Solutions: Integers
Introduction to Integers
Exercise | Problem | Solution |
1 | Write an integer to represent the following situation: Earnings of 15 dollars |
^{+}15 |
2 | Write an integer to represent the following situation: A loss of 20 yards |
^{–}20 |
3 | What is the opposite of ^{–}231? | ^{+}231 or 231 |
4 | What is the opposite of ^{+}1096? (Do not enter a comma in your answer.) |
^{–}1096 |
5 | Solve the following problem using integers. Jenny has $2. She earns $5, spends $10, earns $4, then spends $3. How many dollars does she have or owe? (Enter an integer in the space below.) |
$^{–}2 |
Absolute Value
Exercise | Problem | Solution |
1 | Find the absolute value of -6. | 6 |
2 | Find |+15| | 15 |
3 | Find |-31| | 31 |
4 | Find |+31| | 31 |
5 | How many values of y will you get when you solve |y| = 29? | 2 |
Comparing and Ordering Integers
Exercise | Problem | Solution |
1 | Compare these integers and enter < or > in the space provided. | ^{–}10 < ^{+}9 |
2 | Compare these integers and enter < or > in the space provided. | ^{+}7 > ^{–}8 |
3 | Which of the following choices lists these integers in order from least to greatest? ^{–}15, 0, ^{+}14, ^{–}17, ^{+}16, ^{–}19 0, ^{+}14, ^{–}15, ^{+}16, ^{–}17, ^{–}19 |
^{–}19, ^{–}17, ^{–}15, 0, ^{+}14, ^{+}16 |
4 | Which of the following sets of integers is listed in order from least to greatest?
^{–}21, ^{–}22, 0, ^{+}13, ^{+}24, ^{+}29 |
^{–}39, ^{–}17, ^{–}12, 0, ^{+}32, ^{+}49 |
5 | Which of the following set of integers is listed in order from greatest to least?
^{+}28, ^{+}19, 0, ^{–}21, ^{–}36, ^{–}39 |
^{+}28, ^{+}19, 0, ^{–}21, ^{–}36, ^{–}39 |
Addition of Integers
Exercise | Problem | Solution |
1 | ^{–}6 + ^{–}9 = ? | ^{–}15 |
2 | ^{+}7 + ^{+}11 = ? | ^{+}18 or 18 |
3 | ^{+}5 + ^{–}3 = ? | ^{+}2 or 2 |
4 | ^{–}2 + ^{+}7 = ? | ^{+}5 or 5 |
5 | ^{+}9 + ^{–}12 = ? | ^{–}3 |
Subtraction of Integers
Exercise | Problem | Solution |
1 | ^{+}6 – ^{+}9 = ? | ^{+}6 + ^{–}9 = ^{–}3 |
2 | ^{+}11 – ^{–}8 = ? | ^{+}11 + ^{+}8 = ^{+}19 or 19 |
3 | ^{–}13 – ^{+}5 = ? | ^{–}13 + ^{–}5 = ^{–}18 |
4 | ^{–}2 – ^{–}15 = ? | ^{–}2 + ^{+}15 = ^{+}13 or 13 |
5 | ^{–}9 – ^{+}14 = ? | ^{–}9 + ^{–}14 = ^{–}23 |
Multiplication of Integers
Exercise | Problem | Solution |
1 | (^{–}2) (^{+}7) = ? | ^{–}14 |
2 | (^{–}8) (^{–}9) = ? | ^{+}72 or 72 |
3 | (^{+}9) (^{+}7) = ? | ^{+}63 or 63 |
4 | (^{+}16) (^{–}3) = ? | ^{–}48 |
5 | (^{+}4) (^{–}5) (^{–}2) = ? | ^{+}40 or 40 |
Division of Integers
Exercise | Problem | Solution |
1 | ^{–}81 ÷ ^{+}3 = ? | ^{–}27 |
2 | ^{–}150 ÷ ^{–}6 = ? | ^{+}25 or 25 |
3 | ^{+}96 ÷ ^{–}16 = ? | ^{–}6 |
4 | ^{+}102 ÷ ^{+}34 = ? | ^{+}3 or 3 |
5 | ^{–}144 ÷ ^{+}12 = ? | ^{–}12 |
Operations With Integers
Exercise | Problem | Solution |
1 | ^{–}8 + ^{–}15 = ? | ^{–}23 |
2 | (^{–}16) (^{–}3) = ? | ^{+}48 or 48 |
3 | ^{+}72 ÷ ^{+}2 = ? | ^{+}36 or 36 |
4 | ^{+}7 – ^{–}21 = ? | ^{+}7 + ^{+}21 = ^{+}28 or 28 |
5 | (^{+}8) (^{–}7) = ? | ^{–}56 |
6 | ^{–}108 ÷ ^{–}12 = ? | ^{+}9 or 9 |
7 | ^{–}6 – ^{–}15 = ? | ^{–}6 + ^{+}15 = ^{+}9 or 9 |
8 | ^{+}23 + ^{–}30 = ? | ^{–}7 |
Practice Exercises
Exercise | Problem | Solution |
1 | Find |^{–}79| | 79 (Note: The result of an absolute value is an unsigned number) |
2 | Find |^{+}54| | 54 (Note: The result of an absolute value is an unsigned number) |
3 | Which of the following sets of integers is listed in order from least to greatest?
^{+}36, ^{+}27, ^{+}23, 0, ^{–}21, ^{–}28 0, ^{+}12, ^{+}13, ^{–}15, ^{–}18 ^{–}27, ^{–}20, 0, ^{+}11, ^{+}23, ^{+}25 None of the above. |
^{–}27, ^{–}20, 0, ^{+}11, ^{+}23, ^{+}25 |
4 | Which of the following sets of integers is listed in order from greatest to least?
^{–}29, ^{–}26, ^{–}15, 0, ^{+}22, ^{+}25 ^{+}39, ^{+}17, 0, ^{–}11, ^{–}15, ^{–}19 ^{+}46, ^{+}37, ^{+}29, 0, ^{–}33, ^{–}25 None of the above. |
^{+}39, ^{+}17, 0, ^{–}11, ^{–}15, ^{–}19 |
5 | Which of the following sets of integers is listed in order from least to greatest?
^{–}51, ^{–}48, ^{–}43, 0, ^{+}45, ^{+}47 ^{–}12, ^{–}13, 0, ^{+}15, ^{+}18, ^{+}25 ^{+}45, ^{+}42, 0, ^{–}40, ^{–}37, ^{–}35 None of the above. |
^{–}51, ^{–}48, ^{–}43, 0, ^{+}45, ^{+}47 |
6 | ^{–}5 + ^{+}12 = ? | ^{–}5 + ^{+}12 = ^{+}7 or 7 |
7 | (^{–}18) (^{–}4) = ? | (^{–}18) (^{–}4) = ^{+}72 or 72 |
8 | ^{–}102 ÷ ^{+}3 = ? | ^{–}102 ÷ ^{+}3 = ^{–}34 |
9 | ^{+}18 – ^{+}23 = ? | ^{+}18 – ^{+}23 = ^{+}18 + ^{–}23 = ^{–}5 |
10 | (^{–}2) (^{+}6) (^{–}4) = ? | (^{–}2) (^{+}6) (^{–}4) = (^{–}12) (^{–}4) = ^{+}48 or 48 |
Challenge Exercises: Integers and the Real World
Exercise | Problem | Solution |
1 | Mt. Everest, the highest elevation in Asia, is 29,028 feet above sea level. The Dead Sea, the lowest elevation, is 1,312 feet below sea level. What is the difference of these two elevations? (Do not enter a comma in your answer.) | ^{+}29,028 – ^{–}1,312 = ^{+}29,028 + ^{+}1,312 = ^{+}30,340 Answer: ^{+}30340 or 30340 |
2 | In Buffalo, New York, the temperature was ^{–}14°F in the morning. If the temperature dropped 7°F, what is the temperature now? | ^{–}14 – ^{+}7 = ^{–}14 + ^{–}7 = ^{–}21 Answer: ^{–}21°F |
3 | A submarine was situated 800 kilometers below sea level. If it ascends 250 kilometers, what is its new position? | ^{–}800 + ^{+}250 = ^{–}550 |
4 | Maggie owes the candy store $35. Each of 5 friends will help her pay off her debt. How much will each friend pay? | ^{–}35 ÷ ^{+}5 = ^{–}7 Answer: $-7 |
5 | Roman Civilization began in 509 B.C. and ended in 476 A.D. How long did Roman Civilization last? | ^{+}476 – ^{–}509 = ^{+}476 + ^{+}509 = ^{+}985 Answer: ^{+}985 or 985 years |
6 | Lilly bought 4 pairs of blue jeans at $32 each. How much money did she pay the clerk? | (^{+}4) (^{–}32) = ^{–}128 Answer: $^{–}128 |
7 | A submarine was situated 450 kilometers below sea level. If it descends 300 kilometers, what is its new position? | ^{–}450 – ^{+}300 = ^{–}450 + ^{–}300 = ^{–}750 |
8 | In the Sahara Desert one day it was 136°F. In the Gobi Desert a temperature of ^{–}50°F was recorded. What is the difference between these two temperatures? | ^{+}136 – ^{–}50 = ^{+}136 + ^{+}50 = ^{+}186 Answer: +186 or 186 °F |
9 | The Punic Wars began in 264 B.C. and ended in 146 B.C. How long did the Punic Wars last? | Subtract the smaller integer from the larger integer: ^{–}146 – ^{–}264 = ^{–}146 + ^{+}264 = ^{+}118 Answer: +118 or 118 years |
10 | Metal mercury at room temperature is a liquid. Its melting point is ^{–}39°C. The freezing point of alcohol is^{–}114°C. How much colder is the freezing point of alcohol than the melting point of mercury? | Subtract the smaller integer from the larger integer: ^{–}39 – ^{–}114 = ^{–}39 + ^{+}114 = ^{+}75 Answer: +75 or 75 °F |