Chapter 3

$<$

$14$

$20$

$3+\left(-7\right)$

$5$

$20-\left(-15\right)$

$-11$

$20÷13$

$-15$

$-3$

$0$

$16$

$x-5$

1

5

2

3

16

9

5 yards

−30 feet

6

7

−6

−7

−2

−3

2

3

−50

−70

13

0

9

13

196

8

−7 + 4 = −3

−8 + (−6) = −14

[9 + (−16)] + 4 = −3

[−8 + (−12)] + 7 = −13

4 degrees Celsius

−33 feet

14-yard line

37-yard line

2

3

−2

−3

−10

−11

10

11

ⓐ

ⓑ

ⓒ

ⓓ

ⓐ

ⓑ

ⓒ

ⓓ

ⓐ

−2
ⓑ

4

ⓐ

−3
ⓑ

3

−29

−26

3

13

−69

−47

45 degrees Fahrenheit

9 degrees Fahrenheit

10,103 feet

233 feet

−63

−84

29

52

4

9

21

6

39

13

−8

19

−5 (12) = −60

8 (−13) = −104

−63 ÷ −9 = 7

−72 ÷ −9 = 8

−4

−19

−6

−4

4x = 12; x = 3

3x = 6; x = 2

7

11

−12

−9

x + 7 = −2; x = −9

y + 11 = 2; y = −9

p − 2 = −4; p = −2

q − 7 = −3; q = 4

132 = −12y; y = −11

117 = −13z; z = −9

4

15

4

56

0

8

80

−6 degrees

−40 feet

−12 yards

$3

+1

Sample answer: I have experienced negative temperatures.

11

−9

−2

1

−80

32

−135

0

−22

108

−4

29

−8

10

64

121

−14 + 5 = −9

−2 + 8 = 6

−15 + (−10) = −25

[−1 + (−12)] + 6 = −7

[10 + (−19)] + 4 = −5

7°F

−$118

−8 yards

25-yard line

20 feet

−32

Sample answer: In the first case, there are more negatives so the sum is negative. In the second case, there are more positives so the sum is positive.

6

−4

−9

12

27

29

−39

−48

−42

−59

−51

9

−2

−2

22

53

−20

0

4

6

–8

−11

−8

−192

−10°

96°

21-yard line

$65

−$40

$26

13°

Sample answer: On a number line, 9 is 15 units away from −6.

−32

−35

36

−63

−6

14

−4

−8

13

−12

−49

−47

43

−125

64

−16

90

−88

9

41

−5

−9

−29

5

11

21

38

−56

−3·15 = −45

−60 ÷ (−20) = 3

$\frac{\mathrm{-6}}{a+b}$

−10 (p − q)

−$3,600

Sample answer: Multiplying two integers with the same sign results in a positive product. Multiplying two integers with different signs results in a negative product.

Sample answer: In the first expression the base is positive and after you raise it to the power you should take the opposite. Then in the second expression the base is negative so you simply raise it to the power.

n = −7

p = −17

u = −4

h = 6

x = −16

r = −14

3x = 6; x = 2

2x = 8; x = 4

x = 9

c = −8

p = 3

q = −12

x = 20

z = 0

n + 4 = 1; n = −3

8 + p = −3; p = −11

a − 3 = −14; a = −11

−42 = −7x; x = 6

−15f = 75; f = −5

−6 + c = 4; c = 10

m − 9 = −4; m = 5

a = 20

m = 7

u = −52

r = −9

d = 5

x = −42

17 cookies

Sample answer: It is helpful because it shows how the counters can be divided among the envelopes.

Sample answer: The operation used in the equation is multiplication. The inverse of multiplication is division, not addition.

<

>

>

−6

4

21

36

0

14

−33

<

=

55; −55

7

54

−1

−16

−3

−10°

10

1

96

−50

−1

21

−27

−8 + 2 = −6

10 + [−5 + (−6)] = −1

16 degrees

5

7

8

−38

−58

−1

41

−12 − 5 = −17

−2 degrees

−36

121

−7

−8

−45

−9

−81

54

4

−66

−58

−12(6) = −72

−12

−7

3x = 9; x = 3

9

4

−6y = −42; y = 7

m + 4 = −48; m = −52

Answers will vary.

5

−27

11

54

−8

22

39

34

−7 − (−4) = −3

4°F

n = −1

r = 6

y − 8 = −32; y = −24