.
–14

21. 1
Need Another Example?
2
3
4
5
Step-by-Step Example
7. The temperatures on the Moon vary from –173°C to 127°C.
Find the difference between the maximum and minimum
temperatures.
Simplify.
100 – (–200)
Subtract the lower temperature from the higher temperature.
To subtract –173, add 173.127 – (–173) = 127 + 173
Estimate
= 300
So, the difference between the temperatures is 300°C.

22. Answer
Need Another Example?
In Mongolia, the temperature can fall to –45°
Celsius in January. The temperature in July may
reach 40° Celsius. Find the difference between
these two temperatures in Mongolia.
85°C

23. How did what you learned
today help you answer the
WHAT happens when you add,
subtract, multiply, and divide integers?
Course 2, Lesson 3-3
The Number System

24. How did what you learned
today help you answer the
WHAT happens when you add,
subtract, multiply, and divide integers?
Course 2, Lesson 3-3
The Number System
Sample answers:
• When you subtract an integer, you add its additive
inverse.

25. Find the value of – 14 – 8.
Ratios and Proportional RelationshipsThe Number System
Course 2, Lesson 3-3