Identifying and Writing Integers

Locate Positive and Negative Numbers on the Number Line

In the following exercises, locate and label the given points on a number line.

Exercise 1

1. ⓐ = [latex]2[/latex]
2. ⓑ = [latex]-2[/latex]
3. ⓒ = [latex]-5[/latex]

Exercise 2

1. ⓐ = [latex]5[/latex]
2. ⓑ = [latex]-5[/latex]
3. ⓒ = [latex]-2[/latex]

Exercise 3

1. ⓐ = [latex]-8[/latex]
2. ⓑ = [latex]8[/latex]
3. ⓒ = [latex]-6[/latex]

Exercise 4

1. ⓐ = [latex]-7[/latex]
2. ⓑ = [latex]7[/latex]
3. ⓒ = [latex]-1[/latex]

Order Positive and Negative Numbers on the Number Line

In the following exercises, order each of the following pairs of numbers, using < or >.

1. [latex]9\text{__}4[/latex]
   Show Solution

   >
2. [latex]-3\text{__}6[/latex]
   Show Solution

   <
3. [latex]-8\text{__}-2[/latex]
   Show Solution

   <
4. [latex]1\text{__}-10[/latex]
   Show Solution

   >
5. [latex]6\text{__}2[/latex]
6. [latex]-7\text{__}4[/latex]
7. [latex]-9\text{__}-1[/latex]
8. [latex]9\text{__}-3[/latex]
9. [latex]-5\text{__}1[/latex]
   Show Solution

   <
10. [latex]-4\text{__}-9[/latex]
    Show Solution

    >
11. [latex]6\text{__}10[/latex]
    Show Solution

    <
12. [latex]3\text{__}-8[/latex]
    Show Solution

    >
13. [latex]-7\text{__}3[/latex]
14. [latex]-10\text{__}-5[/latex]
15. [latex]2\text{__}-6[/latex]
16. [latex]8\text{__}9[/latex]

Find Opposites

In the following exercises, find the opposite of each number.

1. [latex]2[/latex]
   Show Solution

   −2
2. [latex]-6[/latex]
   Show Solution

   6
3. [latex]9[/latex]
4. [latex]-4[/latex]
5. [latex]-8[/latex]
   Show Solution

   8
6. [latex]1[/latex]
   Show Solution

   -1
7. [latex]-2[/latex]
8. [latex]6[/latex]

Simplify Negatives

In the following exercises, simplify.

1. [latex]-\left(-4\right)[/latex]
   Show Solution

   4
2. [latex]-\left(-8\right)[/latex]
3. [latex]-\left(-15\right)[/latex]
   Show Solution

   15
4. [latex]-\left(-11\right)[/latex]

Simplify Negatives

In the following exercises, evaluate.

Exercise 1

[latex]-m[/latex] when

1.  [latex]m=3[/latex]
   Show Solution

   −3
2. [latex]m=-3[/latex]
   Show Solution

   3

Exercise 2

[latex]-p[/latex] when

1.  [latex]p=6[/latex]
2. [latex]p=-6[/latex]

Exercise 3

[latex]-c[/latex] when

1.  [latex]c=12[/latex]
   Show Solution

   −12
2. [latex]c=-12[/latex]
   Show Solution

   12

Exercise 3

[latex]-d[/latex] when

1. [latex]d=21[/latex]
2. [latex]d=-21[/latex]

Simplify Expressions with Absolute Value

In the following exercises, simplify each absolute value expression.

Exercise 1

1. [latex]|7|[/latex]
   Show Solution

   7
2. [latex]|-25|[/latex]
   Show Solution

   25
3.  [latex]|0|[/latex]
   Show Solution

   0
4.  [latex]|5|[/latex]
5.  [latex]|20|[/latex]
6.  [latex]|-19|[/latex]
7.  [latex]|-32|[/latex]
   Show Solution

   32
8. [latex]|-18|[/latex]
   Show Solution

   18
9.  [latex]|16|[/latex]
   Show Solution

   16
10. [latex]|-41|[/latex]
11.  [latex]|-40|[/latex]
12. [latex]|22|[/latex]

Simplify Expressions with Absolute Value

In the following exercises, evaluate each absolute value expression.

1.  [latex]|x|\text{ when }x=-28[/latex]
   Show Solution

   28
2.  [latex]|-u|\text{ when }u=-15[/latex]
   Show Solution

   15
3. [latex]|y|\text{ when }y=-37[/latex]
4. [latex]|-z|\text{ when }z=-24[/latex]
5. [latex]-|p|\text{ when }p=19[/latex]
   Show Solution

   −19
6. [latex]-|q|\text{ when }q=-33[/latex]
   Show Solution

   −33
7. [latex]-|a|\text{ when }a=60[/latex]
8. [latex]-|b|\text{ when }b=-12[/latex]

Simplify Expressions with Absolute Value

In the following exercises, fill in [latex]\text{<},\text{>},\text{or}=[/latex] to compare each expression.

1. [latex]-6\text{__}|-6|[/latex]
   Show Solution

   <
2. [latex]-|-3|\text{__}-3[/latex]
   Show Solution

   =
3. [latex]-8\text{__}|-8|[/latex]
4. [latex]-|-2|\text{__}-2[/latex]
5. [latex]|-3|\text{__}-|-3|[/latex]
   Show Solution

   >
6. [latex]4\text{__}-|-4|[/latex]
   Show Solution

   >
7. [latex]|-5|\text{__}-|-5|[/latex]
8. [latex]9\text{__}-|-9|[/latex]

Simplify Expressions with Absolute Value

In the following exercises, simplify each expression.

1. [latex]|8 - 4|[/latex]
   Show Solution

   4
2. [latex]|9 - 6|[/latex]
3. [latex]8|-7|[/latex]
   Show Solution

   56
4. [latex]5|-5|[/latex]
5. [latex]|15 - 7|-|14 - 6|[/latex]
   Show Solution

   0
6. [latex]|17 - 8|-|13 - 4|[/latex]
7. [latex]18-|2\left(8 - 3\right)|[/latex]
   Show Solution

   8
8. [latex]15-|3\left(8 - 5\right)|[/latex]
9. [latex]8\left(14 - 2|-2|\right)[/latex]
   Show Solution

   80
10. [latex]6\left(13 - 4|-2|\right)[/latex]

Translate Word Phrases into Expressions with Integers

Translate each phrase into an expression with integers. Do not simplify.

Exercise 1

1. the opposite of [latex]8[/latex]
   Show Solution

   −8
2. the opposite of [latex]-6[/latex]
   Show Solution

   −(−6), or 6
3. negative three
   Show Solution

   −3
4. [latex]4[/latex] minus negative [latex]3[/latex]
   Show Solution

   4−(−3)
5. the opposite of [latex]11[/latex]
6. the opposite of [latex]-4[/latex]
7. negative nine
8. [latex]8[/latex] minus negative [latex]2[/latex]
9. the opposite of [latex]20[/latex]
   Show Solution

   −20
10. the opposite of [latex]-5[/latex]
    Show Solution

    −(−5), or 5
11. the opposite of [latex]12[/latex]
    Show Solution

    −12
12. [latex]18[/latex] minus negative [latex]7[/latex]
    Show Solution

    18−(−7)
13. the opposite of [latex]15[/latex]
14. the opposite of [latex]-9[/latex]
15. negative sixty
16. [latex]12[/latex] minus [latex]5[/latex]
17. a temperature of [latex]6\text{degrees}[/latex] below zero
    Show Solution

    −6 degrees
18. a temperature of [latex]14\text{degrees}[/latex] below zero
19. an elevation of [latex]40\text{ feet }[/latex] below sea level
    Show Solution

    −40 feet
20. an elevation of [latex]65\text{ feet }[/latex] below sea level
21. a football play loss of [latex]12\text{ yards }[/latex]
    Show Solution

    −12 yards
22. a football play gain of [latex]4\text{ yards }[/latex]
23. a stock gain of [latex]\$3[/latex]
    Show Solution

    $3
24. a stock loss of [latex]\$5[/latex]
25. a golf score one above par
    Show Solution

    +1
26. a golf score of [latex]3[/latex] below par

Adding Integers

Model Addition of Integers

In the following exercises, model the expression to simplify.

1. [latex]7+4[/latex]
   Show Solution

   
   11
2. [latex]8+5[/latex]
3. [latex]-6+\left(-3\right)[/latex]
   Show Solution

   
   −9 
4. [latex]-5+\left(-5\right)[/latex]
5. [latex]-7+5[/latex]
   Show Solution

   
   −2
6. [latex]-9+6[/latex]
7. [latex]8+\left(-7\right)[/latex]
   Show Solution

   
   1
8. [latex]9+\left(-4\right)[/latex]

Simplify Expressions with Integers

In the following exercises, simplify each expression.

1. [latex]-21+\left(-59\right)[/latex]
   Show Solution

   −80
2. [latex]-35+\left(-47\right)[/latex]
3. [latex]48+\left(-16\right)[/latex]
   Show Solution

   32
4. [latex]34+\left(-19\right)[/latex]
5. [latex]-200+65[/latex]
   Show Solution

   −135
6. [latex]-150+45[/latex]
7. [latex]2+\left(-8\right)+6[/latex]
   Show Solution

   0
8. [latex]4+\left(-9\right)+7[/latex]
9. [latex]-14+\left(-12\right)+4[/latex]
   Show Solution

   −22
10. [latex]-17+\left(-18\right)+6[/latex]
11. [latex]135+\left(-110\right)+83[/latex]
    Show Solution

    108
12. [latex]140+\left(-75\right)+67[/latex]
13. [latex]-32+24+\left(-6\right)+10[/latex]
    Show Solution

    −4
14. [latex]-38+27+\left(-8\right)+12[/latex]
15. [latex]19+2\left(-3+8\right)[/latex]
    Show Solution

    29
16. [latex]24+3\left(-5+9\right)[/latex]

Evaluate Variable Expressions with Integers

In the following exercises, evaluate each expression.

Exercise 1

[latex]x+8[/latex] when

1.  [latex]x=-26[/latex]
   Show Solution

   −18
2. [latex]x=-95[/latex]
   Show Solution

   −87

Exercise 2

[latex]y+9[/latex] when

1.  [latex]y=-29[/latex]
2. [latex]y=-84[/latex]

Exercise 3

[latex]y+\left(-14\right)[/latex] when

1. [latex]y=-33[/latex]
   Show Solution

   −47
2. [latex]y=30[/latex]
   Show Solution

   16

Exercise 4

[latex]x+\left(-21\right)[/latex] when

1.  [latex]x=-27[/latex]
2. [latex]x=44[/latex]

Exercise 5

When [latex]a=-7[/latex], evaluate:

1.  [latex]a+3[/latex]
   Show Solution

   −4
2. [latex]-a+3[/latex]
   Show Solution

   10

Exercise 6

When [latex]b=-11[/latex], evaluate:

1. [latex]b+6[/latex]
2. [latex]-b+6[/latex]

Exercise 7

When [latex]c=-9[/latex], evaluate:

1. [latex]c+\left(-4\right)[/latex]
   Show Solution

   −13
2. [latex]-c+\left(-4\right)[/latex]
   Show Solution

   5

Exercise 8

When [latex]d=-8[/latex], evaluate:

1. [latex]d+\left(-9\right)[/latex]
2. [latex]-d+\left(-9\right)[/latex]

Evaluate Variable Expressions with Integers

In the following exercises, evaluate each expression.

1. [latex]m+n[/latex] when, [latex]m=-15[/latex] , [latex]n=7[/latex]
   Show Solution

   −8
2. [latex]p+q[/latex] when, [latex]p=-9[/latex] , [latex]q=17[/latex]
3. [latex]r - 3s[/latex] when, [latex]r=16[/latex] , [latex]s=2[/latex]
   Show Solution

   10
4. [latex]2t+u[/latex] when, [latex]t=-6[/latex] , [latex]u=-5[/latex]
5. [latex]{\left(a+b\right)}^{2}[/latex] when, [latex]a=-7[/latex] , [latex]b=15[/latex]
   Show Solution

   64
6. [latex]{\left(c+d\right)}^{2}[/latex] when, [latex]c=-5[/latex] , [latex]d=14[/latex]
7. [latex]{\left(x+y\right)}^{2}[/latex] when, [latex]x=-3[/latex] , [latex]y=14[/latex]
   Show Solution

   121
8. [latex]{\left(y+z\right)}^{2}[/latex] when, [latex]y=-3[/latex] , [latex]z=15[/latex]

Translate Word Phrases to Algebraic Expressions

In the following exercises, translate each phrase into an algebraic expression and then simplify.

1. The sum of [latex]-14[/latex] and [latex]5[/latex]
   Show Solution

   −14 + 5 = −9
2. The sum of [latex]-22[/latex] and [latex]9[/latex]
3. [latex]8[/latex] more than [latex]-2[/latex]
   Show Solution

   −2 + 8 = 6
4. [latex]5[/latex] more than [latex]-1[/latex]
5. [latex]-10[/latex] added to [latex]-15[/latex]
   Show Solution

   −15 + (−10) = −25
6. [latex]-6[/latex] added to [latex]-20[/latex]
7. [latex]6[/latex] more than the sum of [latex]-1[/latex] and [latex]-12[/latex]
   Show Solution

   [−1 + (−12)] + 6 = −7
8. [latex]3[/latex] more than the sum of [latex]-2[/latex] and [latex]-8[/latex]
9. the sum of [latex]10[/latex] and [latex]-19[/latex], increased by [latex]4[/latex]
   Show Solution

   [10 + (−19)] + 4 = −5
10. the sum of [latex]12[/latex] and [latex]-15[/latex], increased by [latex]1[/latex]

Add Integers in Applications

In the following exercises, solve.

Temperature

The temperature in St. Paul, Minnesota was [latex]-19^{\circ}\text{ F}[/latex] at sunrise. By noon the temperature had risen [latex]26^{\circ}\text{ F.}[/latex] What was the temperature at noon?

Temperature

The temperature in Chicago was [latex]-15^{\circ}\text{ F}[/latex] at 6 am. By afternoon the temperature had risen [latex]28^{\circ}\text{ F}[/latex]. What was the afternoon temperature?

Credit Cards

Lupe owes [latex]\$73[/latex] on her credit card. Then she charges [latex]\$45[/latex] more. What is the new balance?

Credit Cards

Frank owes [latex]\$212[/latex] on his credit card. Then he charges [latex]\$105[/latex] more. What is the new balance?

Weight Loss

Angie lost [latex]\text{3 pounds}[/latex] the first week of her diet. Over the next three weeks, she lost [latex]\text{2 pounds,}[/latex] gained [latex]\text{1 pound,}[/latex] and then lost [latex]\text{4 pounds.}[/latex] What was the change in her weight over the four weeks?

Weight Loss

April lost [latex]\text{5 pounds}[/latex] the first week of her diet. Over the next three weeks, she lost [latex]\text{3 pounds,}[/latex] gained [latex]\text{2 pounds,}[/latex] and then lost [latex]\text{1 pound.}[/latex] What was the change in her weight over the four weeks?

Football

The Rams took possession of the football on their own [latex]\text{35-yard line.}[/latex] In the next three plays, they lost [latex]\text{12 yards,}[/latex] gained [latex]\text{8 yards,}[/latex] then lost [latex]\text{6 yards.}[/latex] On what yard line was the ball at the end of those three plays?

Football

The Cowboys began with the ball on their own [latex]\text{20-yard line.}[/latex] They gained [latex]\text{15 yards,}[/latex] lost [latex]\text{3 yards}[/latex] and then gained [latex]\text{6 yards}[/latex] on the next three plays. Where was the ball at the end of these plays?

Calories

Lisbeth walked from her house to get a frozen yogurt, and then she walked home. By walking for a total of [latex]\text{20 minutes,}[/latex] she burned [latex]\text{90 calories.}[/latex] The frozen yogurt she ate was [latex]\text{110 calories.}[/latex] What was her total calorie gain or loss?

Calories

Ozzie rode his bike for [latex]\text{30 minutes,}[/latex] burning [latex]\text{168 calories.}[/latex] Then he had a [latex]\text{140-calorie}[/latex] iced blended mocha. Represent the change in calories as an integer.

Subtracting Integers

Model Subtraction of Integers

In the following exercises, model each expression and simplify.

1. [latex]8 - 2[/latex]
   Show Solution

   
   6
2. [latex]9 - 3[/latex]
3. [latex]-5-\left(-1\right)[/latex]
   Show Solution

   
   –4
4. [latex]-6-\left(-4\right)[/latex]
5. [latex]-5 - 4[/latex]
   Show Solution

   
   –9
6. [latex]-7 - 2[/latex]
7. [latex]8-\left(-4\right)[/latex]
   Show Solution

   
   12 
8. [latex]7-\left(-3\right)[/latex]

Simplify Expressions with Integers

In the following exercises, simplify each expression.

1.  [latex]15 - 6[/latex]
   Show Solution

   9
2. [latex]15+\left(-6\right)[/latex]
   Show Solution

   9
3. [latex]12 - 9[/latex]
4. [latex]12+\left(-9\right)[/latex]
5. [latex]44 - 28[/latex]
   Show Solution

   16
6. [latex]44+\left(-28\right)[/latex]
   Show Solution

   16
7.  [latex]35 - 16[/latex]
8. [latex]35+\left(-16\right)[/latex]
9. [latex]8-\left(-9\right)[/latex]
   Show Solution

   17
10. [latex]8+9[/latex]
    Show Solution

    17
11. [latex]4-\left(-4\right)[/latex]
12. [latex]4+4[/latex]
13. [latex]27-\left(-18\right)[/latex]
    Show Solution

    45
14. [latex]27+18[/latex]
    Show Solution

    45
15. [latex]46-\left(-37\right)[/latex]
16. [latex]46+37[/latex]

Simplify Expressions with Integers

In the following exercises, simplify each expression.

1. [latex]15-\left(-12\right)[/latex]
   Show Solution

   27
2. [latex]14-\left(-11\right)[/latex]
3. [latex]10-\left(-19\right)[/latex]
   Show Solution

   29
4. [latex]11-\left(-18\right)[/latex]
5. [latex]48 - 87[/latex]
   Show Solution

   −39
6. [latex]45 - 69[/latex]
7. [latex]31 - 79[/latex]
   Show Solution

   −48
8. [latex]39 - 81[/latex]
9. [latex]-31 - 11[/latex]
   Show Solution

   −42
10. [latex]-32 - 18[/latex]
11. [latex]-17 - 42[/latex]
    Show Solution

    −59
12. [latex]-19 - 46[/latex]
13. [latex]-103-\left(-52\right)[/latex]
    Show Solution

    −51
14. [latex]-105-\left(-68\right)[/latex]
15. [latex]-45-\left(-54\right)[/latex]
    Show Solution

    9
16. [latex]-58-\left(-67\right)[/latex]
17. [latex]8 - 3 - 7[/latex]
    Show Solution

    −2
18. [latex]9 - 6 - 5[/latex]
19. [latex]-5 - 4+7[/latex]
    Show Solution

    −2
20. [latex]-3 - 8+4[/latex]
21. [latex]-14-\left(-27\right)+9[/latex]
    Show Solution

    22
22. [latex]-15-\left(-28\right)+5[/latex]
23. [latex]71+\left(-10\right)-8[/latex]
    Show Solution

    53
24. [latex]64+\left(-17\right)-9[/latex]
25. [latex]-16-\left(-4+1\right)-7[/latex]
    Show Solution

    −20
26. [latex]-15-\left(-6+4\right)-3[/latex]
27. [latex]\left(2 - 7\right)-\left(3 - 8\right)[/latex]
    Show Solution

    0
28. [latex]\left(1 - 8\right)-\left(2 - 9\right)[/latex]
29. [latex]-\left(6 - 8\right)-\left(2 - 4\right)[/latex]
    Show Solution

    4
30. [latex]-\left(4 - 5\right)-\left(7 - 8\right)[/latex]
31. [latex]25-\left[10-\left(3 - 12\right)\right][/latex]
    Show Solution

    6
32. [latex]32-\left[5-\left(15 - 20\right)\right][/latex]
33. [latex]6\cdot 3 - 4\cdot 3 - 7\cdot 2[/latex]
    Show Solution

    −8
34. [latex]5\cdot 7 - 8\cdot 2 - 4\cdot 9[/latex]
35. [latex]{5}^{2}-{6}^{2}[/latex]
    Show Solution

    −11
36. [latex]{6}^{2}-{7}^{2}[/latex]

Evaluate Variable Expressions with Integers

In the following exercises, evaluate each expression for the given values.

Exercise 1

[latex]x - 6\text{ when }[/latex]

1.  [latex]x=3[/latex]
   Show Solution

   -3
2. [latex]x=-3[/latex]
   Show Solution

   −9

Exercise 2

[latex]x - 4\text{ when }[/latex]

1.  [latex]x=5[/latex]
2. [latex]x=-5[/latex]

Exercise 3

[latex]5-y\text{ when }[/latex]

1. [latex]y=2[/latex]
   Show Solution

   3
2. [latex]y=-2[/latex]
   Show Solution

   7

Exercise 4

[latex]8-y\text{ when }[/latex]

1.  [latex]y=3[/latex]
2. [latex]y=-3[/latex]

Exercise 5

1. [latex]4{x}^{2}-15x+1\text{ when }x=3[/latex]
   Show Solution

   −8
2. [latex]5{x}^{2}-14x+7\text{ when }x=2[/latex]
3. [latex]-12 - 5{x}^{2}\text{ when }x=6[/latex]
   Show Solution

   −192
4. [latex]-19 - 4{x}^{2}\text{ when }x=5[/latex]

Translate Word Phrases to Algebraic Expressions

In the following exercises, translate each phrase into an algebraic expression and then simplify.

1. The difference of [latex]3[/latex] and [latex]-10[/latex]
   Show Solution

   −3 − (−10) = 13
2. Subtract [latex]-20[/latex] from [latex]45[/latex]
   Show Solution

   45 − (−20) = 65
3. The difference of [latex]8[/latex] and [latex]-12[/latex]
4. Subtract [latex]-13[/latex] from [latex]50[/latex]
5. The difference of [latex]-6[/latex] and [latex]9[/latex]
   Show Solution

   −6 − 9 = −15
6.  Subtract [latex]-12[/latex] from [latex]-16[/latex]
   Show Solution

   −16 − (−12) = −4
7. The difference of [latex]-8[/latex] and [latex]9[/latex]
8. Subtract [latex]-15[/latex] from [latex]-19[/latex]
9. [latex]8[/latex] less than [latex]-17[/latex]
   Show Solution

   −17 − 8 = −25
10. [latex]-24[/latex] minus [latex]37[/latex]
    Show Solution

    −24 − 37 = −61
11. [latex]5[/latex] less than [latex]-14[/latex]
12. [latex]-13[/latex] minus [latex]42[/latex]
13. [latex]21[/latex] less than [latex]6[/latex]
    Show Solution

    6 − 21 = −15
14. [latex]31[/latex] subtracted from [latex]-19[/latex]
    Show Solution

    −19 − 31 = −50
15. [latex]34[/latex] less than [latex]7[/latex]
16. [latex]29[/latex] subtracted from [latex]-50[/latex]

Subtract Integers in Applications

In the following exercises, solve the following applications.

Temperature

One morning, the temperature in Urbana, Illinois, was [latex]28^{\circ}\text{ Fahrenheit}[/latex]. By evening, the temperature had dropped [latex]38^{\circ}\text{ Fahrenheit}[/latex]. What was the temperature that evening?

Temperature

On Thursday, the temperature in Spincich Lake, Michigan, was [latex]22^{\circ}\text{ Fahrenheit}[/latex]. By Friday, the temperature had dropped [latex]35^{\circ}\text{ Fahrenheit}[/latex]. What was the temperature on Friday?

Temperature

On January 15, the high temperature in Anaheim, California, was [latex]84^{\circ}\text{ Fahrenheit}[/latex]. That same day, the high temperature in Embarrass, Minnesota was [latex]-12^{\circ}\text{ Fahrenheit}[/latex]. What was the difference between the temperature in Anaheim and the temperature in Embarrass?

Temperature

On January 21, the high temperature in Palm Springs, California, was [latex]89^{\circ}[/latex], and the high temperature in Whitefield, New Hampshire was [latex]-31^{\circ}[/latex]. What was the difference between the temperature in Palm Springs and the temperature in Whitefield?

Football

At the first down, the Warriors football team had the ball on their [latex]30\text{-yard line}[/latex]. On the next three downs, they gained [latex]2\text{ yards}[/latex], lost [latex]7\text{ yards}[/latex], and lost [latex]4\text{ yards}[/latex]. What was the yard line at the end of the third down?

Football

At the first down, the Barons football team had the ball on their [latex]20\text{-yard line}[/latex]. On the next three downs, they lost [latex]\text{8 yards,}[/latex] gained [latex]5\text{ yards}[/latex], and lost [latex]6\text{ yards}[/latex]. What was the yard line at the end of the third down?

Checking Account

John has [latex]\$148[/latex] in his checking account. He writes a check for [latex]\$83[/latex]. What is the new balance in his checking account?

Checking Account

Ellie has [latex]\$426[/latex] in her checking account. She writes a check for [latex]\$152[/latex]. What is the new balance in her checking account?

Checking Account

Gina has [latex]\$210[/latex] in her checking account. She writes a check for [latex]\$250[/latex]. What is the new balance in her checking account?

Checking Account

Frank has [latex]\$94[/latex] in his checking account. He writes a check for [latex]\$110[/latex]. What is the new balance in his checking account?

Checking Account

Bill has a balance of [latex]-\$14[/latex] in his checking account. He deposits [latex]\$40[/latex] to the account. What is the new balance?

Checking Account

Patty has a balance of [latex]-\$23[/latex] in her checking account. She deposits [latex]\$80[/latex] to the account. What is the new balance?

Multiplying and Dividing Integers

Multiply Integers

In the following exercises, multiply each pair of integers.

1. [latex]-4\cdot 8[/latex]
   Show Solution

   −32
2. [latex]-3\cdot 9[/latex]
3. [latex]-5\left(7\right)[/latex]
   Show Solution

   −35
4. [latex]-8\left(6\right)[/latex]
5. [latex]-18\left(-2\right)[/latex]
   Show Solution

   36
6. [latex]-10\left(-6\right)[/latex]
7. [latex]9\left(-7\right)[/latex]
   Show Solution

   −63
8. [latex]13\left(-5\right)[/latex]
9. [latex]-1\cdot 6[/latex]
   Show Solution

   −6
10. [latex]-1\cdot 3[/latex]
11. [latex]-1\left(-14\right)[/latex]
    Show Solution

    14
12. [latex]-1\left(-19\right)[/latex]

Divide Integers

In the following exercises, divide.

1. [latex]-24\div 6[/latex]
   Show Solution

   −4
2. [latex]-28\div 7[/latex]
3. [latex]56\div \left(-7\right)[/latex]
   Show Solution

   −8
4. [latex]35\div \left(-7\right)[/latex]
5. [latex]-52\div \left(-4\right)[/latex]
   Show Solution

   13
6. [latex]-84\div \left(-6\right)[/latex]
7. [latex]-180\div 15[/latex]
   Show Solution

   −12
8. [latex]-192\div 12[/latex]
9. [latex]49\div \left(-1\right)[/latex]
   Show Solution

   −49
10. [latex]62\div \left(-1\right)[/latex]

Simplify Expressions with Integers

In the following exercises, simplify each expression.

1. [latex]5\left(-6\right)+7\left(-2\right)-3[/latex]
   Show Solution

   −47
2. [latex]8\left(-4\right)+5\left(-4\right)-6[/latex]
3. [latex]-8\left(-2\right)-3\left(-9\right)[/latex]
   Show Solution

   43
4. [latex]-7\left(-4\right)-5\left(-3\right)[/latex]
5. [latex]{\left(-5\right)}^{3}[/latex]
   Show Solution

   −125
6. [latex]{\left(-4\right)}^{3}[/latex]
7. [latex]{\left(-2\right)}^{6}[/latex]
   Show Solution

   64
8. [latex]{\left(-3\right)}^{5}[/latex]
9. [latex]-{4}^{2}[/latex]
   Show Solution

   −16
10. [latex]-{6}^{2}[/latex]
11. [latex]-3\left(-5\right)\left(6\right)[/latex]
    Show Solution

    90
12. [latex]-4\left(-6\right)\left(3\right)[/latex]
13. [latex]-4\cdot 2\cdot 11[/latex]
    Show Solution

    −88
14. [latex]-5\cdot 3\cdot 10[/latex]
15. [latex]\left(8 - 11\right)\left(9 - 12\right)[/latex]
    Show Solution

    9
16. [latex]\left(6 - 11\right)\left(8 - 13\right)[/latex]
17. [latex]26 - 3\left(2 - 7\right)[/latex]
    Show Solution

    41
18. [latex]23 - 2\left(4 - 6\right)[/latex]
19. [latex]-10\left(-4\right)\div \left(-8\right)[/latex]
    Show Solution

    −5
20. [latex]-8\left(-6\right)\div \left(-4\right)[/latex]
21. [latex]65\div \left(-5\right)+\left(-28\right)\div \left(-7\right)[/latex]
    Show Solution

    −9
22. [latex]52\div \left(-4\right)+\left(-32\right)\div \left(-8\right)[/latex]
23. [latex]9 - 2\left[3 - 8\left(-2\right)\right][/latex]
    Show Solution

    −29
24. [latex]11 - 3\left[7 - 4\left(-2\right)\right][/latex]
25. [latex]{\left(-3\right)}^{2}-24\div \left(8 - 2\right)[/latex]
    Show Solution

    5
26. [latex]{\left(-4\right)}^{2}-32\div \left(12 - 4\right)[/latex]

Evaluate Variable Expressions with Integers

In the following exercises, evaluate each expression.

Exercise 1

[latex]-2x+17\text{ when }[/latex]

1.  [latex]x=8[/latex]
   Show Solution

   1
2. [latex]x=-8[/latex]
   Show Solution

   33

Exercise 2

[latex]-5y+14\text{ when }[/latex]

1. [latex]y=9[/latex]
2. [latex]y=-9[/latex]

Exercise 3

[latex]10 - 3m\text{ when }[/latex]

1. [latex]m=5[/latex]
   Show Solution

   −5
2. [latex]m=-5[/latex]
   Show Solution

   25

Exercise 4

1. [latex]18 - 4n\text{ when }[/latex]
2. [latex]n=3[/latex]

Exercise 5

[latex]n=-3[/latex]

1. [latex]{p}^{2}-5p+5\text{ when }p=-1[/latex]
   Show Solution

   8
2. [latex]{q}^{2}-2q+9\text{ when }q=-2[/latex]
3. [latex]2{w}^{2}-3w+7\text{ when }w=-2[/latex]
   Show Solution

   21
4. [latex]3{u}^{2}-4u+5\text{ when }u=-3[/latex]
5. [latex]6x - 5y+15\text{ when }x=3\text{ and }y=-1[/latex]
   Show Solution

   38
6. [latex]3p - 2q+9\text{ when }p=8\text{ and }q=-2[/latex]
7. [latex]9a - 2b - 8\text{ when }a=-6\text{ and }b=-3[/latex]
   Show Solution

   −56
8. [latex]7m - 4n - 2\text{ when }m=-4\text{ and }n=-9[/latex]

Translate Word Phrases to Algebraic Expressions

In the following exercises, translate to an algebraic expression and simplify if possible.

1. The product of [latex]-3[/latex] and 15
   Show Solution

   −3·15 = −45
2. The product of [latex]-4[/latex] and [latex]16[/latex]
3. The quotient of [latex]-60[/latex] and [latex]-20[/latex]
   Show Solution

   −60 ÷ (−20) = 3
4. The quotient of [latex]-40[/latex] and [latex]-20[/latex]
5. The quotient of [latex]-6[/latex] and the sum of [latex]a[/latex] and [latex]b[/latex]
   Show Solution

   [latex]\Large\frac{-6}{a+b}[/latex]
6. The quotient of [latex]-7[/latex] and the sum of [latex]m[/latex] and [latex]n[/latex]
7. The product of [latex]-10[/latex] and the difference of [latex]p\text{ and }q[/latex]
   Show Solution

   −10 (p − q)
8. The product of [latex]-13[/latex] and the difference of [latex]c\text{ and }d[/latex]