Introduction to Whole Number Basics

Identify Counting Numbers and Whole Numbers

In the following exercises, determine which of the following numbers are a) counting numbers and b) whole numbers.

1. [latex]0,\frac{2}{3},5,8.1,125[/latex]
   Show Solution

   a) Counting numbers: 5, 125
   b) Whole numbers: 0, 5, 125
2. [latex]0,\frac{7}{10},3,20.5,300[/latex]
3. [latex]0,\frac{4}{9},3.9,50,221[/latex]
   Show Solution

   a) Counting numbers: 50, 221
   b) Whole numbers: 0, 50, 221
4. [latex]0,\frac{3}{5},10,303,422.6[/latex]

Model Whole Numbers

In the following exercises, use place value notation to find the value of the number modeled by the [latex]\text{base -10}[/latex] blocks.

Exercise 1

Exercise 2

Exercise 3

Exercises 4

Identify the Place Value of a Digit

In the following exercises, find the place value of the given digits.

Exercise 1

[latex]579,601[/latex]

1. 9
2. 6
3. 0
4. 7
5. 5

Exercise 2

[latex]398,127[/latex]

1. 9
2. 3
3. 2
4. 8
5. 7

Exercise 3

[latex]56,804,379[/latex]

1. 8
2. 6
3. 4
4. 7
5. 0

Exercise 4

[latex]78,320,465[/latex]

1. 8
2. 4
3. 2
4. 6
5. 7

Use Place Value to Name Whole Numbers

In the following exercises, name each number in words.

Exercise 1

1. [latex]1,078[/latex]
   Show Solution

   One thousand, seventy-eight
2. [latex]5,902[/latex]
3. [latex]364,510[/latex]
   Show Solution

   Three hundred sixty-four thousand, five hundred ten
4. [latex]146,023[/latex]
5. [latex]5,846,103[/latex]
   Show Solution

   Five million, eight hundred forty-six thousand, one hundred three
6. [latex]1,458,398[/latex]
7. [latex]37,889,005[/latex]
   Show Solution

   Thirty seven million, eight hundred eighty-nine thousand, five
8. [latex]62,008,465[/latex]

Exercise 2

1. The height of Mount Ranier is [latex]14,410[/latex] feet.
   Show Solution

   Fourteen thousand, four hundred ten
2. The height of Mount Adams is [latex]12,276[/latex] feet.
3. Seventy years is [latex]613,200[/latex] hours.
   Show Solution

   Six hundred thirteen thousand, two hundred
4. One year is [latex]525,600[/latex] minutes.
5. The U.S. Census estimate of the population of Miami-Dade county was [latex]2,617,176[/latex].
   Show Solution

   Two million, six hundred seventeen thousand, one hundred seventy-six
6. The population of Chicago was [latex]2,718,782[/latex].
7. There are projected to be [latex]23,867,000[/latex] college and university students in the US in five years.
   Show Solution

   Twenty three million, eight hundred sixty-seven thousand
8. About twelve years ago there were [latex]20,665,415[/latex] registered automobiles in California.
9. The population of China is expected to reach [latex]1,377,583,156[/latex] in [latex]2016[/latex].
   Show Solution

   One billion, three hundred seventy-seven million, five hundred eighty-three thousand, one hundred fifty-six
10. The population of India is estimated at [latex]1,267,401,849[/latex] as of July [latex]1,2014[/latex].

Use Place Value to Write Whole Numbers

In the following exercises, write each number as a whole number using digits.

1. four hundred twelve
   Show Solution

   412
2. two hundred fifty-three
3. thirty-five thousand, nine hundred seventy-five
   Show Solution

   35,975
4. sixty-one thousand, four hundred fifteen
5. eleven million, forty-four thousand, one hundred sixty-seven
   Show Solution

   11,044,167
6. eighteen million, one hundred two thousand, seven hundred eighty-three
7. three billion, two hundred twenty-six million, five hundred twelve thousand, seventeen
   Show Solution

   3,226,512,017
8. eleven billion, four hundred seventy-one million, thirty-six thousand, one hundred six
9. The population of the world was estimated to be seven billion, one hundred seventy-three million people.
   Show Solution

   7,173,000,000
10. The age of the solar system is estimated to be four billion, five hundred sixty-eight million years.
11. Lake Tahoe has a capacity of thirty-nine trillion gallons of water.
    Show Solution

    39,000,000,000,000
12. The federal government budget was three trillion, five hundred billion dollars.

Round Whole Numbers

In the following exercises, round to the indicated place value.

Round to the nearest ten:

1. [latex]386[/latex]
   Show Solution

   390
2. [latex]2,931[/latex]
   Show Solution

   2,930

Round to the nearest ten:

1. [latex]792[/latex]
   Show Solution

   790
2. [latex]5,647[/latex]
   Show Solution

   5,650

Round to the nearest hundred:

1. [latex]13,748[/latex]
   Show Solution

   13,700
2. [latex]391,794[/latex]
   Show Solution

   391,800

Round to the nearest hundred:

1. [latex]28,166[/latex]
   Show Solution

   28,200
2. [latex]481,628[/latex]
   Show Solution

   481,700

Round to the nearest ten:

1. [latex]1,492[/latex]
   Show Solution

   1,490
2. [latex]1,497[/latex]
   Show Solution

   1,500

Round to the nearest thousand:

1. [latex]2,391[/latex]
   Show Solution

   2,000
2. [latex]2,795[/latex]
   Show Solution

   3,000

Round to the nearest hundred:

1. [latex]63,994[/latex]
   Show Solution

   [latex]64,000[/latex]
2. [latex]63,949[/latex]
   Show Solution

   [latex]63,900[/latex]

Round to the nearest thousand:

1. [latex]163,584[/latex]
   Show Solution

   164,000
2. [latex]163,246[/latex]
   Show Solution

   163,000

Adding Whole Numbers

Use Addition Notation

In the following exercises, translate the following from math expressions to words.

1. [latex]5+2[/latex]
   Show Solution

   five plus two; the sum of 5 and 2.
2. [latex]6+3[/latex]
3. [latex]13+18[/latex]
   Show Solution

   thirteen plus eighteen; the sum of 13 and 18.
4. [latex]15+16[/latex]
5. [latex]214+642[/latex]
   Show Solution

   two hundred fourteen plus six hundred forty-two; the sum of 214 and 642
6. [latex]438+113[/latex]

Model Addition of Whole Numbers

In the following exercises, model the addition.

1. [latex]2+4[/latex]
   Show Solution

   
   [latex]2+4=6[/latex]
2. [latex]5+3[/latex]
3. [latex]8+4[/latex]
   Show Solution

   
   [latex]8+4=12[/latex]
4. [latex]5+9[/latex]
5. [latex]14+75[/latex]
   Show Solution

   
   [latex]14+75=89[/latex]
6. [latex]15+63[/latex]
7. [latex]16+25[/latex]
   Show Solution

   
   [latex]16+25=41[/latex]
8. [latex]14+27[/latex]

Add Whole Numbers

In the following exercises, fill in the missing values in each chart.

Exercise 1

Exercise 2

Exercises 3

Exercise 4

Exercise 5

Exercise 6

Add Whole Numbers

In the following exercises, add.

1. [latex]0+13[/latex]
   Show Solution

   13
2. [latex]13+0[/latex]
   Show Solution

   13
3. [latex]0+5,280[/latex]
4. [latex]5,280+0[/latex]
5. [latex]8+3[/latex]
   Show Solution

   11
6. [latex]3+8[/latex]
   Show Solution

   11
7. [latex]7+5[/latex]
8. [latex]5+7[/latex]
9. [latex]45+33[/latex]
   Show Solution

   [latex]78[/latex]
10. [latex]37+22[/latex]
11. [latex]71+28[/latex]
    Show Solution

    [latex]99[/latex]
12. [latex]43+53[/latex]
13. [latex]26+59[/latex]
    Show Solution

    [latex]85[/latex]
14. [latex]38+17[/latex]
15. [latex]64+78[/latex]
    Show Solution

    [latex]142[/latex]
16. [latex]92+39[/latex]
17. [latex]168+325[/latex]
    Show Solution

    [latex]493[/latex]
18. [latex]247+149[/latex]
19. [latex]584+277[/latex]
    Show Solution

    [latex]861[/latex]
20. [latex]175+648[/latex]
21. [latex]832+199[/latex]
    Show Solution

    [latex]1,031[/latex]
22. [latex]775+369[/latex]
23. [latex]6,358+492[/latex]
    Show Solution

    [latex]6,850[/latex]
24. [latex]9,184+578[/latex]
25. [latex]3,740+18,593[/latex]
    Show Solution

    [latex]22,333[/latex]
26. [latex]6,118+15,990[/latex]
27. [latex]485,012+619,848[/latex]
    Show Solution

    [latex]1,104,860[/latex]
28. [latex]368,911+857,289[/latex]
29. [latex]24,731+592+3,868[/latex]
    Show Solution

    [latex]29,191[/latex]
30. [latex]28,925+817+4,593[/latex]
31. [latex]8,015+76,946+16,570[/latex]
    Show Solution

    [latex]101,531[/latex]
32. [latex]6,291+54,107+28,635[/latex]

Translate Word Phrases to Math Notation

In the following exercises, translate each phrase into math notation and then simplify.

1. the sum of [latex]13[/latex] and [latex]18[/latex]
   Show Solution

   [latex]13+18=31[/latex]
2. the sum of [latex]12[/latex] and [latex]19[/latex]
3. the sum of [latex]90[/latex] and [latex]65[/latex]
   Show Solution

   [latex]90+65=155[/latex]
4. the sum of [latex]70[/latex] and [latex]38[/latex]
5. [latex]33[/latex] increased by [latex]49[/latex]
   Show Solution

   [latex]33+49=82[/latex]
6. [latex]68[/latex] increased by [latex]25[/latex]
7. [latex]250[/latex] more than [latex]599[/latex]
   Show Solution

   [latex]250+599=849[/latex]
8. [latex]115[/latex] more than [latex]286[/latex]
9. the total of [latex]628[/latex] and [latex]77[/latex]
   Show Solution

   [latex]628+77=705[/latex]
10. the total of [latex]593[/latex] and [latex]79[/latex]
11. [latex]1,482[/latex] added to [latex]915[/latex]
    Show Solution

    [latex]915+1,482=2,397[/latex]
12. [latex]2,719[/latex] added to [latex]682[/latex]

Add Whole Numbers in Applications

In the following exercises, solve the problem.

Home remodeling

Sophia remodeled her kitchen and bought a new range, microwave, and dishwasher. The range cost [latex]\$1,100[/latex], the microwave cost [latex]\$250[/latex], and the dishwasher cost [latex]\$525[/latex]. What was the total cost of these three appliances?

Sports equipment

Aiden bought a baseball bat, helmet, and glove. The bat cost [latex]\$299[/latex], the helmet cost [latex]\$35[/latex], and the glove cost [latex]\$68[/latex]. What was the total cost of Aiden’s sports equipment?

Bike riding

Ethan rode his bike [latex]14[/latex] miles on Monday, [latex]19[/latex] miles on Tuesday, [latex]12[/latex] miles on Wednesday, [latex]25[/latex] miles on Friday, and [latex]68[/latex] miles on Saturday. What was the total number of miles Ethan rode?

Business

Chloe has a flower shop. Last week she made [latex]19[/latex] floral arrangements on Monday, [latex]12[/latex] on Tuesday, [latex]23[/latex] on Wednesday, [latex]29[/latex] on Thursday, and [latex]44[/latex] on Friday. What was the total number of floral arrangements Chloe made?

Apartment size

Jackson lives in a 7 room apartment. The number of square feet in each room is [latex]238,120,156,196,100,132[/latex], and [latex]225[/latex]. What is the total number of square feet in all [latex]7[/latex] rooms?

Weight

Seven men rented a fishing boat. The weights of the men were [latex]175,192,148,169,205,181[/latex], and [latex]\text{225}[/latex] pounds. What was the total weight of the seven men?

Salary

Last year Natalie’s salary was [latex]\$82,572[/latex]. Two years ago, her salary was [latex]\$79,316[/latex], and three years ago it was [latex]\$75,298[/latex]. What is the total amount of Natalie’s salary for the past three years?

Home sales

Emma is a realtor. Last month, she sold three houses. The selling prices of the houses were [latex]\$292,540,\$505,875[/latex], and [latex]\$423,699[/latex]. What was the total of the three selling prices?

Finding Perimeter

In the following exercises, find the perimeter of each figure.

Exercise 1

Exercise 2

Exercise 3

Exercise 4

Exercise 5

Exercise 6

Exercise 7

Exercise 8

Subtracting Whole Numbers

Use Subtraction Notation

In the following exercises, translate from math notation to words.

1. [latex]15 - 9[/latex]
   Show Solution

   fifteen minus nine; the difference of fifteen and nine
2. [latex]18 - 16[/latex]
3. [latex]42 - 35[/latex]
   Show Solution

   forty-two minus thirty-five; the difference of forty-two and thirty-five
4. [latex]83 - 64[/latex]
5. [latex]675 - 350[/latex]
   Show Solution

   hundred seventy-five minus three hundred fifty; the difference of six hundred seventy-five and three hundred fifty
6. [latex]790 - 525[/latex]

Model Subtraction of Whole Numbers

In the following exercises, model the subtraction.

1. [latex]5 - 2[/latex]
   Show Solution

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

   
4. [latex]7 - 5[/latex]
5. [latex]18 - 5[/latex]
   Show Solution

   
6. [latex]19 - 8[/latex]
7. [latex]17 - 8[/latex]
   Show Solution

   
8. [latex]17 - 9[/latex]
9. [latex]35 - 13[/latex]
   Show Solution

   
10. [latex]32 - 11[/latex]
11. [latex]61 - 47[/latex]
    Show Solution

    
12. [latex]55 - 36[/latex]

Subtract Whole Numbers

In the following exercises, subtract and then check by adding.

1. [latex]9 - 4[/latex]
   Show Solution

   5
2. [latex]9 - 3[/latex]
3. [latex]8 - 0[/latex]
   Show Solution

   8
4. [latex]2 - 0[/latex]
5. [latex]38 - 16[/latex]
   Show Solution

   22
6. [latex]45 - 21[/latex]
7. [latex]85 - 52[/latex]
   Show Solution

   33
8. [latex]99 - 47[/latex]
9. [latex]493 - 370[/latex]
   Show Solution

   123
10. [latex]268 - 106[/latex]
11. [latex]5,946 - 4,625[/latex]
    Show Solution

    1,321
12. [latex]7,775 - 3,251[/latex]
13. [latex]75 - 47[/latex]
    Show Solution

    28
14. [latex]63 - 59[/latex]
15. [latex]461 - 239[/latex]
    Show Solution

    222
16. [latex]486 - 257[/latex]
17. [latex]525 - 179[/latex]
    Show Solution

    346
18. [latex]542 - 288[/latex]
19. [latex]6,318 - 2,799[/latex]
    Show Solution

    3,519
20. [latex]8,153 - 3,978[/latex]
21. [latex]2,150 - 964[/latex]
    Show Solution

    1,186
22. [latex]4,245 - 899[/latex]
23. [latex]43,650 - 8,982[/latex]
    Show Solution

    34,668
24. [latex]35,162 - 7,885[/latex]

Translate Word Phrases to Algebraic Expressions

In the following exercises, translate and simplify.

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

   10 − 3; 7
2. The difference of [latex]12[/latex] and [latex]8[/latex]
3. The difference of [latex]15[/latex] and [latex]4[/latex]
   Show Solution

   15 − 4; 11
4. The difference of [latex]18[/latex] and [latex]7[/latex]
5. Subtract [latex]6[/latex] from [latex]9[/latex]
   Show Solution

   9 − 6; 3
6. Subtract [latex]8[/latex] from [latex]9[/latex]
7. Subtract [latex]28[/latex] from [latex]75[/latex]
   Show Solution

   75 − 28; 47
8. Subtract [latex]59[/latex] from [latex]81[/latex]
9. [latex]45[/latex] decreased by [latex]20[/latex]
   Show Solution

   45 − 20; 25
10. [latex]37[/latex] decreased by [latex]24[/latex]
11. [latex]92[/latex] decreased by [latex]67[/latex]
    Show Solution

    92 − 67; 25
12. [latex]75[/latex] decreased by [latex]49[/latex]
13. [latex]12[/latex] less than [latex]16[/latex]
    Show Solution

    16 − 12; 4
14. [latex]15[/latex] less than [latex]19[/latex]
15. [latex]38[/latex] less than [latex]61[/latex]
    Show Solution

    61 − 38; 23
16. [latex]47[/latex] less than [latex]62[/latex]

Mixed Practice

In the following exercises, simplify.

1. [latex]76 - 47[/latex]
   Show Solution

   29
2. [latex]91 - 53[/latex]
3. [latex]256 - 184[/latex]
   Show Solution

   72
4. [latex]305 - 262[/latex]
5. [latex]719+341[/latex]
   Show Solution

   1,060
6. [latex]647+528[/latex]
7. [latex]2,015 - 1,993[/latex]
   Show Solution

   22
8. [latex]2,020 - 1,984[/latex]

In the following exercises, translate and simplify.

1. Seventy more than thirty-five
   Show Solution

   75 + 35; 110
2. Sixty more than ninety-three
3. [latex]13[/latex] less than [latex]41[/latex]
   Show Solution

   41 − 13; 28
4. [latex]28[/latex] less than [latex]36[/latex]
5. The difference of [latex]100[/latex] and [latex]76[/latex]
   Show Solution

   100 − 76; 24
6. The difference of [latex]1,000[/latex] and [latex]945[/latex]

Subtract Whole Numbers in Applications

In the following exercises, solve.

Temperature

The high temperature on June 2 in Las Vegas was 80 degrees and the low temperature was 63 degrees. What was the difference between the high and low temperatures?

Temperature

The high temperature on June 1 in Phoenix was 97 degrees and the low was 73 degrees. What was the difference between the high and low temperatures?

Class size

Olivia’s third grade class has [latex]35[/latex] children. Last year, her second grade class had [latex]22[/latex] children. What is the difference between the number of children in Olivia’s third grade class and her second grade class?

Class size

There are [latex]82[/latex] students in the school band and [latex]46[/latex] in the school orchestra. What is the difference between the number of students in the band and the orchestra?

Shopping

A mountain bike is on sale for [latex]\$399[/latex]. Its regular price is [latex]\$650[/latex]. What is the difference between the regular price and the sale price?

Shopping

A mattress set is on sale for [latex]\$755[/latex]. Its regular price is [latex]\$1,600[/latex]. What is the difference between the regular price and the sale price?

Savings

John wants to buy a laptop that costs [latex]\$840[/latex]. He has [latex]\$685[/latex] in his savings account. How much more does he need to save in order to buy the laptop?

Banking

Mason had [latex]\$1,125[/latex] in his checking account. He spent [latex]\$892[/latex]. How much money does he have left?

Multiplying Whole Numbers

Use Multiplication Notation

In the following exercises, translate from math notation to words.

1. [latex]4\times 7[/latex]
   Show Solution

   four times seven; the product of four and seven
2. [latex]8\times 6[/latex]
3. [latex]5\cdot 12[/latex]
   Show Solution

   five times twelve; the product of five and twelve
4. [latex]3\cdot 9[/latex]
5. [latex]\left(10\right)\left(25\right)[/latex]
   Show Solution

   ten times twenty-five; the product of ten and twenty-five
6. [latex]\left(20\right)\left(15\right)[/latex]
7. [latex]42\left(33\right)[/latex]
   Show Solution

   forty-two times thirty-three; the product of forty-two and thirty-three
8. [latex]39\left(64\right)[/latex]

Model Multiplication of Whole Numbers

In the following exercises, model the multiplication.

1. [latex]3\times 6[/latex]
   Show Solution

   
2. [latex]4\times 5[/latex]
3. [latex]5\times 9[/latex]
   Show Solution

   
4. [latex]3\times 9[/latex]

Multiply Whole Numbers

In the following exercises, fill in the missing values in each chart.

Exercise 1

Exercise 2

Exercise 3

Exercise 4

Exercise 5

Exercise 6

Exercise 7

Exercise 8

Multiply Whole Numbers

In the following exercises, multiply.

1. [latex]0\cdot 15[/latex]
   Show Solution

   0
2. [latex]0\cdot 41[/latex]
3. [latex]\left(99\right)0[/latex]
   Show Solution

   0
4. [latex]\left(77\right)0[/latex]
5. [latex]1\cdot 43[/latex]
   Show Solution

   43
6. [latex]1\cdot 34[/latex]
7. [latex]\left(28\right)1[/latex]
   Show Solution

   28
8. [latex]\left(65\right)1[/latex]
9. [latex]1\left(240,055\right)[/latex]
   Show Solution

   240,055
10. [latex]1\left(189,206\right)[/latex]
11. [latex]7\cdot 6[/latex]
    Show Solution

    42
12. [latex]6\cdot 7[/latex]
    Show Solution

    42
13. [latex]8\times 9[/latex]
14. [latex]9\times 8[/latex]
15. [latex]\left(79\right)\left(5\right)[/latex]
    Show Solution

    395
16. [latex]\left(58\right)\left(4\right)[/latex]
17. [latex]275\cdot 6[/latex]
    Show Solution

    1,650
18. [latex]638\cdot 5[/latex]
19. [latex]3,421\times 7[/latex]
    Show Solution

    23,947
20. [latex]9,143\times 3[/latex]
21. [latex]52\left(38\right)[/latex]
    Show Solution

    1,976
22. [latex]37\left(45\right)[/latex]
23. [latex]96\cdot 73[/latex]
    Show Solution

    7,008
24. [latex]89\cdot 56[/latex]
25. [latex]27\times 85[/latex]
    Show Solution

    2,295
26. [latex]53\times 98[/latex]
27. [latex]23\cdot 10[/latex]
    Show Solution

    230
28. [latex]19\cdot 10[/latex]
29. [latex]\left(100\right)\left(36\right)[/latex]
    Show Solution

    360
30. [latex]\left(100\right)\left(25\right)[/latex]
31. [latex]1,000\left(88\right)[/latex]
    Show Solution

    88,000
32. [latex]1,000\left(46\right)[/latex]
33. [latex]50\times 1,000,000[/latex]
    Show Solution

    50,000,000
34. [latex]30\times 1,000,000[/latex]
35. [latex]247\times 139[/latex]
    Show Solution

    34,333
36. [latex]156\times 328[/latex]
37. [latex]586\left(721\right)[/latex]
    Show Solution

    422,506
38. [latex]472\left(855\right)[/latex]
39. [latex]915\cdot 879[/latex]
    Show Solution

    804,285
40. [latex]968\cdot 926[/latex]
41. [latex]\left(104\right)\left(256\right)[/latex]
    Show Solution

    26,624
42. [latex]\left(103\right)\left(497\right)[/latex]
43. [latex]348\left(705\right)[/latex]
    Show Solution

    245,340
44. [latex]485\left(602\right)[/latex]
45. [latex]2,719\times 543[/latex]
    Show Solution

    1,476,417
46. [latex]3,581\times 724[/latex]

Translate Word Phrases to Math Notation

In the following exercises, translate and simplify.

1. the product of [latex]18[/latex] and [latex]33[/latex]
   Show Solution

   18 · 33; 594
2. the product of [latex]15[/latex] and [latex]22[/latex]
3. fifty-one times sixty-seven
   Show Solution

   51(67); 3,417
4. forty-eight times seventy-one
5. twice [latex]249[/latex]
   Show Solution

   2(249); 498
6. twice [latex]589[/latex]
7. ten times three hundred seventy-five
   Show Solution

   10(375); 3,750
8. ten times two hundred fifty-five

Mixed Practice, Part I

In the following exercises, simplify.

1. [latex]38\times 37[/latex]
   Show Solution

   1,406
2. [latex]86\times 29[/latex]
3. [latex]415 - 267[/latex]
   Show Solution

   148
4. [latex]341 - 285[/latex]
5. [latex]6,251+4,749[/latex]
   Show Solution

   11,000
6. [latex]3,816+8,184[/latex]
7. [latex]\left(56\right)\left(204\right)[/latex]
   Show Solution

   11,424
8. [latex]\left(77\right)\left(801\right)[/latex]
9. [latex]947\cdot 0[/latex]
   Show Solution

   0
10. [latex]947+0[/latex]
11. [latex]15,382+1[/latex]
    Show Solution

    15,383
12. [latex]15,382\cdot 1[/latex]

Mixed Practice, Part II

In the following exercises, translate and simplify.

1. the difference of 50 and 18
   Show Solution

   50 − 18; 32
2. the difference of 90 and 66
3. twice 35
   Show Solution

   2(35); 70
4. twice 140
5. 20 more than 980
   Show Solution

   20 + 980; 1,000
6. 65 more than 325
7. the product of 12 and 875
   Show Solution

   12(875); 10,500
8. the product of 15 and 905
9. subtract 74 from 89
   Show Solution

   89 − 74; 15
10. subtract 45 from 99
11. the sum of 3,075 and 95
    Show Solution

    3,075 + 950; 4,025
12. the sum of 6,308 and 724
13. 366 less than 814
    Show Solution

    814 − 366; 448
14. 388 less than 925

Multiply Whole Numbers in Applications

In the following exercises, solve.

Party supplies

Tim brought 9 six-packs of soda to a club party. How many cans of soda did Tim bring?

Sewing

Kanisha is making a quilt. She bought 6 cards of buttons. Each card had four buttons on it. How many buttons did Kanisha buy?

Field trip

Seven school busses let off their students in front of a museum in Washington, DC. Each school bus had 44 students. How many students were there?

Gardening

Kathryn bought 8 flats of impatiens for her flower bed. Each flat has 24 flowers. How many flowers did Kathryn buy?

Charity

Rey donated 15 twelve-packs of t-shirts to a homeless shelter. How many t-shirts did he donate?

School

There are 28 classrooms at Anna C. Scott elementary school. Each classroom has 26 student desks. What is the total number of student desks?

Recipe

Stephanie is making punch for a party. The recipe calls for twice as much fruit juice as club soda. If she uses 10 cups of club soda, how much fruit juice should she use?

Gardening

Hiroko is putting in a vegetable garden. He wants to have twice as many lettuce plants as tomato plants. If he buys 12 tomato plants, how many lettuce plants should he get?

Government

The United States Senate has twice as many senators as there are states in the United States. There are 50 states. How many senators are there in the United States Senate?

Recipe

Andrea is making potato salad for a buffet luncheon. The recipe says the number of servings of potato salad will be twice the number of pounds of potatoes. If she buys 30 pounds of potatoes, how many servings of potato salad will there be?

Painting

Jane is painting one wall of her living room. The wall is rectangular, 13 feet wide by 9 feet high. What is the area of the wall?

Home décor

Shawnte bought a rug for the hall of her apartment. The rug is 3 feet wide by 18 feet long. What is the area of the rug?

Room size

The meeting room in a senior center is rectangular, with length 42 feet and width 34 feet. What is the area of the meeting room?

Gardening

June has a vegetable garden in her yard. The garden is rectangular, with length 23 feet and width 28 feet. What is the area of the garden?

NCAA basketball

According to NCAA regulations, the dimensions of a rectangular basketball court must be 94 feet by 50 feet. What is the area of the basketball court?

NCAA football

According to NCAA regulations, the dimensions of a rectangular football field must be 360 feet by 160 feet. What is the area of the football field?

Dividing Whole Numbers

Use Division Notation

In the following exercises, translate from math notation to words.

1. [latex]54\div 9[/latex]
   Show Solution

   fifty-four divided by nine; the quotient of fifty-four and nine
2. [latex]\frac{56}{7}[/latex]
3. [latex]\frac{32}{8}[/latex]
   Show Solution

   thirty-two divided by eight; the quotient of thirty-two and eight
4. [latex]6\overline{)42}[/latex]
5. [latex]48\div 6[/latex]
   Show Solution

   forty-eight divided by six; the quotient of forty-eight and six
6. [latex]\frac{63}{9}[/latex]
7. [latex]7\overline{)63}[/latex]
   Show Solution

   sixty-three divided by seven; the quotient of sixty-three and seven
8. [latex]72\div 8[/latex]

Model Division of Whole Numbers

In the following exercises, model the division.

1. [latex]15\div 5[/latex]
   Show Solution

   
2. [latex]10\div 5[/latex]
3. [latex]\frac{14}{7}[/latex]
   Show Solution

   
4. [latex]\frac{18}{6}[/latex]
5. [latex]4\overline{)20}[/latex]
   Show Solution

   
6. [latex]3\overline{)15}[/latex]
7. [latex]24\div 6[/latex]
   Show Solution

   
8. [latex]16\div 4[/latex]

Divide Whole Numbers

In the following exercises, divide. Then check by multiplying.

1. [latex]18\div 2[/latex]
   Show Solution

   9
2. [latex]14\div 2[/latex]
3. [latex]\frac{27}{3}[/latex]
   Show Solution

   9
4. [latex]\frac{30}{3}[/latex]
5. [latex]4\overline{)28}[/latex]
   Show Solution

   7
6. [latex]4\overline{)36}[/latex]
7. [latex]\frac{45}{5}[/latex]
   Show Solution

   9
8. [latex]\frac{35}{5}[/latex]
9. [latex]72/8[/latex]
   Show Solution

   9
10. [latex]8\overline{)64}[/latex]
11. [latex]\frac{35}{7}[/latex]
    Show Solution

    5
12. [latex]42\div 7[/latex]
13. [latex]15\overline{)15}[/latex]
    Show Solution

    1
14. [latex]12\overline{)12}[/latex]
15. [latex]43\div 43[/latex]
    Show Solution

    1
16. [latex]37\div 37[/latex]
17. [latex]\frac{23}{1}[/latex]
    Show Solution

    23
18. [latex]\frac{29}{1}[/latex]
19. [latex]19\div 1[/latex]
    Show Solution

    19
20. [latex]17\div 1[/latex]
21. [latex]0\div 4[/latex]
    Show Solution

    0
22. [latex]0\div 8[/latex]
23. [latex]\frac{5}{0}[/latex]
    Show Solution

    undefined
24. [latex]\frac{9}{0}[/latex]
25. [latex]\frac{26}{0}[/latex]
    Show Solution

    undefined
26. [latex]\frac{32}{0}[/latex]
27. [latex]12\overline{)0}[/latex]
    Show Solution

    0
28. [latex]16\overline{)0}[/latex]
29. [latex]72\div 3[/latex]
    Show Solution

    24
30. [latex]57\div 3[/latex]
31. [latex]\frac{96}{8}[/latex]
    Show Solution

    12
32. [latex]\frac{78}{6}[/latex]
33. [latex]5\overline{)465}[/latex]
    Show Solution

    93
34. [latex]4\overline{)528}[/latex]
35. [latex]924\div 7[/latex]
    Show Solution

    132
36. [latex]861\div 7[/latex]
37. [latex]\frac{5,226}{6}[/latex]
    Show Solution

    871
38. [latex]\frac{3,776}{8}[/latex]
39. [latex]4\overline{)31,324}[/latex]
    Show Solution

    7,831
40. [latex]5\overline{)46,855}[/latex]
41. [latex]7,209\div 3[/latex]
    Show Solution

    2,403
42. [latex]4,806\div 3[/latex]
43. [latex]5,406\div 6[/latex]
    Show Solution

    901
44. [latex]3,208\div 4[/latex]
45. [latex]4\overline{)2,816}[/latex]
    Show Solution

    704
46. [latex]6\overline{)3,624}[/latex]
47. [latex]\frac{91,881}{9}[/latex]
    Show Solution

    10,209
48. [latex]\frac{83,256}{8}[/latex]
49. [latex]2,470\div 7[/latex]
    Show Solution

    352 R6
50. [latex]3,741\div 7[/latex]
51. [latex]8\overline{)55,305}[/latex]
    Show Solution

    6,913 R1
52. [latex]9\overline{)51,492}[/latex]
53. [latex]\frac{431,174}{5}[/latex]
    Show Solution

    86,234 R4
54. [latex]\frac{297,277}{4}[/latex]
55. [latex]130,016\div 3[/latex]
    Show Solution

    43,338 R2
56. [latex]105,609\div 2[/latex]
57. [latex]15\overline{)5,735}[/latex]
    Show Solution

    382 R5
58. [latex]\frac{4,933}{21}[/latex]
59. [latex]56,883\div 67[/latex]
    Show Solution

    849
60. [latex]43,725/75[/latex]
61. [latex]\frac{30,144}{314}[/latex]
    Show Solution

    96
62. [latex]26,145\div 415[/latex]
63. [latex]273\overline{)542,195}[/latex]
    Show Solution

    1,986 R17
64. [latex]816,243\div 462[/latex]

Mixed Practice

In the following exercises, simplify.

1. [latex]15\left(204\right)[/latex]
   Show Solution

   3,060
2. [latex]74\cdot 391[/latex]
3. [latex]256 - 184[/latex]
   Show Solution

   72
4. [latex]305 - 262[/latex]
5. [latex]719+341[/latex]
   Show Solution

   1,060
6. [latex]647+528[/latex]
7. [latex]25\overline{)875}[/latex]
   Show Solution

   35
8. [latex]1104\div 23[/latex]

Translate Word Phrases to Algebraic Expressions

In the following exercises, translate and simplify.

1. the quotient of [latex]45[/latex] and [latex]15[/latex]
   Show Solution

   45 ÷ 15; 3
2. the quotient of [latex]64[/latex] and [latex]16[/latex]
3. the quotient of [latex]288[/latex] and [latex]24[/latex]
   Show Solution

   288 ÷ 24; 12
4. the quotient of [latex]256[/latex] and [latex]32[/latex]

Divide Whole Numbers in Applications

In the following exercises, solve.

Trail mix

Ric bought [latex]64[/latex] ounces of trail mix. He wants to divide it into small bags, with [latex]2[/latex] ounces of trail mix in each bag. How many bags can Ric fill?

Crackers

Evie bought a [latex]42[/latex] ounce box of crackers. She wants to divide it into bags with [latex]3[/latex] ounces of crackers in each bag. How many bags can Evie fill?

Astronomy class

There are [latex]125[/latex] students in an astronomy class. The professor assigns them into groups of [latex]5[/latex]. How many groups of students are there?

Flower shop

Melissa’s flower shop got a shipment of [latex]152[/latex] roses. She wants to make bouquets of [latex]8[/latex] roses each. How many bouquets can Melissa make?

Baking

One roll of plastic wrap is [latex]48[/latex] feet long. Marta uses [latex]3[/latex] feet of plastic wrap to wrap each cake she bakes. How many cakes can she wrap from one roll?

Dental floss

One package of dental floss is [latex]54[/latex] feet long. Brian uses [latex]2[/latex] feet of dental floss every day. How many days will one package of dental floss last Brian?

Mixed Practice (Applications)

In the following exercises, solve.

Miles per gallon

Susana’s hybrid car gets [latex]45[/latex] miles per gallon. Her son’s truck gets [latex]17[/latex] miles per gallon. What is the difference in miles per gallon between Susana’s car and her son’s truck?

Distance

Mayra lives [latex]53[/latex] miles from her mother’s house and [latex]71[/latex] miles from her mother-in-law’s house. How much farther is Mayra from her mother-in-law’s house than from her mother’s house?

Field trip

The [latex]45[/latex] students in a Geology class will go on a field trip, using the college’s vans. Each van can hold [latex]9[/latex] students. How many vans will they need for the field trip?

Potting soil

Aki bought a [latex]128[/latex] ounce bag of potting soil. How many [latex]4[/latex] ounce pots can he fill from the bag?

Hiking

Bill hiked [latex]8[/latex] miles on the first day of his backpacking trip, [latex]14[/latex] miles the second day, [latex]11[/latex] miles the third day, and [latex]17[/latex] miles the fourth day. What is the total number of miles Bill hiked?

Reading

Last night Emily read [latex]6[/latex] pages in her Business textbook, [latex]26[/latex] pages in her History text, [latex]15[/latex] pages in her Psychology text, and [latex]9[/latex] pages in her math text. What is the total number of pages Emily read?

Patients

LaVonne treats [latex]12[/latex] patients each day in her dental office. Last week she worked [latex]4[/latex] days. How many patients did she treat last week?

Scouts

There are [latex]14[/latex] boys in Dave’s scout troop. At summer camp, each boy earned [latex]5[/latex] merit badges. What was the total number of merit badges earned by Dave’s scout troop at summer camp?

Chapter Review Exercises