1. 2-1
Integers
Course 2
Warm Up
Problem of the Day
Lesson Presentation

2. Warm Up
Compare. Use <, >, or =
>
<
>
>

3. Problem of the Day
Place 4, 5, 6, 7, 8, and 9 in the empty circles so that each side has the same sum. 1 6 9 7 5 3 4 8 2

4. Learn to compare and order integers and to determine absolute value.

5. Vocabulary
opposite
integer
absolute value

6. The opposite of a number is the same
distance from 0 on a number line as the
original number, but on the other side
of 0. Zero is its own opposite.
–4 and 4 are opposites –4 4 • •
–5–4–3–2–1 0
Negative integers
Positive integers
0 is neither positive
nor negative

7. The integers are the set of whole numbers and their opposites
The integers are the set of whole numbers and their opposites. By using integers, you can express elevations above, below, and at sea level. Sea level has an elevation of 0 feet.
The whole numbers are the counting numbers and zero: 0, 1, 2, 3,
Remember!

8. Graph the integer -7 and its opposite on a number line.
Additional Example 1: Graphing Integers and Their Opposites on a Number Line
Graph the integer -7 and its opposite on a number line.
7 units units
–7–6–5–4–3–2–1 0
The opposite of –7 is 7.

9. Graph the integer -5 and its opposite on a number line.
Check It Out: Example 1
Graph the integer -5 and its opposite on a number line.
5 units units
–7–6–5–4–3–2–1 0
The opposite of –5 is 5.

10. You can compare and order integers by graphing them on a number line
You can compare and order integers by graphing them on a number line. Integers increase in value as you move to the right along a number line. They decrease in value as you move to the left.

11. Additional Example 2A: Comparing Integers Using a Number Line
Compare the integers. Use < or >.
>
–7–6–5–4–3–2–1 0
4 is farther to the right than -4, so 4 > -4.
The symbol < means “is less than,” and the symbol > means “is greater than.”
Remember!

12. Additional Example 2B: Comparing Integers Using a Number Line
Compare the integers. Use < or >.
>
-9 is farther to the right than -15, so -15 < -9.

13. Compare the integers. Use < or >.
Check It Out: Example 2A
Compare the integers. Use < or >.
>
–7–6–5–4–3–2–1 0
6 is farther to the right than -6, so 6 > -6.

14. Compare the integers. Use < or >.
Check It Out: Example 2B
Compare the integers. Use < or >.
>
-4 is farther to the right than -11, so -4 > -11.

15. Additional Example 3: Ordering Integers Using a Number Line.
Use a number line to order the integers from least to greatest.
–3, 6, –5, 2, 0, –8
–8 –7–6 –5–4 –3 –2 –1 0
The numbers in order from least to greatest are –8, –5, –3, 0, 2, and 6.

16. Use a number line to order the integers from least to greatest.
Check It Out: Example 3
Use a number line to order the integers from least to greatest.
–5, 4, –3, 2, –1, –2
–8 –7–6–5–4 –3–2 –1 0
The numbers in order from least to greatest are –5, –3, –2, –1, 2, and 4.

17. A number’s absolute value is its distance from 0 on a number line
A number’s absolute value is its distance from 0 on a number line. Since distance can never be negative, absolute values are never negative. They are always positive or zero.

18. Additional Example 4A: Finding Absolute Value
Use a number line to find each absolute value.
|8|
8 units
–8 –7–6–5–4 –3–2 –1 0
8 is 8 units from 0, so |8| = 8.

19. The symbol is read as “the absolute value of
The symbol is read as “the absolute value of.” For example -3 is the absolute value of -3.
Reading Math

20. Additional Example 4B: Finding Absolute Value
Use a number line to find each absolute value.
|–12|
12 units
–12 –11 –10 –9 –8 –7 –6 –5 –4 –3 –2 –
–12 is 12 units from 0, so |–12| = 12.

21. Use a number line to find each absolute value.
Check It Out: Example 4A
Use a number line to find each absolute value.
|3|
3 units
–8 –7–6–5–4 –3–2 –1 0
3 is 3 units from 0, so |3| = 3.

22. Use a number line to find the absolute value.
Check It Out: Example 4B
Use a number line to find the absolute value.
|–9|
9 units
–12 –11 –10 –9 –8 –7 –6 –5 –4 –3 –2 –
–9 is 9 units from 0, so |–9| = 9.

23. Compare. Use <, >, or =. 1. –32 32 2. 26 |–26| 3. –8 –12
Lesson Quiz: Part I
Compare. Use <, >, or =.
1. –
|–26|
3. –8 –12
4. Use a number line to order the integers –2, 3, –4, 5, and –1 from least to greatest.
< =
> •
–5–4 –3 –2–1 0
–4, –2, –1, 3, 5

24. Use a number line to find the absolute value. 5. -3
Lesson Quiz: Part II
Use a number line to find the absolute value.
3 units •
–5 –4 –3 –2 –1 0 3

25. 2-2 Adding Integers Warm Up Problem of the Day Lesson Presentation
Course 2
Warm Up
Problem of the Day
Lesson Presentation

26. 2-2 Adding Integers Warm Up Find each absolute value. 1. |8| 2. |–6|
Course 2
2-2
Adding Integers
Warm Up
Find each absolute value.
1. |8|
2. |–6|
3. |–9|
4. |–7|
5. |–12|
6. |53| 8 6 9 7 12 53

27. 2-2 Adding Integers Problem of the Day
Course 2
2-2
Adding Integers
Problem of the Day
Jan’s yearly salary is $30,000, and it will be increased by $3,000 each year. Phil’s salary is $20,000, and it will be increased by $5,000 each year. In how many years will Jan and Phil both have the same yearly salary?
5 years

28. Course 2
2-2
Adding Integers
Learn to add integers.

29. Additional Example 1A: Modeling Integer Addition
Course 2
2-2
Adding Integers
Additional Example 1A: Modeling Integer Addition
Use a number line to find each sum.
–7 + (–4)
+(–4) –7 2
–14 –12 –10 –8 –6 –4 –
Start at 0. Move left 7 spaces. Then move left
4 more spaces.
–7 + (–4) = –11

30. Additional Example 1B: Modeling Integer Addition
Course 2
2-2
Adding Integers
Additional Example 1B: Modeling Integer Addition
Use a number line to find each sum. – 19
–12
–12 –10 –8 –6 –4 –
Start at 0. Move left 12 spaces. Then move
right 19 spaces.
– = 7

31. Insert Lesson Title Here
Course 2
2-2
Adding Integers
Insert Lesson Title Here
Check It Out: Example 1A
Use a number line to find each sum.
–4 + (–5)
+(–5) –4 2
–14 –12 –10 –8 –6 –4 –
Start at 0. Move left 4 spaces. Then move left
5 more spaces.
–4 + (–5) = –9

32. Insert Lesson Title Here
Course 2
2-2
Adding Integers
Insert Lesson Title Here
Check It Out: Example 1B
Use a number line to find each sum.
–7 + 12 12 –7
–12 –10 –8 –6 –4 –
Start at 0. Move left 7 spaces. Then move
right 12 spaces.
– = 5

33. Adding Integers 2-2 Adding Integers
Course 2
2-2
Adding Integers
Adding Integers
To add two integers with the same sign, find the sum of their absolute values. Use the sign of the two integers.
To add two integers with different signs, find the difference of their absolute values. Use the sign of the integer with the greater absolute value.

34. Additional Example 2A: Adding Integers Using Absolute Values
Course 2
2-2
Adding Integers
Additional Example 2A: Adding Integers Using Absolute Values
Find each sum.
–4 + 8
The signs are different. Find the difference of the absolute values.
–4 + 8
Think: 8 – 4 = 4.
Use the sign of the integer with the
greater absolute value. 4

35. Additional Example 2B: Adding Integers Using Absolute Values
Course 2
2-2
Adding Integers
Additional Example 2B: Adding Integers Using Absolute Values
Find each sum.
23 + (–35)
The signs are different. Find the difference of the absolute values.
23 + (–35)
Think: 35 – 23 = 12.
Use the sign of the integer with the
greater absolute value.
–12

36. Insert Lesson Title Here
Course 2
2-2
Adding Integers
Insert Lesson Title Here
Check It Out: Example 2A
Find each sum.
–5 + 3
The signs are different. Find the difference of the absolute values.
–5 + 3
Think: 5 – 3 = 2.
Use the sign of the integer with the
greater absolute value. –2

37. Insert Lesson Title Here
Course 2
2-2
Adding Integers
Insert Lesson Title Here
Check It Out: Example 2B
Find each sum.
–13 + (–24)
The signs are the same. Find the sum of the absolute values.
–13 + (–24)
Think: = 37.
–37
Use the sign of the two integers.

38. Additional Example 3: Evaluating Expressions with Integers
Course 2
2-2
Adding Integers
Additional Example 3: Evaluating Expressions with Integers
Evaluate x + y for x = –42, y = 71.
x + y
Substitute for x and y. –
The signs are different. Think = 29
Use the sign of the integer with the
greater absolute value (positive). 29
When adding integers, think: if the signs are the same, find the sum. If the signs are different, find the difference.
Helpful Hint

39. Insert Lesson Title Here
Course 2
2-2
Adding Integers
Insert Lesson Title Here
Check It Out: Example 3
Evaluate x + y for x = –24, y = 17.
x + y
Substitute for x and y. –
The signs are different. Think: 24 – 17 = 7. –7
Use the sign of the integer with the
greater absolute value (negative).

40. Additional Example 4: Application
Course 2
2-2
Adding Integers
Additional Example 4: Application
The jazz band’s income from a bake sale was $286. Expenses were $21. Use integer addition to find the band’s total profit or loss.
286 + (–21)
Use negative for the expenses.
Find the differences of the
absolute values.
286 – 21
265
The answer is positive.
The band earned $265.

41. Insert Lesson Title Here
Course 2
2-2
Adding Integers
Insert Lesson Title Here
Check it Out: Example 4
The French Club was raising money for a trip to Washington D.C. Their car wash raised $730. They had expenses of $52. Use integer addition to find the club’s total profit or loss.
730 + (–52)
Use negative for the expenses.
Find the differences of the
absolute values.
730 – 52
678
The answer is positive.
The club earned $678.

42. Insert Lesson Title Here
Course 2
2-2
Adding Integers
Insert Lesson Title Here
Lesson Quiz: Part I
Use a number line to find the sum.
1. –7 + (–6)
Find each sum.
2. – (–9)
3. – (–3)
4. Evaluate x + y for x = –2 and y = –15.
–13 2
–14 –12 –10 –8 –6 –4 –
–20
–17

43. Insert Lesson Title Here
Course 2
2-2
Adding Integers
Insert Lesson Title Here
Lesson Quiz: Part II
5. The math club’s income from a bake sale was $217. Advertising expenses were $32. Use integer addition to find the club’s total profit or loss?
$185 profit

44. 2-3 Subtracting Integers Warm Up Problem of the Day
Course 2
Warm Up
Problem of the Day
Lesson Presentation

45. 2-3 Subtracting Integers Warm Up Add. 1. –2 + 6 2. –3 + (–4)
Course 2
2-3
Subtracting Integers
Warm Up
Add.
1. – –3 + (–4)
(–5) (–4)
5. –6 + (–1) 6. –6 + 1 4 –7 2 –1 –7 –5

46. 2-3 Subtracting Integers Problem of the Day
Course 2
2-3
Subtracting Integers
Problem of the Day
Ray earned $172 shoveling walks and $188 babysitting. He spent $21 for a shovel and rock salt and $26 for toys for children. Which job was more profitable?
babysitting

47. Course 2
2-3
Subtracting Integers
Learn to subtract integers.

48. 2-3 Subtracting Integers
Course 2
2-3
Subtracting Integers
During its flight to and from Earth, the space shuttle may be exposed to temperatures as cold as –250°F and as hot as 3,000°F.
To find the differences in these temperatures, you need to know how to subtract integers with different signs.
You can model the difference between two integers by using a number line. When you subtract a positive number, the difference is less than the original number, so you move to the left. To subtract a negative number, move to the right.

49. 2-3 Subtracting Integers Helpful Hint
Course 2
2-3
Subtracting Integers
If the number being subtracted is less than the number it is being subtracted from, the answer will be positive. If the number being subtracted is greater, the answer will be negative.
Helpful Hint

50. Additional Example 1A: Modeling Integer Subtraction
Course 2
2-3
Subtracting Integers
Additional Example 1A: Modeling Integer Subtraction
Use a number line to find each difference.
4 – 1 –1 4
–2–1 0
Start at 0. Move right 4 spaces. To subtract 1,
move to the left.
4 – 1 = 3

51. Additional Example 1B: Modeling Integer Subtraction
Course 2
2-3
Subtracting Integers
Additional Example 1B: Modeling Integer Subtraction
Use a number line to find each difference.
–3 – 1 –1 –3
1 2
–6–5–4 –3 –2–1 0
Start at 0. Move 3 spaces left. To subtract 1,
move to the left.
–3 – 1 = –4

52. Additional Example 1C: Modeling Integer Subtraction
Course 2
2-3
Subtracting Integers
Additional Example 1C: Modeling Integer Subtraction
Use a number line to find each difference.
–2 – (–4)
–(–4) –2
–4 –3 –2–1 0
Start at 0. Move left 2 spaces. To subtract –4,
move to the right.
–2 – (–4) = 2

53. Insert Lesson Title Here
Course 2
2-3
Subtracting Integers
Insert Lesson Title Here
Check It Out: Example 1A
Use a number line to find each difference.
3 – 2 –2 3
–2–1 0
Start at 0. Move right 3 spaces. To subtract 2,
move to the left.
3 – 2 = 1

54. Insert Lesson Title Here
Course 2
2-3
Subtracting Integers
Insert Lesson Title Here
Check It Out: Example 1B
Use a number line to find each difference.
–2 – 4 –4 –2
1 2
–6–5–4 –3 –2–1 0
Start at 0. Move 2 spaces left. To subtract 4,
move to the left.
–2 – 4 = –6

55. Insert Lesson Title Here
Course 2
2-3
Subtracting Integers
Insert Lesson Title Here
Check It Out: Example 1C
Use a number line to find each difference.
–4 – (–2)
–(–2) –4
–4 –3 –2–1 0
Start at 0. Move left 4 spaces. To subtract –2,
move to the right.
–4 – (–2) = –2

56. 2-3 Subtracting Integers Addition and subtraction are inverse
Course 2
2-3
Subtracting Integers
Addition and subtraction are inverse
operations—they “undo” each other.
Instead of subtracting a number you
can add its opposite.

57. Additional Example 2: Subtracting Integers by Adding the Opposite
Course 2
2-3
Subtracting Integers
Additional Example 2: Subtracting Integers by Adding the Opposite
Find each difference.
A. 5 – (–2)
5 + 2
Add the opposite of –2. 7
B. –3 – 7
–3 + (–7)
Add the opposite of 7.
–10
C. – 1 – (–8)
–1 + 8
Add the opposite of –8. 7

58. Insert Lesson Title Here
Course 2
2-3
Subtracting Integers
Insert Lesson Title Here
Check It Out: Example 2
Find each difference.
A. 4 – 2
4 + (–2)
Add the opposite of 2. 2
B. –2 – (–6)
–2 + 6
Add the opposite of –6. 4
C. –1 – 4
–1 + (–4)
Add the opposite of 4. –5

59. Additional Example 3: Evaluating Expressions with Integers
Course 2
2-3
Subtracting Integers
Additional Example 3: Evaluating Expressions with Integers
Evaluate x – y for each set of values.
A. x = –3 and y = 2
x – y
–3 – 2 = –3 + (–2)
Substitute for x and y.
= –5
Add the opposite of 2.
B. x = 4 and y = –6
x – y
4 – (–6) = 4 + 6
Substitute for x and y.
Add the opposite –6.
= 10

60. Insert Lesson Title Here
Course 2
2-3
Subtracting Integers
Insert Lesson Title Here
Check It Out: Example 3A & B
Evaluate x – y for each set of values.
A. x = –4 and y = –3
x – y
–4 – (–3) = –4 + 3
Substitute for x and y.
= –1
Add the opposite of –3.
B. x = –4 and y = 5
x – y
–4 – 5 = –4 + (–5)
Substitute for x and y.
Add the opposite of 5.
= –9

61. Additional Example 4: Temperature Application
Course 2
2-3
Subtracting Integers
Additional Example 4: Temperature Application
Find the difference between 32°F and –10°F.
32 – (–10)
= 42
Add the opposite of –10.
The difference in temperature is 42˚F.

62. Insert Lesson Title Here
Course 2
2-3
Subtracting Integers
Insert Lesson Title Here
Check It Out: Example 4
Find the difference between 8°F and –5°F.
8 – (–5)
8 + 5 = 13
Add the opposite of 5.
The difference in temperature is 13˚F.

63. Insert Lesson Title Here
Course 2
2-3
Subtracting Integers
Insert Lesson Title Here
Lesson Quiz: Part I
Use a number line to find the difference.
1. 3 – 9
Find each difference.
2. –7 – 4
3. –3 – (–5)
4. Evaluate x – y + z for x = –4, y = 5, and z = –10. –6
–11 2
–19

64. Insert Lesson Title Here
Course 2
2-3
Subtracting Integers
Insert Lesson Title Here
Lesson Quiz: Part II
5. On January 1, 2002, the high temperature was 81˚F in Kona, Hawaii. The low temperature was –29˚F in Barrow, Alaska. What was the difference between the two temperatures?
110˚F