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Study Guides > ALGEBRA / TRIG I

Problem Set: Whole Numbers

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. 0,23,5,8.1,1250,\frac{2}{3},5,8.1,125

    Answer: a) Counting numbers: 5, 125 b) Whole numbers: 0, 5, 125

  2. 0,710,3,20.5,3000,\frac{7}{10},3,20.5,300
  3. 0,49,3.9,50,2210,\frac{4}{9},3.9,50,221

    Answer: a) Counting numbers: 50, 221 b) Whole numbers: 0, 50, 221

  4. 0,35,10,303,422.60,\frac{3}{5},10,303,422.6

Model Whole Numbers

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

Exercise 1

An image consisting of three items. The first item is five squares of 100 blocks each, 10 blocks wide and 10 blocks tall. The second item is six horizontal rods containing 10 blocks each. The third item is 1 individual block.

Answer: 561

Exercise 2

An image consisting of three items. The first item is three squares of 100 blocks each, 10 blocks wide and 10 blocks tall. The second item is eight horizontal rods containing 10 blocks each. The third item is 4 individual blocks.

Exercise 3

An image consisting of two items. The first item is four squares of 100 blocks each, 10 blocks wide and 10 blocks tall. The second item is 7 individual blocks.

Answer: 407

Exercises 4

An image consisting of two items. The first item is six squares of 100 blocks each, 10 blocks wide and 10 blocks tall. The second item is 2 horizontal rods with 10 blocks each.

Identify the Place Value of a Digit

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

Exercise 1

579,601579,601
  1. 9
  2. 6
  3. 0
  4. 7
  5. 5

Answer:

  1. thousands
  2. hundreds
  3. tens
  4. ten thousands
  5. hundred thousands

Exercise 2

398,127398,127
  1. 9
  2. 3
  3. 2
  4. 8
  5. 7

Exercise 3

56,804,37956,804,379
  1. 8
  2. 6
  3. 4
  4. 7
  5. 0

Answer:

  1. hundred thousands
  2. millions
  3. thousands
  4. tens
  5. ten thousands

Exercise 4

78,320,46578,320,465
  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. 1,0781,078

    Answer: One thousand, seventy-eight

  2. 5,9025,902
  3. 364,510364,510

    Answer: Three hundred sixty-four thousand, five hundred ten

  4. 146,023146,023
  5. 5,846,1035,846,103

    Answer: Five million, eight hundred forty-six thousand, one hundred three

  6. 1,458,3981,458,398
  7. 37,889,00537,889,005

    Answer: Thirty-seven million, eight hundred eighty-nine thousand, five

  8. 62,008,46562,008,465

Exercise 2

  1. The height of Mount Ranier is 14,41014,410 feet.

    Answer: Fourteen thousand, four hundred ten

  2. The height of Mount Adams is 12,27612,276 feet.
  3. Seventy years is 613,200613,200 hours.

    Answer: Six hundred thirteen thousand, two hundred

  4. One year is 525,600525,600 minutes.
  5. The U.S. Census estimate of the population of Miami-Dade county was 2,617,1762,617,176.

    Answer: Two million, six hundred seventeen thousand, one hundred seventy-six

  6. The population of Chicago was 2,718,7822,718,782.
  7. There are projected to be 23,867,00023,867,000 college and university students in the US in five years.

    Answer: Twenty-three million, eight hundred sixty-seven thousand

  8. About twelve years ago there were 20,665,41520,665,415 registered automobiles in California.
  9. The population of China is expected to reach 1,377,583,1561,377,583,156 in 20162016.

    Answer: One billion, three hundred seventy-seven million, five hundred eighty-three thousand, one hundred fifty-six

  10. The population of India is estimated at 1,267,401,8491,267,401,849 as of July 1,20141,2014.

Use Place Value to Write Whole Numbers

In the following exercises, write each number as a whole number using digits.
  1. four hundred twelve

    Answer: 412

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

    Answer: 35,975

  4. sixty-one thousand, four hundred fifteen
  5. eleven million, forty-four thousand, one hundred sixty-seven

    Answer: 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

    Answer: 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.

    Answer: 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.

    Answer: 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. 386386

    Answer: 390

  2. 2,9312,931

    Answer: 2,930

Round to the nearest ten:
  1. 792792

    Answer: 790

  2. 5,6475,647

    Answer: 5,650

Round to the nearest hundred:
  1. 13,74813,748

    Answer: 13,700

  2. 391,794391,794

    Answer: 391,800

Round to the nearest hundred:
  1. 28,16628,166

    Answer: 28,200

  2. 481,628481,628

    Answer: 481,700

Round to the nearest ten:
  1. 1,4921,492

    Answer: 1,490

  2. 1,4971,497

    Answer: 1,500

Round to the nearest thousand:
  1. 2,3912,391

    Answer: 2,000

  2. 2,7952,795

    Answer: 3,000

Round to the nearest hundred:
  1. 63,99463,994

    Answer: 64,00064,000

  2. 63,94963,949

    Answer: 63,90063,900

Round to the nearest thousand:
  1. 163,584163,584

    Answer: 164,000

  2. 163,246163,246

    Answer: 163,000

Everyday Math

Writing a Check

Jorge bought a car for $24,493\$24,493. He paid for the car with a check. Write the purchase price in words.

Answer: Twenty four thousand, four hundred ninety-three dollars

Writing a Check

Marissa’s kitchen remodeling cost $18,549\$18,549. She wrote a check to the contractor. Write the amount paid in words.

Buying a Car

Jorge bought a car for $24,493\$24,493. Round the price to the nearest:
  1. ten dollars
  2. hundred dollars
  3. thousand dollars
  4. ten-thousand dollars

Answer:

  1. $24,490
  2. $24,500
  3. $24,000
  4. $20,000

Remodeling a Kitchen

Marissa’s kitchen remodeling cost $18,549\$18,549. Round the cost to the nearest:
  1. ten dollars
  2. hundred dollars
  3. thousand dollars
  4. ten-thousand dollars

Population

The population of China was 1,355,692,5441,355,692,544 in 2014. Round the population to the nearest:
  1. billion people
  2. hundred-million people
  3. million people

Answer:

  1. 1,000,000,0001,000,000,000
  2. 1,400,000,0001,400,000,000
  3. 1,356,000,0001,356,000,000

Astronomy

The average distance between Earth and the sun is 149,597,888149,597,888 kilometers. Round the distance to the nearest:
  1. hundred-million kilometers
  2. ten-million kilometers
  3. million kilometers

Writing Exercises

In your own words, explain the difference between the counting numbers and the whole numbers. [practice-area rows="4"][/practice-area]

Answer: Answers may vary. The whole numbers are the counting numbers with the inclusion of zero.

Give an example from your everyday life where it helps to round numbers. [practice-area rows="4"][/practice-area]

Adding Whole Numbers

Use Addition Notation

In the following exercises, translate the following from math expressions to words.
  1. 5+25+2

    Answer: five plus two; the sum of 5 and 2.

  2. 6+36+3
  3. 13+1813+18

    Answer: thirteen plus eighteen; the sum of 13 and 18.

  4. 15+1615+16
  5. 214+642214+642

    Answer: two hundred fourteen plus six hundred forty-two; the sum of 214 and 642

  6. 438+113438+113

Model Addition of Whole Numbers

In the following exercises, model the addition.
  1. 2+42+4

    Answer: No Alt Text 2+4=62+4=6

  2. 5+35+3
  3. 8+48+4

    Answer: No Alt Text 8+4=128+4=12

  4. 5+95+9
  5. 14+7514+75

    Answer: No Alt Text 14+75=8914+75=89

  6. 15+6315+63
  7. 16+2516+25

    Answer: No Alt Text 16+25=4116+25=41

  8. 14+2714+27

Add Whole Numbers

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

Exercise 1

An image of a table with 11 columns and 11 rows. The cells in the first row and first column are shaded darker than the other cells. The first column has the values

Answer: No Alt Text

Exercise 2

An image of a table with 11 columns and 11 rows. The cells in the first row and first column are shaded darker than the other cells. The first column has the values

Exercises 3

An image of a table with 8 columns and 5 rows. The cells in the first row and first column are shaded darker than the other cells. The cells not in the first row or column are all null. The first column has the values

Answer: No Alt Text

Exercise 4

An image of a table with 8 columns and 5 rows. The cells in the first row and first column are shaded darker than the other cells. The cells not in the first row or column are all null. The first row has the values

Exercise 5

An image of a table with 6 columns and 6 rows. The cells in the first row and first column are shaded darker than the other cells. The cells not in the first row or column are all null. The first row has the values

Answer: No Alt Text

Exercise 6

An image of a table with 5 columns and 5 rows. The cells in the first row and first column are shaded darker than the other cells. The cells not in the first row or first column are all null. The first row has the values

Add Whole Numbers

In the following exercises, add.
  1. 0+130+13

    Answer: 13

  2. 13+013+0

    Answer: 13

  3. 0+5,2800+5,280
  4. 5,280+05,280+0
  5. 8+38+3

    Answer: 11

  6. 3+83+8

    Answer: 11

  7. 7+57+5
  8. 5+75+7
  9. 45+3345+33

    Answer: 7878

  10. 37+2237+22
  11. 71+2871+28

    Answer: 9999

  12. 43+5343+53
  13. 26+5926+59

    Answer: 8585

  14. 38+1738+17
  15. 64+7864+78

    Answer: 142142

  16. 92+3992+39
  17. 168+325168+325

    Answer: 493493

  18. 247+149247+149
  19. 584+277584+277

    Answer: 861861

  20. 175+648175+648
  21. 832+199832+199

    Answer: 1,0311,031

  22. 775+369775+369
  23. 6,358+4926,358+492

    Answer: 6,8506,850

  24. 9,184+5789,184+578
  25. 3,740+18,5933,740+18,593

    Answer: 22,33322,333

  26. 6,118+15,9906,118+15,990
  27. 485,012+619,848485,012+619,848

    Answer: 1,104,8601,104,860

  28. 368,911+857,289368,911+857,289
  29. 24,731+592+3,86824,731+592+3,868

    Answer: 29,19129,191

  30. 28,925+817+4,59328,925+817+4,593
  31. 8,015+76,946+16,5708,015+76,946+16,570

    Answer: 101,531101,531

  32. 6,291+54,107+28,6356,291+54,107+28,635

Translate Word Phrases to Math Notation

In the following exercises, translate each phrase into math notation and then simplify.
  1. the sum of 1313 and 1818

    Answer: 13+18=3113+18=31

  2. the sum of 1212 and 1919
  3. the sum of 9090 and 6565

    Answer: 90+65=15590+65=155

  4. the sum of 7070 and 3838
  5. 3333 increased by 4949

    Answer: 33+49=8233+49=82

  6. 6868 increased by 2525
  7. 250250 more than 599599

    Answer: 250+599=849250+599=849

  8. 115115 more than 286286
  9. the total of 628628 and 7777

    Answer: 628+77=705628+77=705

  10. the total of 593593 and 7979
  11. 1,4821,482 added to 915915

    Answer: 915+1,482=2,397915+1,482=2,397

  12. 2,7192,719 added to 682682

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 $1,100\$1,100, the microwave cost $250\$250, and the dishwasher cost $525\$525. What was the total cost of these three appliances?

Answer: The total cost was $1,875.

Sports equipment

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

Bike riding

Ethan rode his bike 1414 miles on Monday, 1919 miles on Tuesday, 1212 miles on Wednesday, 2525 miles on Friday, and 6868 miles on Saturday. What was the total number of miles Ethan rode?

Answer: Ethan rode 138 miles.

Business

Chloe has a flower shop. Last week she made 1919 floral arrangements on Monday, 1212 on Tuesday, 2323 on Wednesday, 2929 on Thursday, and 4444 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 238,120,156,196,100,132238,120,156,196,100,132, and 225225. What is the total number of square feet in all 77 rooms?

Answer: The total square footage in the rooms is 1,167 square feet.

Weight

Seven men rented a fishing boat. The weights of the men were 175,192,148,169,205,181175,192,148,169,205,181, and 225\text{225} pounds. What was the total weight of the seven men?

Salary

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

Answer: Natalie’s total salary is $237,186.

Home sales

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

Finding Perimeter

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

Exercise 1

An image of a triangle with side lengths of 14 inches, 12 inches, and 18 inches.

Answer: The perimeter of the figure is 44 inches.

Exercise 2

An image of a right triangle with base of 12 centimeters, height of 5 centimeters, and diagonal hypotenuse of 13 centimeters.

Exercise 3

A rectangle 21 meters wide and 7 meters tall.

Answer: The perimeter of the figure is 56 meters.

Exercise 4

A rectangle 19 feet wide and and 14 feet tall.

Exercise 5

A trapezoid with horizontal top length of 19 yards, the side lengths are 18 yards and are diagonal, and the horizontal bottom length is 16 yards.

Answer: The perimeter of the figure is 71 yards.

Exercise 6

A trapezoid with horizontal top length of 24 meters, the side lengths are 17 meters and are diagonal, and the horizontal bottom length is 29 meters.

Exercise 7

This is a rectangle-like image with six sides. Starting from the top left of the figure, the first line runs right for 24 feet. From the end of this line, the second line runs down for 7 feet. Then the third line runs left from this point for 19 feet. The fourth line runs up 3 feet. The fifth line runs left for 5 feet. The sixth line runs up for 4 feet, connecting it at a corner with start of the first line.

Answer: The perimeter of the figure is 62 feet.

Exercise 8

This is an image with 6 straight sides. Starting from the top left of the figure, the first line runs right for 25 inches. From the end of this line, the second line runs down for 10 inches. Then the third line runs left from this point for 14 inches. The fourth line runs up 7 inches. The fifth line runs left for 11 inches. The sixth line runs up, connecting it at a corner with start of the first line.

Everyday Math

Calories

Paulette had a grilled chicken salad, ranch dressing, and a 16-ounce\text{16-ounce} drink for lunch. On the restaurant’s nutrition chart, she saw that each item had the following number of calories:
  • Grilled chicken salad – 320320 calories
  • Ranch dressing – 170170 calories
  • 16-ounce\text{16-ounce} drink – 150150 calories
What was the total number of calories of Paulette’s lunch?

Answer: The total number of calories was 640.

Calories

Fred had a grilled chicken sandwich, a small order of fries, and a 12-oz\text{12-oz} chocolate shake for dinner. The restaurant’s nutrition chart lists the following calories for each item:
  • Grilled chicken sandwich – 420420 calories
  • Small fries – 230230 calories
  • 12-oz\text{12-oz} chocolate shake – 580580 calories
What was the total number of calories of Fred’s dinner?

Test scores

A students needs a total of 400400 points on five tests to pass a course. The student scored 82,91,75,88,and7082,91,75,88,\text{and}70. Did the student pass the course?

Answer: Yes, he scored 406 points.

Elevators

The maximum weight capacity of an elevator is 11501150 pounds. Six men are in the elevator. Their weights are 210, 145, 183, 230, 159, and 164 pounds. Is the total weight below the elevators’ maximum capacity?

Writing Exercises

How confident do you feel about your knowledge of the addition facts? If you are not fully confident, what will you do to improve your skills? [practice-area rows="4"][/practice-area] How have you used models to help you learn the addition facts? [practice-area rows="4"][/practice-area]

Subtracting Whole Numbers

Use Subtraction Notation

In the following exercises, translate from math notation to words.
  1. 15915 - 9

    Answer: fifteen minus nine; the difference of fifteen and nine

  2. 181618 - 16
  3. 423542 - 35

    Answer: forty-two minus thirty-five; the difference of forty-two and thirty-five

  4. 836483 - 64
  5. 675350675 - 350

    Answer: hundred seventy-five minus three hundred fifty; the difference of six hundred seventy-five and three hundred fifty

  6. 790525790 - 525

Model Subtraction of Whole Numbers

In the following exercises, model the subtraction.
  1. 525 - 2

    Answer: No Alt Text

  2. 848 - 4
  3. 636 - 3

    Answer: No Alt Text

  4. 757 - 5
  5. 18518 - 5

    Answer: No Alt Text

  6. 19819 - 8
  7. 17817 - 8

    Answer: No Alt Text

  8. 17917 - 9
  9. 351335 - 13

    Answer: No Alt Text

  10. 321132 - 11
  11. 614761 - 47

    Answer: No Alt Text

  12. 553655 - 36

Subtract Whole Numbers

In the following exercises, subtract and then check by adding.
  1. 949 - 4

    Answer: 5

  2. 939 - 3
  3. 808 - 0

    Answer: 8

  4. 202 - 0
  5. 381638 - 16

    Answer: 22

  6. 452145 - 21
  7. 855285 - 52

    Answer: 33

  8. 994799 - 47
  9. 493370493 - 370

    Answer: 123

  10. 268106268 - 106
  11. 5,9464,6255,946 - 4,625

    Answer: 1,321

  12. 7,7753,2517,775 - 3,251
  13. 754775 - 47

    Answer: 28

  14. 635963 - 59
  15. 461239461 - 239

    Answer: 222

  16. 486257486 - 257
  17. 525179525 - 179

    Answer: 346

  18. 542288542 - 288
  19. 6,3182,7996,318 - 2,799

    Answer: 3,519

  20. 8,1533,9788,153 - 3,978
  21. 2,1509642,150 - 964

    Answer: 1,186

  22. 4,2458994,245 - 899
  23. 43,6508,98243,650 - 8,982

    Answer: 34,668

  24. 35,1627,88535,162 - 7,885

Translate Word Phrases to Algebraic Expressions

In the following exercises, translate and simplify.
  1. The difference of 1010 and 33

    Answer: 10 − 3; 7

  2. The difference of 1212 and 88
  3. The difference of 1515 and 44

    Answer: 15 − 4; 11

  4. The difference of 1818 and 77
  5. Subtract 66 from 99

    Answer: 9 − 6; 3

  6. Subtract 88 from 99
  7. Subtract 2828 from 7575

    Answer: 75 − 28; 47

  8. Subtract 5959 from 8181
  9. 4545 decreased by 2020

    Answer: 45 − 20; 25

  10. 3737 decreased by 2424
  11. 9292 decreased by 6767

    Answer: 92 − 67; 25

  12. 7575 decreased by 4949
  13. 1212 less than 1616

    Answer: 16 − 12; 4

  14. 1515 less than 1919
  15. 3838 less than 6161

    Answer: 61 − 38; 23

  16. 4747 less than 6262

Mixed Practice

In the following exercises, simplify.
  1. 764776 - 47

    Answer: 29

  2. 915391 - 53
  3. 256184256 - 184

    Answer: 72

  4. 305262305 - 262
  5. 719+341719+341

    Answer: 1,060

  6. 647+528647+528
  7. 2,0151,9932,015 - 1,993

    Answer: 22

  8. 2,0201,9842,020 - 1,984
In the following exercises, translate and simplify.
  1. Seventy more than thirty-five

    Answer: 75 + 35; 110

  2. Sixty more than ninety-three
  3. 1313 less than 4141

    Answer: 41 − 13; 28

  4. 2828 less than 3636
  5. The difference of 100100 and 7676

    Answer: 100 − 76; 24

  6. The difference of 1,0001,000 and 945945

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?

Answer: The difference between the high and low temperature was 17 degrees

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 3535 children. Last year, her second grade class had 2222 children. What is the difference between the number of children in Olivia’s third grade class and her second grade class?

Answer: The difference between the third grade and second grade was 13 children.

Class size

There are 8282 students in the school band and 4646 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 $399\$399. Its regular price is $650\$650. What is the difference between the regular price and the sale price?

Answer: The difference between the regular price and sale price is $251.

Shopping

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

Savings

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

Answer: John needs to save $155 more.

Banking

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

Everyday Math

Road trip

Noah was driving from Philadelphia to Cincinnati, a distance of 502502 miles. He drove 115115 miles, stopped for gas, and then drove another 230230 miles before lunch. How many more miles did he have to travel?

Answer: 157 miles

Test Scores

Sara needs 350350 points to pass her course. She scored 75,50,70,and8075,50,70,\text{and}80 on her first four tests. How many more points does Sara need to pass the course?

Writing Exercises

Explain how subtraction and addition are related. [practice-area rows="4"][/practice-area] How does knowing addition facts help you to subtract numbers? [practice-area rows="4"][/practice-area]

Multiplying Whole Numbers

Use Multiplication Notation

In the following exercises, translate from math notation to words.
  1. 4×74\times 7

    Answer: four times seven; the product of four and seven

  2. 8×68\times 6
  3. 5125\cdot 12

    Answer: five times twelve; the product of five and twelve

  4. 393\cdot 9
  5. (10)(25)\left(10\right)\left(25\right)

    Answer: ten times twenty-five; the product of ten and twenty-five

  6. (20)(15)\left(20\right)\left(15\right)
  7. 42(33)42\left(33\right)

    Answer: forty-two times thirty-three; the product of forty-two and thirty-three

  8. 39(64)39\left(64\right)

Model Multiplication of Whole Numbers

In the following exercises, model the multiplication.
  1. 3×63\times 6

    Answer: No Alt Text

  2. 4×54\times 5
  3. 5×95\times 9

    Answer: No Alt Text

  4. 3×93\times 9

Multiply Whole Numbers

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

Exercise 1

An image of a table with 11 columns and 11 rows. The cells in the first row and first column are shaded darker than the other cells. The first column has the values

Answer: No Alt Text

Exercise 2

An image of a table with 11 columns and 11 rows. The cells in the first row and first column are shaded darker than the other cells. The first column has the values

Exercise 3

An image of a table with 8 columns and 7 rows. The cells in the first row and first column are shaded darker than the other cells. The cells not in the first row or column are all null. The first column has the values

Answer: No Alt Text

Exercise 4

PROD: An image of a table with 7 columns and 8 rows. The cells in the first row and first column are shaded darker than the other cells. The cells not in the first row or column are all null. The first column has the values

Exercise 5

An image of a table with 8 columns and 5 rows. The cells in the first row and first column are shaded darker than the other cells. The cells not in the first row or column are all null. The first row has the values

Answer: No Alt Text

Exercise 6

An image of a table with 5 columns and 8 rows. The cells in the first row and first column are shaded darker than the other cells. The cells not in the first row or column are all null. The first column has the values

Exercise 7

PROD: An image of a table with 6 columns and 6 rows. The cells in the first row and first column are shaded darker than the other cells. The cells not in the first row or column are all null. The first column has the values

Answer: No Alt Text

Exercise 8

An image of a table with 6 columns and 6 rows. The cells in the first row and first column are shaded darker than the other cells. The cells not in the first row or column are all null. The first column has the values

Multiply Whole Numbers

In the following exercises, multiply.
  1. 0150\cdot 15

    Answer: 0

  2. 0410\cdot 41
  3. (99)0\left(99\right)0

    Answer: 0

  4. (77)0\left(77\right)0
  5. 1431\cdot 43

    Answer: 43

  6. 1341\cdot 34
  7. (28)1\left(28\right)1

    Answer: 28

  8. (65)1\left(65\right)1
  9. 1(240,055)1\left(240,055\right)

    Answer: 240,055

  10. 1(189,206)1\left(189,206\right)
  11. 767\cdot 6

    Answer: 42

  12. 676\cdot 7

    Answer: 42

  13. 8×98\times 9
  14. 9×89\times 8
  15. (79)(5)\left(79\right)\left(5\right)

    Answer: 395

  16. (58)(4)\left(58\right)\left(4\right)
  17. 2756275\cdot 6

    Answer: 1,650

  18. 6385638\cdot 5
  19. 3,421×73,421\times 7

    Answer: 23,947

  20. 9,143×39,143\times 3
  21. 52(38)52\left(38\right)

    Answer: 1,976

  22. 37(45)37\left(45\right)
  23. 967396\cdot 73

    Answer: 7,008

  24. 895689\cdot 56
  25. 27×8527\times 85

    Answer: 2,295

  26. 53×9853\times 98
  27. 231023\cdot 10

    Answer: 230

  28. 191019\cdot 10
  29. (100)(36)\left(100\right)\left(36\right)

    Answer: 360

  30. (100)(25)\left(100\right)\left(25\right)
  31. 1,000(88)1,000\left(88\right)

    Answer: 88,000

  32. 1,000(46)1,000\left(46\right)
  33. 50×1,000,00050\times 1,000,000

    Answer: 50,000,000

  34. 30×1,000,00030\times 1,000,000
  35. 247×139247\times 139

    Answer: 34,333

  36. 156×328156\times 328
  37. 586(721)586\left(721\right)

    Answer: 422,506

  38. 472(855)472\left(855\right)
  39. 915879915\cdot 879

    Answer: 804,285

  40. 968926968\cdot 926
  41. (104)(256)\left(104\right)\left(256\right)

    Answer: 26,624

  42. (103)(497)\left(103\right)\left(497\right)
  43. 348(705)348\left(705\right)

    Answer: 245,340

  44. 485(602)485\left(602\right)
  45. 2,719×5432,719\times 543

    Answer: 1,476,417

  46. 3,581×7243,581\times 724

Translate Word Phrases to Math Notation

In the following exercises, translate and simplify.
  1. the product of 1818 and 3333

    Answer: 18 · 33; 594

  2. the product of 1515 and 2222
  3. fifty-one times sixty-seven

    Answer: 51(67); 3,417

  4. forty-eight times seventy-one
  5. twice 249249

    Answer: 2(249); 498

  6. twice 589589
  7. ten times three hundred seventy-five

    Answer: 10(375); 3,750

  8. ten times two hundred fifty-five

Mixed Practice, Part I

In the following exercises, simplify.
  1. 38×3738\times 37

    Answer: 1,406

  2. 86×2986\times 29
  3. 415267415 - 267

    Answer: 148

  4. 341285341 - 285
  5. 6,251+4,7496,251+4,749

    Answer: 11,000

  6. 3,816+8,1843,816+8,184
  7. (56)(204)\left(56\right)\left(204\right)

    Answer: 11,424

  8. (77)(801)\left(77\right)\left(801\right)
  9. 9470947\cdot 0

    Answer: 0

  10. 947+0947+0
  11. 15,382+115,382+1

    Answer: 15,383

  12. 15,382115,382\cdot 1

Mixed Practice, Part II

In the following exercises, translate and simplify.
  1. the difference of 50 and 18

    Answer: 50 − 18; 32

  2. the difference of 90 and 66
  3. twice 35

    Answer: 2(35); 70

  4. twice 140
  5. 20 more than 980

    Answer: 20 + 980; 1,000

  6. 65 more than 325
  7. the product of 12 and 875

    Answer: 12(875); 10,500

  8. the product of 15 and 905
  9. subtract 74 from 89

    Answer: 89 − 74; 15

  10. subtract 45 from 99
  11. the sum of 3,075 and 95

    Answer: 3,075 + 950; 4,025

  12. the sum of 6,308 and 724
  13. 366 less than 814

    Answer: 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?

Answer: Tim brought 54 cans of soda to the party.

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?

Answer: There were 308 students.

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?

Answer: Rey donated 180 t-shirts.

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?

Answer: Stephanie should use 20 cups of fruit juice.

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?

Answer: There are 100 senators in the U.S. 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?

Answer: The area of the wall is 117 square feet.

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?

Answer: The area of the room is 1,428 square feet.

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?

Answer: The area of the court is 4,700 square feet.

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?

Everyday Math

Stock market

Javier owns 300 shares of stock in one company. On Tuesday, the stock price rose $12\$12 per share. How much money did Javier’s portfolio gain?

Answer: Javier’s portfolio gained $3,600.

Salary

Carlton got a $200\$200 raise in each paycheck. He gets paid 24 times a year. How much higher is his new annual salary?

Writing Exercises

How confident do you feel about your knowledge of the multiplication facts? If you are not fully confident, what will you do to improve your skills? [practice-area rows="4"][/practice-area] How have you used models to help you learn the multiplication facts? [practice-area rows="4"][/practice-area]

Dividing Whole Numbers

Use Division Notation

In the following exercises, translate from math notation to words.
  1. 54÷954\div 9

    Answer: fifty-four divided by nine; the quotient of fifty-four and nine

  2. 567\frac{56}{7}
  3. 328\frac{32}{8}

    Answer: thirty-two divided by eight; the quotient of thirty-two and eight

  4. 6)426\overline{)42}
  5. 48÷648\div 6

    Answer: forty-eight divided by six; the quotient of forty-eight and six

  6. 639\frac{63}{9}
  7. 7)637\overline{)63}

    Answer: sixty-three divided by seven; the quotient of sixty-three and seven

  8. 72÷872\div 8

Model Division of Whole Numbers

In the following exercises, model the division.
  1. 15÷515\div 5

    Answer: No Alt Text

  2. 10÷510\div 5
  3. 147\frac{14}{7}

    Answer: No Alt Text

  4. 186\frac{18}{6}
  5. 4)204\overline{)20}

    Answer: No Alt Text

  6. 3)153\overline{)15}
  7. 24÷624\div 6

    Answer: No Alt Text

  8. 16÷416\div 4

Divide Whole Numbers

In the following exercises, divide. Then check by multiplying.
  1. 18÷218\div 2

    Answer: 9

  2. 14÷214\div 2
  3. 273\frac{27}{3}

    Answer: 9

  4. 303\frac{30}{3}
  5. 4)284\overline{)28}

    Answer: 7

  6. 4)364\overline{)36}
  7. 455\frac{45}{5}

    Answer: 9

  8. 355\frac{35}{5}
  9. 72/872/8

    Answer: 9

  10. 8)648\overline{)64}
  11. 357\frac{35}{7}

    Answer: 5

  12. 42÷742\div 7
  13. 15)1515\overline{)15}

    Answer: 1

  14. 12)1212\overline{)12}
  15. 43÷4343\div 43

    Answer: 1

  16. 37÷3737\div 37
  17. 231\frac{23}{1}

    Answer: 23

  18. 291\frac{29}{1}
  19. 19÷119\div 1

    Answer: 19

  20. 17÷117\div 1
  21. 0÷40\div 4

    Answer: 0

  22. 0÷80\div 8
  23. 50\frac{5}{0}

    Answer: undefined

  24. 90\frac{9}{0}
  25. 260\frac{26}{0}

    Answer: undefined

  26. 320\frac{32}{0}
  27. 12)012\overline{)0}

    Answer: 0

  28. 16)016\overline{)0}
  29. 72÷372\div 3

    Answer: 24

  30. 57÷357\div 3
  31. 968\frac{96}{8}

    Answer: 12

  32. 786\frac{78}{6}
  33. 5)4655\overline{)465}

    Answer: 93

  34. 4)5284\overline{)528}
  35. 924÷7924\div 7

    Answer: 132

  36. 861÷7861\div 7
  37. 5,2266\frac{5,226}{6}

    Answer: 871

  38. 3,7768\frac{3,776}{8}
  39. 4)31,3244\overline{)31,324}

    Answer: 7,831

  40. 5)46,8555\overline{)46,855}
  41. 7,209÷37,209\div 3

    Answer: 2,403

  42. 4,806÷34,806\div 3
  43. 5,406÷65,406\div 6

    Answer: 901

  44. 3,208÷43,208\div 4
  45. 4)2,8164\overline{)2,816}

    Answer: 704

  46. 6)3,6246\overline{)3,624}
  47. 91,8819\frac{91,881}{9}

    Answer: 10,209

  48. 83,2568\frac{83,256}{8}
  49. 2,470÷72,470\div 7

    Answer: 352 R6

  50. 3,741÷73,741\div 7
  51. 8)55,3058\overline{)55,305}

    Answer: 6,913 R1

  52. 9)51,4929\overline{)51,492}
  53. 431,1745\frac{431,174}{5}

    Answer: 86,234 R4

  54. 297,2774\frac{297,277}{4}
  55. 130,016÷3130,016\div 3

    Answer: 43,338 R2

  56. 105,609÷2105,609\div 2
  57. 15)5,73515\overline{)5,735}

    Answer: 382 R5

  58. 4,93321\frac{4,933}{21}
  59. 56,883÷6756,883\div 67

    Answer: 849

  60. 43,725/7543,725/75
  61. 30,144314\frac{30,144}{314}

    Answer: 96

  62. 26,145÷41526,145\div 415
  63. 273)542,195273\overline{)542,195}

    Answer: 1,986 R17

  64. 816,243÷462816,243\div 462

Mixed Practice

In the following exercises, simplify.
  1. 15(204)15\left(204\right)

    Answer: 3,060

  2. 7439174\cdot 391
  3. 256184256 - 184

    Answer: 72

  4. 305262305 - 262
  5. 719+341719+341

    Answer: 1,060

  6. 647+528647+528
  7. 25)87525\overline{)875}

    Answer: 35

  8. 1104÷231104\div 23

Translate Word Phrases to Algebraic Expressions

In the following exercises, translate and simplify.
  1. the quotient of 4545 and 1515

    Answer: 45 ÷ 15; 3

  2. the quotient of 6464 and 1616
  3. the quotient of 288288 and 2424

    Answer: 288 ÷ 24; 12

  4. the quotient of 256256 and 3232

Divide Whole Numbers in Applications

In the following exercises, solve.

Trail mix

Ric bought 6464 ounces of trail mix. He wants to divide it into small bags, with 22 ounces of trail mix in each bag. How many bags can Ric fill?

Answer: Ric can fill 32 bags.

Crackers

Evie bought a 4242 ounce box of crackers. She wants to divide it into bags with 33 ounces of crackers in each bag. How many bags can Evie fill?

Astronomy class

There are 125125 students in an astronomy class. The professor assigns them into groups of 55. How many groups of students are there?

Answer: There are 25 groups.

Flower shop

Melissa’s flower shop got a shipment of 152152 roses. She wants to make bouquets of 88 roses each. How many bouquets can Melissa make?

Baking

One roll of plastic wrap is 4848 feet long. Marta uses 33 feet of plastic wrap to wrap each cake she bakes. How many cakes can she wrap from one roll?

Answer: Marta can wrap 16 cakes from 1 roll.

Dental floss

One package of dental floss is 5454 feet long. Brian uses 22 feet of dental floss every day. How many days will one package of dental floss last Brian?

Everyday Math

Contact lenses

Jenna puts in a new pair of contact lenses every 1414 days. How many pairs of contact lenses does she need for 365365 days?

Answer: Jenna uses 26 pairs of contact lenses, but there is 1 day left over, so she needs 27 pairs for 365 days.

Cat food

One bag of cat food feeds Lara’s cat for 2525 days. How many bags of cat food does Lara need for 365365 days?

Writing Exercises

Explain how you use the multiplication facts to help with division. [practice-area rows="4"][/practice-area]

Answer: Answers may vary. Using multiplication facts can help you check your answers once you’ve finished division.

Oswaldo divided 300300 by 88 and said his answer was 3737 with a remainder of 44. How can you check to make sure he is correct? [practice-area rows="4"][/practice-area]

Mixed Practice (Applications)

In the following exercises, solve.

Miles per gallon

Susana’s hybrid car gets 4545 miles per gallon. Her son’s truck gets 1717 miles per gallon. What is the difference in miles per gallon between Susana’s car and her son’s truck?

Answer: The difference is 28 miles per gallon.

Distance

Mayra lives 5353 miles from her mother’s house and 7171 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 4545 students in a Geology class will go on a field trip, using the college’s vans. Each van can hold 99 students. How many vans will they need for the field trip?

Answer: They will need 5 vans for the field trip

Potting soil

Aki bought a 128128 ounce bag of potting soil. How many 44 ounce pots can he fill from the bag?

Hiking

Bill hiked 88 miles on the first day of his backpacking trip, 1414 miles the second day, 1111 miles the third day, and 1717 miles the fourth day. What is the total number of miles Bill hiked?

Answer: Bill hiked 50 miles

Reading

Last night Emily read 66 pages in her Business textbook, 2626 pages in her History text, 1515 pages in her Psychology text, and 99 pages in her math text. What is the total number of pages Emily read?

Patients

LaVonne treats 1212 patients each day in her dental office. Last week she worked 44 days. How many patients did she treat last week?

Answer: LaVonne treated 48 patients last week.

Scouts

There are 1414 boys in Dave’s scout troop. At summer camp, each boy earned 55 merit badges. What was the total number of merit badges earned by Dave’s scout troop at summer camp?

Chapter Review Exercises

Introduction to Whole Numbers

Identify Counting Numbers and Whole Numbers

In the following exercises, determine which of the following are (a) counting numbers (b) whole numbers.
  1. 0,2,990,2,99

    Answer: a) Counting numbers: 2, 99 b) Whole numbers: 0, 2, 99

  2. 0,3,250,3,25
  3. 0,4,900,4,90

    Answer: a) Counting numbers: 4, 90 b) Whole numbers: 0, 4, 90

  4. 0,1,750,1,75

Model Whole Numbers

In the following exercises, model each number using base - 10\text{base - 10} blocks and then show its value using place value notation.
  1. 258

    Answer: No Alt Text

  2. 104

Identify the Place Value of a Digit

In the following exercises, find the place value of the given digits. 472,981472,981
  1. 88
  2. 44
  3. 11
  4. 77
  5. 22

Answer:

  1. tens
  2. hundred thousands
  3. ones
  4. thousands
  5. ten thousands

12,403,29512,403,295
  1. 44
  2. 00
  3. 11
  4. 99
  5. 33

Use Place Value to Name Whole Numbers

In the following exercises, name each number in words.
  1. 5,2805,280

    Answer: Five thousand two hundred eighty

  2. 204,614204,614
  3. 5,012,5825,012,582

    Answer: Five million twelve thousand five hundred eighty-two

  4. 31,640,97631,640,976

Use Place Value to Write Whole Numbers

In the following exercises, write as a whole number using digits.
  1. six hundred two
  2. fifteen thousand, two hundred fifty-three

    Answer: 15,253

  3. three hundred forty million, nine hundred twelve thousand, sixty-one

    Answer: 340,912,061

  4. two billion, four hundred ninety-two million, seven hundred eleven thousand, two

Round Whole Numbers

In the following exercises, round to the nearest ten.
  1. 412412

    Answer: 410

  2. 648648
  3. 3,5563,556

    Answer: 3,560

  4. 2,7342,734
In the following exercises, round to the nearest hundred.
  1. 38,97538,975

    Answer: 39,000

  2. 26,84926,849
  3. 81,48681,486

    Answer: 81,500

  4. 75,99275,992

Add Whole Numbers

Use Addition Notation

In the following exercises, translate the following from math notation to words.
  1. 4+34+3

    Answer: four plus three; the sum of four and three

  2. 25+1825+18
  3. 571+629571+629

    Answer: five hundred seventy-one plus six hundred twenty-nine; the sum of five hundred seventy-one and six hundred twenty-nine

  4. 10,085+3,49210,085+3,492

Model Addition of Whole Numbers

In the following exercises, model the addition.
  1. 6+76+7

    Answer: No Alt Text

  2. 38+1438+14

Add Whole Numbers

In the following exercises, fill in the missing values in each chart.
Exercise 1
A table with 11 rows down and 11 rows across. The first row and first column are headers and include the numbers 0 through 9 both across and down, with a plus sign in the first cell. The numbers across in the second row down appear as follows: 0,0, 1, null, 3, 4, null, 6, 7, null, 9. The numbers across in the third row down appear as follows: 1, 1, 2, 3, 4, null, null, 7, 8, 9, null. The numbers in the fourth row down appear across as follows: 2, null, 3,4,5,6,7,8, null, 10, 11. The numbers across in the fifth row down appear as follows: 3, 3, null, 5, null, 7, 8, null, 10, null 12. The numbers across in the sixth row down appear as follows: 4, 4, 5, null, null, 8, 9,null, null, 12, null. The numbers across in the seventh row down appear as follows: 5, 5, null, 7, 8, null null, 11, null, 13, null. The numbers across in the eighth row down appear as follows:6, 6, 7, 8, null, 10, null, null, 13, null, 15. The numbers across in the ninth row down appear as follows: null, null, 9, null, null, 12, 13, null, 15, 16. The numbers across in the tenth row down appear as follows: 8,8,9,null, 11, null, null, 14, null, eleventh row down appear as follows: 9, 9, 10, 11, null, 13, 14, null, null, 17, null.

Answer: No Alt Text

Exercise 2
This table is 5 rows and 8 columns. The top row is a header row and includes the numbers 3 through 9, one number to each cell. The rows down include 6, 7, 8, and 9. There is a plus sign in the first cell. All cells are null. In the following exercises, add.
  1. 0+190+19

    Answer: 19

  2. 19+019+0

    Answer: 19

  3. 0+4800+480
  4. 480+0480+0
  5. 7+67+6

    Answer: 13

  6. 6+76+7

    Answer: 13

  7. 23+1823+18
  8. 18+2318+23
  9. 44+3544+35

    Answer: 82

  10. 63+2963+29
  11. 96+5896+58

    Answer: 154

  12. 375+591375+591
  13. 7,281+12,5467,281+12,546

    Answer: 19,827

  14. 5,280+16,324+9,7315,280+16,324+9,731

Translate Word Phrases to Math Notation

In the following exercises, translate each phrase into math notation and then simplify.
  1. the sum of 3030 and 1212

    Answer: 30 + 12; 42

  2. 1111 increased by 88
  3. 2525 more than 3939

    Answer: 39 + 25; 64

  4. total of 1515 and 5050

Add Whole Numbers in Applications

In the following exercises, solve.
Shopping for an interview
Nathan bought a new shirt, tie, and slacks to wear to a job interview. The shirt cost $24\$24, the tie cost $14\$14, and the slacks cost $38\$38. What was Nathan’s total cost?

Answer: $76

Running
Jackson ran 44 miles on Monday, 1212 miles on Tuesday, 11 mile on Wednesday, 88 miles on Thursday, and 55 miles on Friday. What was the total number of miles Jackson ran?

Add Whole Numbers in Applications

In the following exercises, find the perimeter of each figure. An image of a rectangle that is 8 feet tall and 15 feet wide.

Answer: 46 feet

An image of a right triangle that has a base of 12 centimeters, height of 5 centimeters, and diagonal hypotenuse of 13 centimeters.

Subtract Whole Numbers

Use Subtraction Notation

In the following exercises, translate the following from math notation to words.
  1. 14514 - 5

    Answer: fourteen minus five; the difference of fourteen and five

  2. 401540 - 15
  3. 351249351 - 249

    Answer: three hundred fifty-one minus two hundred forty-nine; the difference between three hundred fifty-one and two hundred forty-nine

  4. 5,7242,9185,724 - 2,918

Model Subtraction of Whole Numbers

In the following exercises, model the subtraction.
  1. 18418 - 4

    Answer: No Alt Text

  2. 412941 - 29

Subtract Whole Numbers

In the following exercises, subtract and then check by adding.
  1. 858 - 5

    Answer: 3

  2. 12712 - 7
  3. 23923 - 9

    Answer: 14

  4. 462146 - 21
  5. 825982 - 59

    Answer: 23

  6. 11087110 - 87
  7. 539217539 - 217

    Answer: 322

  8. 415296415 - 296
  9. 1,0206401,020 - 640

    Answer: 380

  10. 8,3553,9478,355 - 3,947
  11. 10,0001510,000 - 15

    Answer: 9,985

  12. 54,92535,64754,925 - 35,647

Translate Word Phrases to Math Notation

In the following exercises, translate and simplify.
  1. the difference of nineteen and thirteen

    Answer: 19 − 13; 6

  2. subtract sixty-five from one hundred
  3. seventy-four decreased by eight

    Answer: 74 − 8; 66

  4. twenty-three less than forty-one

Subtract Whole Numbers in Applications

In the following exercises, solve.
Temperature
The high temperature in Peoria one day was 8686 degrees Fahrenheit and the low temperature was 2828 degrees Fahrenheit. What was the difference between the high and low temperatures?

Answer: 58 degrees Fahrenheit

Savings
Lynn wants to go on a cruise that costs $2,485\$2,485. She has $948\$948 in her vacation savings account. How much more does she need to save in order to pay for the cruise?

Multiply Whole Numbers

Use Multiplication Notation

In the following exercises, translate from math notation to words.
  1. 8×58\times 5

    Answer: eight times five the product of eight and five

  2. 6146\cdot 14
  3. (10)(95)\left(10\right)\left(95\right)

    Answer: ten times ninety-five; the product of ten and ninety-five

  4. 54(72)54\left(72\right)

Model Multiplication of Whole Numbers

In the following exercises, model the multiplication.
  1. 2×42\times 4

    Answer: No Alt Text

  2. 3×83\times 8

Multiply Whole Numbers

In the following exercises, fill in the missing values in each chart.
Exercises 1
A table with 10 rows down and 10 rows across. The first row and first column are headers and include the numbers 0 through 9 both across and down, with a plus sign in the first cell. The numbers across in the second row down appear as follows: 0, 0, 0, 0, 0, 0, null, 0, null, 0,0. The numbers across in the third row down appear as follows: 1, 0, 1, 2, null, 4, 5, 6, 7, null, 9. The numbers across in the fourth row down appear as follows: 2, 0, null, 4, null, 8, 10, null, 14, 16, null. The numbers across in the fifth row down appear as follows: 3, null, 3, null, 9, null, null, 18, null, 24, null. The numbers across in the sixth row down appear as follows: 4, 0, 4, 0, 12, null, null, 24, null, null, 36. The numbers across in the seventh row down appear as follows:5, 0, 5, 10, null, 20, null, 30, 35, 40, 45. The numbers across in the eighth row down appear as follows: 6, null, null, 12, 18, null, null, 36, 42, null, 54. The numbers across in the ninth row down appear as follows: 7, 0, 7, null, 21, null, 35, null, null, 56, 63. The numbers in the tenth row down appear as follows: 8, 0, 8, 16, null, 32, null, 48, null, 64, null. The numbers in the eleventh row down appear across as follows: 9, null, null, 18, 27, 36, null, null, 63, 72, null.

Answer: No Alt Text

Exercises 2
An image of a table with 8 columns and 5 rows. The cells in the first row and first column are shaded darker than the other cells. The first row has the values

Multiply Whole Numbers

In the following exercises, multiply.
  1. 0140\cdot 14

    Answer: 0

  2. (256)0\left(256\right)0
  3. 1991\cdot 99

    Answer: 99

  4. (4,789)1\left(4,789\right)1
  5. 747\cdot 4

    Answer: 28

  6. 474\cdot 7

    Answer: 28

  7. (25)(6)\left(25\right)\left(6\right)
  8. 9,261×39,261\times 3

    Answer: 27,783

  9. 487648\cdot 76
  10. 641064\cdot 10

    Answer: 640

  11. 1,000(22)1,000\left(22\right)
  12. 162×493162\times 493

    Answer: 79,866

  13. (601)(943)\left(601\right)\left(943\right)
  14. 3,624×5173,624\times 517

    Answer: 1,873,608

  15. 10,5382210,538\cdot 22

Translate Word Phrases to Math Notation

In the following exercises, translate and simplify.
  1. the product of 1515 and 2828

    Answer: 15(28); 420

  2. ninety-four times thirty-three
  3. twice 575575

    Answer: 2(575); 1,150

  4. ten times two hundred sixty-four

Multiply Whole Numbers in Applications

In the following exercises, solve.
Gardening
Geniece bought 88 packs of marigolds to plant in her yard. Each pack has 66 flowers. How many marigolds did Geniece buy?

Answer: 48 marigolds

Cooking
Ratika is making rice for a dinner party. The number of cups of water is twice the number of cups of rice. If Ratika plans to use 44 cups of rice, how many cups of water does she need?
Multiplex
There are twelve theaters at the multiplex and each theater has 150150 seats. What is the total number of seats at the multiplex?

Answer: 1,800 seats

Roofing
Lewis needs to put new shingles on his roof. The roof is a rectangle, 3030 feet by 2424 feet. What is the area of the roof?

Divide Whole Numbers

Use Division Notation

Translate from math notation to words.
  1. 54÷954\div 9

    Answer: fifty-four divided by nine; the quotient of fifty-four and nine

  2. 42/742/7
  3. 728\frac{72}{8}

    Answer: seventy-two divided by eight; the quotient of seventy-two and eight

  4. 6)486\overline{)48}

Model Division of Whole Numbers

In the following exercises, model.
  1. 8÷28\div 2

    Answer: No Alt Text

  2. 3)123\overline{)12}

Divide Whole Numbers

In the following exercises, divide. Then check by multiplying.
  1. 14÷214\div 2

    Answer: 7

  2. 328\frac{32}{8}
  3. 52÷452\div 4

    Answer: 13

  4. 26)2626\overline{)26}
  5. 971\frac{97}{1}

    Answer: 97

  6. 0÷520\div 52
  7. 100÷0100\div 0

    Answer: undefined

  8. 3555\frac{355}{5}
  9. 3828÷63828\div 6

    Answer: 638

  10. 31)1,51931\overline{)1,519}
  11. 750525\frac{7505}{25}

    Answer: 300 R5

  12. 5,166÷425,166\div 42

Translate Word Phrases to Math Notation

In the following exercises, translate and simplify.
  1. the quotient of 6464 and 1616

    Answer: 64 ÷ 16; 4

  2. the quotient of 572572 and 5252

Divide Whole Numbers in Applications

In the following exercises, solve.
Ribbon
One spool of ribbon is 2727 feet. Lizbeth uses 33 feet of ribbon for each gift basket that she wraps. How many gift baskets can Lizbeth wrap from one spool of ribbon?

Answer: 9 baskets

Juice
One carton of fruit juice is 128128 ounces. How many 44 ounce cups can Shayla fill from one carton of juice?

Chapter Practice Test

Determine which of the following numbers are a) counting numbers and b) whole numbers.
  1. 0,4,870,4,87

    Answer: a) Counting numbers: 4, 87 b) Whole numbers: 0, 4, 8

Find the place value of the given digits in the number 549,362549,362.
  1. 99
  2. 66
  3. 22
  4. 55
Write each number as a whole number using digits.
  1. six hundred thirteen

    Answer: 613

  2. fifty-five thousand two hundred eight

    Answer: 55,208

Round 25,84925,849 to the nearest hundred. Simplify.
  1. 45+2345+23

    Answer: 68

  2. 654265 - 42
  3. 85÷585\div 5

    Answer: 17

  4. 1,000×81,000\times 8
  5. 905890 - 58

    Answer: 32

  6. 73+8973+89
  7. (0)(12,675)\left(0\right)\left(12,675\right)

    Answer: 0

  8. 634+255634+255
  9. 09\frac{0}{9}

    Answer: 0

  10. 8)1288\overline{)128}
  11. 14579145 - 79

    Answer: 66

  12. 299+836299+836
  13. 74757\cdot 475

    Answer: 3,325

  14. 8,528+7048,528+704
  15. 35(14)35\left(14\right)

    Answer: 490

  16. 260\frac{26}{0}
  17. 733291733 - 291

    Answer: 442

  18. 4,9161,5384,916 - 1,538
  19. 495÷45495\div 45

    Answer: 11

  20. 52×98352\times 983
Translate each phrase to math notation and then simplify.
  1. The sum of 1616 and 5858

    Answer: 16 + 58; 74

  2. The product of 99 and 1515
  3. The difference of 3232 and 1818

    Answer: 32 − 18; 14

  4. The quotient of 6363 and 2121
  5. Twice 524524

    Answer: 2(524); 1,048

  6. 2929 more than 3232
  7. 5050 less than 300300

    Answer: 300 − 50; 250

In the following exercises, solve.
  1. LaVelle buys a jumbo bag of 8484 candies to make favor bags for her son’s party. If she wants to make 1212 bags, how many candies should she put in each bag?
  2. Last month, Stan’s take-home pay was $3,816\$3,816 and his expenses were $3,472\$3,472. How much of his take-home pay did Stan have left after he paid his expenses?

    Answer: Stan had $344 left.

  3. Each class at Greenville School has 2222 children enrolled. The school has 2424 classes. How many children are enrolled at Greenville School?
  4. Clayton walked 1212 blocks to his mother’s house, 66 blocks to the gym, and 99 blocks to the grocery store before walking the last 33 blocks home. What was the total number of blocks that Clayton walked?

    Answer: Clayton walked 30 blocks

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