Signed Numbers
Practice 17
Directions: Compute the positive and negative values indicated in the problems below. Use the
number line to help you with the easier amounts. Remember, always start at 0. Go to the right for
positive values. Go to the left for negative values.
¯9
¯8
¯7
¯6
¯5
¯4
¯3
¯2
¯1
0
1
+
2
+
3
+
4
+
5
+
6
+
7
+
8
+
9
+
1. You have no money. You owe $4 to your best friend. You earn $5 doing chores. How much
money will you have after you pay your friend? _________________
2. John has no money and he owes $9 to his brother. He receives $10 for his birthday. How much
money does he have after paying back his brother? _________________
3. Elizabeth has no money. She owes $7 to Michelle and $4 to Christine. How much money does
she have altogether? _________________
4. What is the sum of ¯9 and +16? _________________
5. James has no money and he owes $9 to Ronny and $12 to Melissa. How much money does he
have altogether? _________________
6. What is the sum of ¯10 and +12? _________________
7. Irene has $15 but she owes $21 to her friend. How much money will she still owe if she pays
back the money she owes to her friend? _________________
8. What is the sum of ¯7 and ¯17? _________________
9. George scored 9 points in one game and 8 points in a second game. What was his point total?
___________________
10. What is the sum of ¯30 and ¯42? _________________
11. What is the sum of ¯19 and ¯13? _________________
12. Allison owes $87 to the bank and $139 to the credit card company. How much money does she
owe altogether? _________________
20
Signed Numbers
Practice 18
Directions: Compute the positive and negative values indicated in the problems below. The first one is
done for you.
Reminders
• A negative times a negative is a positive.
• A positive times a negative is a negative.
• A negative divided by a negative is a positive.
• A positive divided by a negative is a negative.
• A negative divided by a positive is a negative.
1. Jill owes $4 to Jennifer, $4 to Michelle, and $4 to Eileen. How much does she owe altogether?
_________________
2. Joey owes $5 to 4 different friends. How much money does he owe altogether? ______________
3. What is the product of ¯7 and ¯6? _________________
4. The total bill at a restaurant was $49 to be split evenly among 7 friends. How much money did
each friend owe? _________________
5. How much is ¯81 divided by 9? _________________
6. How much is ¯100 divided by ¯10? _________________
7. A group of 18 patrons each owe $15 at a restaurant. What is the total amount owed by all 18
customers? _________________
8. What is the product of ¯12 and ¯13? _________________
9. How much is ¯16 times 4? _________________
10. What is the quotient when ¯45 is divided by ¯9? _________________
11. A group of 15 teenagers owes $75 at a pizza parlor. If they split the bill evenly, how much will
each person owe? _________________
12. How much is ¯200 divided by ¯10? _________________
21
Answer Key
Page 4
1. 279 marbles
2. 146 marbles
3. 188 marbles
4. 55 marbles
5. 1,316 marbles
6. 37 marbles
7. 96 marbles
8. 222 marbles
9. 245 marbles
10. 468 marbles
11. 71 marbles
12 marbles
12. 444 marbles
Page 5
1. addition
19,056 bases
2. subtraction
1,689 at bats
3. addition
2,129 home runs
4. division
177 hits
5. multiplication
3,928,500 tickets
6. subtraction
1,578 strike outs
7. division
2,800 groups
8. subtraction
329 walks
9. division
175 hits (174 R13)
10. division
.600 or 60%
Page 6
1. subtraction
37,036 people
2. subtraction
14,443 people
3. addition
132,118 fans
4. addition
35,292 fans
5. division
860 packages
6. division
2,000 packages
7. subtraction
28,538 fans
8. division
8,250 packages
9. multiplication
601,536 fans
10. multiplication
3,649,050 tickets
47
Page 7
1. 7/12 lb.
2. 1 5/12 lb.
3. 1/8 lb.
4. 1/12 lb.
5. 5 lb.
6. 1/4 feet
7. 1 7/10 lb.
8. 11/24 feet
9. 6 cups
10. 1 19/30 lb.
Page 8
1. 15 ounces
2. 24 3/4 ounces
3. 21/40 ounces
4. 25 students
5. 14 students
6. 1/12 ounces
7. 1 7/10 ounces
8. 27 1/5 ounces
9. 9 3/8 ounces
10. 8 3/4 lb.
11. 1 1/2 ounces
12. 28 cups
Page 9
1. 10 3/8 inches
2. 32 3/4 inches
3. 7/8 inches
4. 51 5/8 inches
5. 83 7/8 inches
6. 3 1/4 lb.
7. 20 1/4 lb.
8. 24 1/6 inches
9. 14 1/8 ounces
10. 20 3/8 inches
Page 10
1. 76 inches
2. 52 1/5 inches
3. 10 prints
4. 8 prints
5. 150 inches
6. 355 inches
7. 23 1/3 inches
8. 7 prints
9. 451 inches
10. 8 prints
Page 11
1. 2 1/4 feet
2. 9 5/6 feet
3. 17 3/4 feet
4. 3 1/8 feet
5. 2 1/3 feet
6. 6 2/5 times
7. 12 lengths
8. 6 1/12 feet
9. 5 1/2 feet
10. 14 7/12 feet
Page 17
1. 467.476 mi.
2. 2,246.8 mi.
3. 32.422 feet
4. 94.14 mi.
5. 15.23 mi.
6. 44.636 mi.
7. 177.813 m.p.h.
8. 3,030.957 lb.
9. 91.05 mi.
10. 880.431 mi.
Page 12
1. $5.04
2. $0.56
3. $63.68
4. $43.45
5. $5.51
6. $5.04
7. $29.25
8. $0.96
9. $10.13
10. $20.15
11. $18.35
12. $17.10
Page 13
1. 7.9 centimeters
2. 87.6 centimeters
3. 30.25 centimeters
4. 220.89 centimeters
5. 204.26 centimeters
6. 347.863 centimeters
7. 24.99 centimeters
8. 1.201 centimeters
9. 56.899 centimeters
10. 59.663 centimeters
11. 26.989 centimeters
12. 181.91 centimeters
Page 14
1. 0.21 lb.
2. 100.2 ounces
3. 1.09 ounces
4. 10.2 candies
5. 45.1 lb.
6. 80.5 ants
7. 969.624 ounces
8. $0.23
9. $0.38
10. 157.68 lb.
Page 15
1. 75%
2. 72%
3. 75%
4. 60%
5. 75%
Page 16
1. $34.00
2. $4.00
3. $1.32
4. $9.52
5. $7.00
6. $2.48
7. $22.80
8. $4.00
9. $18.00
$42.00
10. $5.24
$29.71
6.
7.
8.
9.
10.
80%
64%
67%
70%
82%
Page 18
1. 60 m.p.h.
2. 50 m.p.h.
3. 30 m.p.h.
4. 60 m.p.h.
5. 50 m.p.h.
6. 55 m.p.h.
7. 52 m.p.h.
8. 40 m.p.h.
9. 40 m.p.h.
10. 80 m.p.h.
Page 19
1. 3,200 feet
2. 40 min.
3. 10,000 feet
4. 7,128 feet
5. 396 min.
6. 7,740 feet
7. 24,000 feet
8. 503 min.
9. 410 min.
10. 30,400 feet
Page 20
1. $1
2. $1
3. $11
4. 7
5. $21
6. 2
7. -$6
8. -24
9. 17
10. -72
11. -32
12. $226
Page 21
1. -$12
2. -$20
3. +42
4. -$7
5. -9
6. +10
7. $270
8. +156
9. 64
10. +5
11. -$5
12. +20
Page 22
1. polar bear
2. leopard/camel
dog/cat
3. 2 yr.
4. pig
5. 9 yr.
6. 15 yr..
7. 1 yr.
8. 9 yr.
9. 55 yr.
10. 70 yr.
Page 23
1. 30%
2. 5th/8th
3. 60%
4. no
5. 45%
6. 40%
Page 24
1. 1960
2. 1990–2000
3. 1960
4. 1950–1960
5. 1990–2000
6. 1970–1980
7. 1960–1970
8. the same
9. 10/11
10. 12/13
11. 16
12. 7/8/9
13. taller
14. 14
Page 25
1. 12
2. 1
3. 4
4. 2
5. 2
6. 12
7. 18
8. 1
9. 4
10. dog
11. snake
12. 5
13. 41
14. 27
Frequency
Cat 8
Dog 12
Snake 2
Bird 3
Mouse 3
Hamster 4
Fish 6
Other 3
Page 26
1. 10 m.p.h.
2. the scale starts at 20
rather than 0
11
Brain
Teasers
Less than Nothing
Word Problems with Positive and
Negative Numbers
There are times when you not only have no money at all, you may owe money to a parent or friend.
Negative numbers can be used to represent what you owe or how much you need just to get even.
Negative numbers are also used in recording temperatures and golf games.
Directions: Apply your knowledge of integers (positive and negative numbers and zero) to help you
solve these problems. Write an equation and then do the operations needed.
1. You bought a watch for $12.00. Since you
only had $2.00, you had to borrow money
from your mom. What negative number
shows what you owe?
5. A player on a TV game show called Double
Trouble! had -600 points because of some
hard questions. He then answered several
questions correctly. He received 200 points,
100 points, and 150 points. How many
points did the player have? How many
points did he need to get to 0?
Equation: + 2 – 12 = -10
Answer: You owe $10.00
Equation: __________
Answer: ___________
2. The temperature when water freezes is 32˚ F.
What temperature is 40˚ below freezing?
Equation: __________
Answer: ___________
6. One of the coldest temperatures ever
recorded was -69˚ F in Utah in 1985. What
temperature is 35˚ higher than -69˚ F?
Equation: __________
Answer: ___________
3. A golfer shot -4 (below par) on his first
round of 18 holes. He shot an -11 on his
second round and a -6 on his third round.
How many shots below par was he after his
three rounds?
7. The coldest temperature ever recorded was
-129˚ F in Antarctica. The highest recorded
temperature was 136˚ F in Africa. What is
the difference?
Equation: __________
Answer: ___________
Equation: __________
Answer: ___________
4. The Acey Duecy Card Company owed the
bank $1,000.00. They made a $750.00
payment to the bank. How much did they
still owe the bank?
8. A temperature of -80˚ F was recorded in
Alaska. What is the difference between this
reading and a high of 134˚ F recorded in
Death Valley, California?
Equation: __________
Answer: ___________
Equation: __________
Answer: ___________
43
? ? ?
6. n + 9n + 2n = 144
12n = 144
n = 12
Daniel has 12
stamps.
Bryan has 24
stamps.
George has 108
stamps.
Page 36
1. n + (n + 25) +
(n + 23) = 93
3n + 48 = 93
n = 15
Fred is 15 years
old.
Mom is 38 years
old.
Dad is 40 years old.
2. 3n + 220 = 310
n = 30
The skateboard is
$30.
The scooter is $90.
The bike is $190.
3. 9n + 6 = 3(n + 6)
n=2
Jimmy is 2 years
old.
Brother is 18 years
old.
4. n + (n – 5) +
(n + 2) + (n + 8)
= 53
4n + 5 = 53
n = 12
Jesse is 12 years
old.
Maybelle is 7 years
old.
Ellen is 14 years
old.
Jeanne is 20 years
old.
5. n + (n + 15) +
(n – 10) + (n + 23)
= 108
4n + 28 = 108
n = 20
Joseph had $20.00.
Elsa had $35.00.
• • • • • • • • • • • • • • • • • • • • • • Answer Key
Julian had $10.00.
Martha had $43.00.
6. n + 2n + 4n = 105
7n =105
n = 15
Melissa had $15.00.
Christina had
$30.00.
Charmain had
$60.00.
7. n + 3n + (3n – 10)
= 74
7n – 10 = 74
n = 12
Kristin had $12.00.
Matthew had
$36.00.
Joshua had $26.00.
8. n + (n + 8) + 3n +
(n – 5) = 63
6n + 3 = 63
n = 10
Andrew is 10 years
old.
Kenneth is 18 years
old.
Billy is 30 years
old.
Cameron is 5 years
old.
Page 39
1. 2:3 :: n:18
n = 12 blocks
2. 5:3 :: n:60
n = 100 pages
3. 5:7 :: n:630
n = 450 minutes
4. 14:3 :: n:90
n = 420 gallons
5. 170:4 :: n:240
n = 10,200 gallons
6. 20:3 :: 1000:n
n = 150 hours
7. 145:3 :: n:24
n = 1,160 lb.
Page 40
1. 55:1 :: n:7
n = 385 miles
2. 18:1 :: n:20
n = 360 miles
3. 60:1 :: n:5.5
n = 330 minutes
4. 24:1 :: n:13.5
n = 324 hours
5. 2,000,000:1 :: n:48
n = 96,000,000 tons
6. 2,980:n :: 40:1
n = 74.5 hr.
7. 100:9 :: n:40.5
n = 450 miles
8. 16:1 :: n:45
n = 720 oz.
Page 38
1. 4/7 or 4:7
4/11 or 4:11
7/4 or 7:4
7/11 or 7:11
2. 5/8 or 5:8
5/13 or 5:13
8/5 or 8:5
8/13 or 8:13
3. 6/7 or 6:7
6/13 or 6:13
7/6 or 7:6
7/13 or 7:13
4. 60/1 or 60:1
5. 55/1 or 55:1
6. 16/1 or 16:1
7. 1,200/1 or 1,200:1
8. 24/1 or 24:1
9. 60/1 or 60:1
10. 365/1 or 365:1
11. 8/100 or 8:100
Challenge: 86,400 sec.;
8,760 hr.
Page 41
1. 600 calories
2. 650 calories
3. 400 calories
4. 2,500 calories
5. handball and
bicycling
6. 1,650 calories
7. bicycling and
walking
8. 3-hr. walk
9. Answers will vary.
10. 8 states
11. 7 states
12. 12 states
13. 1 to 5 million
48
14. Answers will vary.
15. California has the
most.
Wyoming has the
least.
16. Answers will vary.
Page 42
1. Friday
2. Thursday
3. 15˚ to 20˚
4. Monday
5. Wednesday and
Friday
6. Tuesday and
Saturday
7. Monday, Saturday,
and Sunday
8. 91.7˚ or 92˚
9. 71.7˚ or 72˚
10. Answers will vary.
11. water
12. nitrogen
13. 32%
14. other category
15. 47%
16. Answers will vary.
Page 43
1. +2 – 12 = -10
You owe $10.00.
2. 32 – 40 = -8
8 below 0
3. -4 + -11 + -6 = -21
21 below par
4. -$1000 + $750 =
$250
$250 owed
5. -600 + 200 + 100 +
150 = -150
He needed 150
points to get to 0.
6. -69 + 35 = -34˚ F
7. -129 – (+)136 =
-265
265˚ difference
8. -80 – (+)134 = -214
214˚ difference
1
Practice
• • • • • • Adding and Subtracting Positive
and Negative Numbers
Directions: On each number line, write the number that X represents.
1.
0
X
2.
0
X
3.
0
X
Directions: Find the sum.
4.
5.
-3
-4
+ -2
5
2
+ 2
6.
7.
8.
-60
-20
+ -30
-2.3
-5.3
+ 10.3
9.
-12
-31
+ 0
10.
11.
-4
8
+ 19
1.30
2.89
+ 3.70
-8
7
-9
+ 4
Directions: Find the difference.
12.
8 – 4 = _____
17.
-30 – (-80) = _____
22.
8 – 3.6 = _____
13.
-4 – 9 = _____
18.
0 – (-12) = _____
23.
3.6 – 8 = _____
14.
(12) – (-3) = _____
19.
4 – 0 = _____
24.
7 – (-11) = _____
15.
-9 – (-3) = _____
20.
9 – 2 = _____
25.
-3 – (-15) = _____
16.
9 – (-3) = _____
21.
2 – 9 = _____
26.
5 – (-12) = _____
Directions: Find the difference or sum.
27.
-7 – 4 – (-2) = _____
31.
(9 – 4) – (1– 3) + (7 + 10) = _____
28.
5 – (-5) – (-6) = _____
32.
(5 – 1) – (3 + 2) – (3 – 9) = _____
29.
-4 – 9 – (-3) = _____
33.
(2 – 8) – 8 – (9 – 4) = _____
30.
9 – 7 – (-5) = _____
34.
(7 – 3) – (7 – 11) + 7 = _____
8
2
Practice
• • • • • • Multiplying and Dividing Positive
and Negative Numbers
Directions: Multiply.
1. 7 x 9 = ____
2. -11 x -6.2 = ____
3. -22 x -2.1 = ____
4. -1(-20)(5) = ____
5. -6(-9)(1) = ____
6. -12(11)(-9 + 2) = ____
7. -2(-3)(-5)(-1 + 3 – 4) = ____
8. (-6)(4)(1) = ____
9. (5)(-7)(2) = ____
10. (5–2)(-3)(3 + 1) = ____
11. (7 – 3)(-3)(-2) = ____
12. (2 + 4)(6 – 3)(-5) = ____
Directions: Divide.
13.
-16 ÷ 4 =
14.
85 ÷ -17 =
15.
21 ÷ -7 =
16.
- 121 =
-11
17.
-54
=
-18
18.
- 72
=
-8
19.
-90
=
-30
20.
5 – 10
15 – 20 =
21.
12 – 3
9–6 =
22.
– 84
=
– 12
23.
9+3
4 – 10 =
24.
8+7
3+2 =
Directions: Find the answers.
25.
-81(-3 + 6) =
9
26.
90(2 – 5)
-5
27.
6(4 + 1) – 7(5 – 4) + (3 + 2) =
28.
-5(8 + 2) + 4(6 – 9) –
29.
-2(5 – 6) + 10(6 – 7) –
30.
6(1 + 2) + 2(4 + 3) +
31.
6(5 – 3) + 2(2 – 6) =
3(9 – 3)
32.
2(1 – 6) – 7(2 + 3) =
-9(3 – 4)
33.
2(7 – 3) + 8(5 + 2) =
2(10 – 2)
34.
8(-10 + 7) + 4(27 – 36) =
4(5 – 2)
[ ]
25
5
=
12
[ ]
[ ]
30
10
=
36
12
=
x
Page 8
1. -2
2. 3
3. -4
4. -9
5. 9
6. -110
7. -43
8. 2.7
9. 23
10. 7.89
11. -6
12. 4
13. -13
14. 15
15. -6
16. 12
17. 50
18. 12
19. 4
20. 7
21. -7
22. 4.4
23. -4.4
24. 18
25. 12
26. 17
27. -9
28. 16
29. -10
30. 7
31. 24
32. 5
33. -19
34. 15
Page 12
1. 63
2. 68.2
3. 46.2
2
–z 2
4 m
• • • • • • • • • • • • • • • • • • • • • Answer Key
4. 100
5. 54
6. 924
7. 60
8. -24
9. -70
10. -36
11. 24
12. -90
13. -4
14. -5
15. -3
16. 11
17. 3
18. 9
19. 3
20. 1
21. 3
22. 7
23. -2
24. 3
25. -27
26. 54
27. 28
28. -65
29. -13
30. 35
31. 2/9
32. -5
33. 4
34. -5
Pages 15 and 16
1. 14/
2. 7
3. – 10
4. + 12
5. + or +
6. /6
7. 4 + 5
8. 4 + 5
9. /3 + 7 or 1/3 +
7
10. 25/
11. 6 +
10
12. 1/2 (8 ) or 8 /2
13. 5 +
7
14. 4 +
10
15. 20 – 4
16. 20 + x
5
17. + 5 or 5 +
18. /3 or 1/3
19. one number added
to another number
20. one number
decreased by
another number
21. 4 times a number
22. 8 divided by a
number
23. 2 times a number,
decreased by 5
24. 8 increased by a
number
25. a number times
another number
26. 22 decreased by a
number
27. 22 less than a
number
28. 4
29. 2
30. 3
31. 32. 1 2/3 + 3
33. 12 2 – 3 +
34. + 1
46
35.
36.
37.
38.
3 – 5 or -5 + 3
3 +2 3–4
-2 + 3
3=1
9 3
39. 3(9) = 27
40. 3/3 + 9/3 =
12/3 = 4
41. 3 + 9 = 12
42. 9 = 3
3
43. 5(-4) = -20
44. -4 + 10 = 6
45. 10 = 2
5
46. 10 – 5 = 5
47. -4 = -2
10 5
Page 20
1. 48
2. 55
3. 46
4. 112
5. -5
6. 2
7. -1 1/3 or -4/3
8. 29
9. 14
10. 5
11. 15º C
12. 135 miles
13. $280
14. 360 feet
15. = -12
16. = 80
17. = 42
18. = 144
19. = 35
20. = -8
21. = -125
22. = 18
Form A
Appendix A: Assessments
Name _____________________________________
Mixed Integers Quiz
Directions: Solve.
79
Appendix C: Answer Keys
Assessment Answers
(cont.)
99
Unit 1: Algebraic Expressions and Integers
Name _____________________________________
Adding Integers 1
Directions: Calculate.
7
Unit 1: Algebraic Expressions and Integers
Name _____________________________________
Multiplying and Dividing Integers
Directions: Calculate.
÷
÷
÷
9
Unit 1: Algebraic Expressions and Integers
Names ____________________________________
Group Activity 1
Directions: Simplify.
÷
÷
10
Appendix C: Answer Keys
Transparency/Guided Practice Book Answers
94
Appendix C: Answer Keys
Guided Practice Book Answers
(cont.)
95