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Study Guides > Prealgebra

Problem Set 1: Whole Numbers

Practice Makes Perfect

Identify Counting Numbers and Whole Numbers In the following exercises, determine which of the following numbers are ⓐ counting numbers ⓑ whole numbers. 0,23,5,8.1,1250,\frac{2}{3},5,8.1,125
  1. 0, 5, 125
  2. 0, 5, 125
0,710,3,20.5,3000,\frac{7}{10},3,20.5,300 0,49,3.9,50,2210,\frac{4}{9},3.9,50,221
  1. 50, 221
  2. 0, 50, 221
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. 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. 561 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. 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. 407 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. 579,601579,601
  1. 9
  2. 6
  3. 0
  4. 7
  5. 5
  1. thousands
  2. hundreds
  3. tens
  4. ten thousands
  5. hundred thousands
398,127398,127
  1. 9
  2. 3
  3. 2
  4. 8
  5. 7
56,804,37956,804,379
  1. 8
  2. 6
  3. 4
  4. 7
  5. 0
  1. hundred thousands
  2. millions
  3. thousands
  4. tens
  5. ten thousands
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. 1,0781,078 One thousand, seventy-eight 5,9025,902 364,510364,510 Three hundred sixty-four thousand, five hundred ten 146,023146,023 5,846,1035,846,103 Five million, eight hundred forty-six thousand, one hundred three 1,458,3981,458,398 37,889,00537,889,005 Thirty seven million, eight hundred eighty-nine thousand, five 62,008,46562,008,465 The height of Mount Ranier is 14,41014,410 feet. Fourteen thousand, four hundred ten The height of Mount Adams is 12,27612,276 feet. Seventy years is 613,200613,200 hours. Six hundred thirteen thousand, two hundred One year is 525,600525,600 minutes. The U.S. Census estimate of the population of Miami-Dade county was 2,617,1762,617,176. Two million, six hundred seventeen thousand, one hundred seventy-six The population of Chicago was 2,718,7822,718,782. There are projected to be 23,867,00023,867,000 college and university students in the US in five years. Twenty three million, eight hundred sixty-seven thousand About twelve years ago there were 20,665,41520,665,415 registered automobiles in California. The population of China is expected to reach 1,377,583,1561,377,583,156 in 20162016. One billion, three hundred seventy-seven million, five hundred eighty-three thousand, one hundred fifty-six 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. four hundred twelve 412 two hundred fifty-three thirty-five thousand, nine hundred seventy-five 35,975 sixty-one thousand, four hundred fifteen eleven million, forty-four thousand, one hundred sixty-seven 11,044,167 eighteen million, one hundred two thousand, seven hundred eighty-three three billion, two hundred twenty-six million, five hundred twelve thousand, seventeen 3,226,512,017 eleven billion, four hundred seventy-one million, thirty-six thousand, one hundred six The population of the world was estimated to be seven billion, one hundred seventy-three million people. 7,173,000,000 The age of the solar system is estimated to be four billion, five hundred sixty-eight million years. Lake Tahoe has a capacity of thirty-nine trillion gallons of water. 39,000,000,000,000 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
  2. 2,9312,931
  1. 390
  2. 2,930
Round to the nearest ten:
  1. 792792
  2. 5,6475,647
  3. 790
  4. 5,650
Round to the nearest hundred:
  1. 13,74813,748
  2. 391,794391,794
  1. 13,700
  2. 391,800
Round to the nearest hundred:
  1. 28,16628,166
  2. 481,628481,628
 
  1. 28,200
  2. 481,700
Round to the nearest ten:
  1. 1,4921,492
  2. 1,4971,497
  1. 1,490
  2. 1,500
Round to the nearest thousand:
  1. 2,3912,391
  2. 2,7952,795
 
  1. 2,000
  2. 3,000
Round to the nearest hundred:
  1. 63,99463,994
  2. 63,94963,949
 
  1. 64,00064,000
  2. 63,90063,900
Round to the nearest thousand:
  1. 163,584163,584
  2. 163,246163,246
 
  1. 164,000
  2. 163,000

Everyday Math

Writing a Check Jorge bought a car for \text{$24,493}. He paid for the car with a check. Write the purchase price in words. Twenty four thousand, four hundred ninety-three dollars Writing a Check Marissa’s kitchen remodeling cost \text{$18,549}. She wrote a check to the contractor. Write the amount paid in words. Buying a Car Jorge bought a car for \text{$24,493}. Round the price to the nearest:
  1. ten dollars
  2. hundred dollars
  3. thousand dollars
  4. ten-thousand dollars
  1. $24,490
  2. $24,500
  3. $24,000
  4. $20,000
Remodeling a Kitchen Marissa’s kitchen remodeling cost \text{$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 20142014. Round the population to the nearest:
  1. billion people
  2. hundred-million people
  3. million people
  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. 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.

Self Check

1. After completing the exercises, use this checklist to evaluate your mastery of the objectives of this section. . 2. If most of your checks were... …confidently. Congratulations! You have achieved the objectives in this section. Reflect on the study skills you used so that you can continue to use them. What did you do to become confident of your ability to do these things? Be specific. …with some help. This must be addressed quickly because topics you do not master become potholes in your road to success. In math, every topic builds upon previous work. It is important to make sure you have a strong foundation before you move on. Who can you ask for help? Your fellow classmates and instructor are good resources. Is there a place on campus where math tutors are available? Can your study skills be improved? …no—I don’t get it! This is a warning sign and you must not ignore it. You should get help right away or you will quickly be overwhelmed. See your instructor as soon as you can to discuss your situation. Together you can come up with a plan to get you the help you need.

Practice Makes Perfect

Use Addition Notation In the following exercises, translate the following from math expressions to words. 5+25+2 five plus two; the sum of 5 and 2. 6+36+3 13+1813+18 thirteen plus eighteen; the sum of 13 and 18. 15+1615+16 214+642214+642 two hundred fourteen plus six hundred forty-two; the sum of 214 and 642 438+113438+113 Model Addition of Whole Numbers In the following exercises, model the addition. 2+42+4 No Alt Text 2+4=62+4=6 5+35+3 8+48+4 No Alt Text 8+4=128+4=12 5+95+9 14+7514+75 No Alt Text 14+75=8914+75=89 15+6315+63 16+2516+25 No Alt Text 16+25=4116+25=41 14+2714+27 Add Whole Numbers In the following exercises, fill in the missing values in each chart. 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 No Alt Text 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 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 No Alt Text 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 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 No Alt Text 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 In the following exercises, add.
  1. 0+130+13
  2. 13+013+0
  1. 13
  2. 13
  1. 0+5,2800+5,280
  2. 5,280+05,280+0
  1. 8+38+3
  2. 3+83+8
  1. 1111
  2. 1111
  1. 7+57+5
  2. 5+75+7
45+3345+33 7878 37+2237+22 71+2871+28 9999 43+5343+53 26+5926+59 8585 38+1738+17 64+7864+78 142142 92+3992+39 168+325168+325 493493 247+149247+149 584+277584+277 861861 175+648175+648 832+199832+199 1,0311,031 775+369775+369 6,358+4926,358+492 6,8506,850 9,184+5789,184+578 3,740+18,5933,740+18,593 22,33322,333 6,118+15,9906,118+15,990 485,012+619,848485,012+619,848 1,104,8601,104,860 368,911+857,289368,911+857,289 24,731+592+3,86824,731+592+3,868 29,19129,191 28,925+817+4,59328,925+817+4,593 8,015+76,946+16,5708,015+76,946+16,570 101,531101,531 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. the sum of 1313 and 1818 13+18=3113+18=31 the sum of 1212 and 1919 the sum of 9090 and 6565 90+65=15590+65=155 the sum of 7070 and 3838 33[/latex]increasedby[latex]4933[/latex] increased by [latex]49 33+49=8233+49=82 68[/latex]increasedby[latex]2568[/latex] increased by [latex]25 250[/latex]morethan[latex]599250[/latex] more than [latex]599 250+599=849250+599=849 115[/latex]morethan[latex]286115[/latex] more than [latex]286 the total of 628628 and 7777 628+77=705628+77=705 the total of 593593 and 7979 1,482[/latex]addedto[latex]9151,482[/latex] added to [latex]915 915+1,482=2,397915+1,482=2,397 2,719[/latex]addedto[latex]6822,719[/latex] added to [latex]682 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 \text{$1,100}, the microwave cost \text{$250}, and the dishwasher cost \text{$525}. What was the total cost of these three appliances? The total cost was $1,875. Sports equipment Aiden bought a baseball bat, helmet, and glove. The bat cost \text{$299}, the helmet cost \text{$35}, and the glove cost \text{$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? 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 77 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? 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 \text{$82,572}. Two years ago, her salary was \text{$79,316}, and three years ago it was \text{$75,298}. What is the total amount of Natalie’s salary for the past three years? 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 \text{$292,540},\text{$505,875}, and $423,699. What was the total of the three selling prices? In the following exercises, find the perimeter of each figure. An image of a triangle with side lengths of 14 inches, 12 inches, and 18 inches. The perimeter of the figure is 44 inches. An image of a right triangle with base of 12 centimeters, height of 5 centimeters, and diagonal hypotenuse of 13 centimeters. A rectangle 21 meters wide and 7 meters tall. The perimeter of the figure is 56 meters. A rectangle 19 feet wide and and 14 feet tall. 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. The perimeter of the figure is 71 yards. 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. 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. The perimeter of the figure is 62 feet. 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? 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? 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,and164210,145,183,230,159,\text{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? Answers will vary. How have you used models to help you learn the addition facts?

Self Check

1. After completing the exercises, use this checklist to evaluate your mastery of the objectives of this section. . 2. After reviewing this checklist, what will you do to become confident for all objectives?

Practice Makes Perfect

Use Subtraction Notation In the following exercises, translate from math notation to words. 15915 - 9 fifteen minus nine; the difference of fifteen and nine 181618 - 16 423542 - 35 forty-two minus thirty-five; the difference of forty-two and thirty-five 836483 - 64 675350675 - 350 hundred seventy-five minus three hundred fifty; the difference of six hundred seventy-five and three hundred fifty 790525790 - 525 Model Subtraction of Whole Numbers In the following exercises, model the subtraction. 525 - 2 No Alt Text 848 - 4 636 - 3 No Alt Text 757 - 5 18518 - 5 No Alt Text 19819 - 8 17817 - 8 No Alt Text 17917 - 9 351335 - 13 No Alt Text 321132 - 11 614761 - 47 No Alt Text 553655 - 36 Subtract Whole Numbers In the following exercises, subtract and then check by adding. 949 - 4 5 939 - 3 808 - 0 8 202 - 0 381638 - 16 22 452145 - 21 855285 - 52 33 994799 - 47 493370493 - 370 123 268106268 - 106 5,9464,6255,946 - 4,625 1,321 7,7753,2517,775 - 3,251 754775 - 47 28 635963 - 59 461239461 - 239 222 486257486 - 257 525179525 - 179 346 542288542 - 288 6,3182,7996,318 - 2,799 3,519 8,1533,9788,153 - 3,978 2,1509642,150 - 964 1,186 4,2458994,245 - 899 43,6508,98243,650 - 8,982 34,668 35,1627,88535,162 - 7,885 Translate Word Phrases to Algebraic Expressions In the following exercises, translate and simplify. The difference of 1010 and 33 10 − 3; 7 The difference of 1212 and 88 The difference of 1515 and 44 15 − 4; 11 The difference of 1818 and 77 Subtract 66 from 99 9 − 6; 3 Subtract 88 from 99 Subtract 2828 from 7575 75 − 28; 47 Subtract 5959 from 8181 45[/latex]decreasedby[latex]2045[/latex] decreased by [latex]20 45 − 20; 25 37[/latex]decreasedby[latex]2437[/latex] decreased by [latex]24 92[/latex]decreasedby[latex]6792[/latex] decreased by [latex]67 92 − 67; 25 75[/latex]decreasedby[latex]4975[/latex] decreased by [latex]49 12[/latex]lessthan[latex]1612[/latex] less than [latex]16 16 − 12; 4 15[/latex]lessthan[latex]1915[/latex] less than [latex]19 38[/latex]lessthan[latex]6138[/latex] less than [latex]61 61 − 38; 23 47[/latex]lessthan[latex]6247[/latex] less than [latex]62 Mixed Practice In the following exercises, simplify. 764776 - 47 29 915391 - 53 256184256 - 184 72 305262305 - 262 719+341719+341 1,060 647+528647+528 2,0151,9932,015 - 1,993 22 2,0201,9842,020 - 1,984 In the following exercises, translate and simplify. Seventy more than thirty-five 75 + 35; 110 Sixty more than ninety-three 13[/latex]lessthan[latex]4113[/latex] less than [latex]41 41 − 13; 28 28[/latex]lessthan[latex]3628[/latex] less than [latex]36 The difference of 100100 and 7676 100 − 76; 24 The difference of 1,0001,000 and 945945 Subtract Whole Numbers in Applications In the following exercises, solve. Temperature The high temperature on June 22 in Las Vegas was 8080 degrees and the low temperature was 6363 degrees. What was the difference between the high and low temperatures? The difference between the high and low temperature was 17 degrees Temperature The high temperature on June 11 in Phoenix was 9797 degrees and the low was 7373 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? 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 \text{$399}. Its regular price is \text{$650}. What is the difference between the regular price and the sale price? The difference between the regular price and sale price is $251. Shopping A mattress set is on sale for \text{$755}. Its regular price is \text{$1,600}. What is the difference between the regular price and the sale price? Savings John wants to buy a laptop that costs \text{$840}. He has \text{$685} in his savings account. How much more does he need to save in order to buy the laptop? John needs to save $155 more. Banking Mason had \text{$1,125} in his checking account. He spent \text{$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? 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. Answers may vary. How does knowing addition facts help you to subtract numbers?

Self Check

1. After completing the exercises, use this checklist to evaluate your mastery of the objectives of this section. . 2. What does this checklist tell you about your mastery of this section? What steps will you take to improve?  

Practice Makes Perfect

Use Multiplication Notation In the following exercises, translate from math notation to words. 4×74\times 7 four times seven; the product of four and seven 8×68\times 6 5125\cdot 12 five times twelve; the product of five and twelve 393\cdot 9 (10)(25)\left(10\right)\left(25\right) ten times twenty-five; the product of ten and twenty-five (20)(15)\left(20\right)\left(15\right) 42(33)42\left(33\right) forty-two times thirty-three; the product of forty-two and thirty-three 39(64)39\left(64\right) Model Multiplication of Whole Numbers In the following exercises, model the multiplication. 3×63\times 6 No Alt Text 4×54\times 5 5×95\times 9 No Alt Text 3×93\times 9 Multiply Whole Numbers In the following exercises, fill in the missing values in each chart. 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 No Alt Text 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 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 No Alt Text 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 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 No Alt Text 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 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 No Alt Text 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 In the following exercises, multiply. 0150\cdot 15 0 0410\cdot 41 (99)0\left(99\right)0 0 (77)0\left(77\right)0 1431\cdot 43 43 1341\cdot 34 (28)1\left(28\right)1 28 (65)1\left(65\right)1 1(240,055)1\left(240,055\right) 240,055 1(189,206)1\left(189,206\right)
  1. 767\cdot 6
  2. 676\cdot 7
  1. 42
  2. 42
8×98\times 9 9×89\times 8 (79)(5)\left(79\right)\left(5\right) 395 (58)(4)\left(58\right)\left(4\right) 2756275\cdot 6 1,650 6385638\cdot 5 3,421×73,421\times 7 23,947 9,143×39,143\times 3 52(38)52\left(38\right) 1,976 37(45)37\left(45\right) 967396\cdot 73 7,008 895689\cdot 56 27×8527\times 85 2,295 53×9853\times 98 231023\cdot 10 230 191019\cdot 10 (100)(36)\left(100\right)\left(36\right) 360 (100)(25)\left(100\right)\left(25\right) 1,000(88)1,000\left(88\right) 88,000 1,000(46)1,000\left(46\right) 50×1,000,00050\times 1,000,000 50,000,000 30×1,000,00030\times 1,000,000 247×139247\times 139 34,333 156×328156\times 328 586(721)586\left(721\right) 422,506 472(855)472\left(855\right) 915879915\cdot 879 804,285 968926968\cdot 926 (104)(256)\left(104\right)\left(256\right) 26,624 (103)(497)\left(103\right)\left(497\right) 348(705)348\left(705\right) 245,340 485(602)485\left(602\right) 2,719×5432,719\times 543 1,476,417 3,581×7243,581\times 724 Translate Word Phrases to Math Notation In the following exercises, translate and simplify. the product of 1818 and 3333 18 · 33; 594 the product of 1515 and 2222 fifty-one times sixty-seven 51(67); 3,417 forty-eight times seventy-one twice 249249 2(249); 498 twice 589589 ten times three hundred seventy-five 10(375); 3,750 ten times two hundred fifty-five Mixed Practice In the following exercises, simplify. 38×3738\times 37 1,406 86×2986\times 29 415267415 - 267 148 341285341 - 285 6,251+4,7496,251+4,749 11,000 3,816+8,1843,816+8,184 (56)(204)\left(56\right)\left(204\right) 11,424 (77)(801)\left(77\right)\left(801\right) 9470947\cdot 0 0 947+0947+0 15,382+115,382+1 15,383 15,382115,382\cdot 1 In the following exercises, translate and simplify. the difference of 50 and 18 50 − 18; 32 the difference of 90 and 66 twice 35 2(35); 70 twice 140 20 more than 980 20 + 980; 1,000 65 more than 325 the product of 12 and 875 12(875); 10,500 the product of 15 and 905 subtract 74 from 89 89 − 74; 15 subtract 45 from 99 the sum of 3,075 and 95 3,075 + 950; 4,025 the sum of 6,308 and 724 366 less than 814 814 − 366; 448 388 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? 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? 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? 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? 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? 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? 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? 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? 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 \text{$}12 per share. How much money did Javier’s portfolio gain? Javier’s portfolio gained $3,600. Salary Carlton got a \text{$}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? Answers will vary. How have you used models to help you learn the multiplication facts?

Self Check

1. After completing the exercises, use this checklist to evaluate your mastery of the objectives of this section. . 2. On a scale of 1–10, how would you rate your mastery of this section in light of your responses on the checklist? How can you improve this?

Practice Makes Perfect

Use Division Notation In the following exercises, translate from math notation to words. 54÷954\div 9 fifty-four divided by nine; the quotient of fifty-four and nine 567\frac{56}{7} 328\frac{32}{8} thirty-two divided by eight; the quotient of thirty-two and eight 6)426\overline{)42} 48÷648\div 6 forty-eight divided by six; the quotient of forty-eight and six 639\frac{63}{9} 7)637\overline{)63} sixty-three divided by seven; the quotient of sixty-three and seven 72÷872\div 8 Model Division of Whole Numbers In the following exercises, model the division. 15÷515\div 5 No Alt Text 10÷510\div 5 147\frac{14}{7} No Alt Text 186\frac{18}{6} 4)204\overline{)20} No Alt Text 3)153\overline{)15} 24÷624\div 6 No Alt Text 16÷416\div 4 Divide Whole Numbers In the following exercises, divide. Then check by multiplying. 18÷218\div 2 9 14÷214\div 2 273\frac{27}{3} 9 303\frac{30}{3} 4)284\overline{)28} 7 4)364\overline{)36} 455\frac{45}{5} 9 355\frac{35}{5} 72/872/8 9 8)648\overline{)64} 357\frac{35}{7} 5 42÷742\div 7 15)1515\overline{)15} 1 12)1212\overline{)12} 43÷4343\div 43 1 37÷3737\div 37 231\frac{23}{1} 23 291\frac{29}{1} 19÷119\div 1 19 17÷117\div 1 0÷40\div 4 0 0÷80\div 8 50\frac{5}{0} undefined 90\frac{9}{0} 260\frac{26}{0} undefined 320\frac{32}{0} 12)012\overline{)0} 0 16)016\overline{)0} 72÷372\div 3 24 57÷357\div 3 968\frac{96}{8} 12 786\frac{78}{6} 5)4655\overline{)465} 93 4)5284\overline{)528} 924÷7924\div 7 132 861÷7861\div 7 5,2266\frac{5,226}{6} 871 3,7768\frac{3,776}{8} 4)31,3244\overline{)31,324} 7,831 5)46,8555\overline{)46,855} 7,209÷37,209\div 3 2,403 4,806÷34,806\div 3 5,406÷65,406\div 6 901 3,208÷43,208\div 4 4)2,8164\overline{)2,816} 704 6)3,6246\overline{)3,624} 91,8819\frac{91,881}{9} 10,209 83,2568\frac{83,256}{8} 2,470÷72,470\div 7 352 R6 3,741÷73,741\div 7 8)55,3058\overline{)55,305} 6,913 R1 9)51,4929\overline{)51,492} 431,1745\frac{431,174}{5} 86,234 R4 297,2774\frac{297,277}{4} 130,016÷3130,016\div 3 43,338 R2 105,609÷2105,609\div 2 15)5,73515\overline{)5,735} 382 R5 4,93321\frac{4,933}{21} 56,883÷6756,883\div 67 849 43,725/7543,725/75 30,144314\frac{30,144}{314} 96 26,145÷41526,145\div 415 273)542,195273\overline{)542,195} 1,986 R17 816,243÷462816,243\div 462 Mixed Practice In the following exercises, simplify. 15(204)15\left(204\right) 3,060 7439174\cdot 391 256184256 - 184 72 305262305 - 262 719+341719+341 1,060 647+528647+528 25)87525\overline{)875} 35 1104÷231104\div 23 Translate Word Phrases to Algebraic Expressions In the following exercises, translate and simplify. the quotient of 4545 and 1515 45 ÷ 15; 3 the quotient of 6464 and 1616 the quotient of 288288 and 2424 288 ÷ 24; 12 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? 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? 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? 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? Mixed Practice 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? 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? 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? 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? 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?

Writing Exercises

Explain how you use the multiplication facts to help with division. 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?

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? 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?

Self Check

1. After completing the exercises, use this checklist to evaluate your mastery of the objectives of this section. . 2. Overall, after looking at the checklist, do you think you are well-prepared for the next Chapter? Why or why not?

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. 0,2,990,2,99
  1. 2, 99
  2.  0, 2, 99
0,3,250,3,25 0,4,900,4,90
  1. 4, 90
  2. 0, 4, 90
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. 258 No Alt Text 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
  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. 5,2805,280 Five thousand two hundred eighty 204,614204,614 5,012,5825,012,582 Five million twelve thousand five hundred eighty-two 31,640,97631,640,976 Use Place Value to Write Whole Numbers In the following exercises, write as a whole number using digits. six hundred two fifteen thousand, two hundred fifty-three 15,253 three hundred forty million, nine hundred twelve thousand, sixty-one 340,912,061 two billion, four hundred ninety-two million, seven hundred eleven thousand, two Round Whole Numbers In the following exercises, round to the nearest ten. 412412 410 648648 3,5563,556 3,560 2,7342,734 In the following exercises, round to the nearest hundred. 38,97538,975 39,000 26,84926,849 81,48681,486 81,500 75,99275,992

Add Whole Numbers

Use Addition Notation In the following exercises, translate the following from math notation to words. 4+34+3 four plus three; the sum of four and three 25+1825+18 571+629571+629 five hundred seventy-one plus six hundred twenty-nine; the sum of five hundred seventy-one and six hundred twenty-nine 10,085+3,49210,085+3,492 Model Addition of Whole Numbers In the following exercises, model the addition. 6+76+7 No Alt Text 38+1438+14 Add Whole Numbers In the following exercises, fill in the missing values in each chart. 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. No Alt Text 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 2. 19+019+0
1.  19 2.  19 1.  0+4800+480 2. 480+0480+0
  1. 7+67+6 2. 6+76+7
1. 13 2. 13
  1. 23+1823+18 2. 18+2318+23
44+3544+35 82 63+2963+29 96+5896+58 154 375+591375+591 7,281+12,5467,281+12,546 19,827 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. the sum of 3030 and 1212 30 + 12; 42 11[/latex]increasedby[latex]811[/latex] increased by [latex]8 25[/latex]morethan[latex]3925[/latex] more than [latex]39 39 + 25; 64 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 \text{$24,} the tie cost \text{$14,} and the slacks cost \text{$38.} What was Nathan’s total cost? $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? In the following exercises, find the perimeter of each figure. An image of a rectangle that is 8 feet tall and 15 feet wide. 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. 14514 - 5 fourteen minus five; the difference of fourteen and five 401540 - 15 351249351 - 249 three hundred fifty-one minus two hundred forty-nine; the difference between three hundred fifty-one and two hundred forty-nine 5,7242,9185,724 - 2,918 Model Subtraction of Whole Numbers In the following exercises, model the subtraction. 18418 - 4 No Alt Text 412941 - 29 Subtract Whole Numbers In the following exercises, subtract and then check by adding. 858 - 5 3 12712 - 7 23923 - 9 14 462146 - 21 825982 - 59 23 11087110 - 87 539217539 - 217 322 415296415 - 296 1,0206401,020 - 640 380 8,3553,9478,355 - 3,947 10,0001510,000 - 15 9,985 54,92535,64754,925 - 35,647 Translate Word Phrases to Math Notation In the following exercises, translate and simplify. the difference of nineteen and thirteen 19 − 13; 6 subtract sixty-five from one hundred seventy-four decreased by eight 74 − 8; 66 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? 58 degrees Fahrenheit Savings Lynn wants to go on a cruise that costs \text{$2,485.} She has \text{$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. 8×58\times 5 eight times five the product of eight and five 6146\cdot 14 (10)(95)\left(10\right)\left(95\right) ten times ninety-five; the product of ten and ninety-five 54(72)54\left(72\right) Model Multiplication of Whole Numbers In the following exercises, model the multiplication. 2×42\times 4 No Alt Text 3×83\times 8 Multiply Whole Numbers In the following exercises, fill in the missing values in each chart. 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. No Alt Text 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 In the following exercises, multiply. 0140\cdot 14 0 (256)0\left(256\right)0 1991\cdot 99 99 (4,789)1\left(4,789\right)1747\cdot 4474\cdot 7
  1. ⓐ 28
  2. ⓑ 28
(25)(6)\left(25\right)\left(6\right) 9,261×39,261\times 3 27,783 487648\cdot 76 641064\cdot 10 640 1,000(22)1,000\left(22\right) 162×493162\times 493 79,866 (601)(943)\left(601\right)\left(943\right) 3,624×5173,624\times 517 1,873,608 10,5382210,538\cdot 22 Translate Word Phrases to Math Notation In the following exercises, translate and simplify. the product of 1515 and 2828 15(28); 420 ninety-four times thirty-three twice 575575 2(575); 1,150 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? 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? 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. 54÷954\div 9 fifty-four divided by nine; the quotient of fifty-four and nine 42/742/7 728\frac{72}{8} seventy-two divided by eight; the quotient of seventy-two and eight 6)486\overline{)48} Model Division of Whole Numbers In the following exercises, model. 8÷28\div 2 No Alt Text 3)123\overline{)12} Divide Whole Numbers In the following exercises, divide. Then check by multiplying. 14÷214\div 2 7 328\frac{32}{8} 52÷452\div 4 13 26)2626\overline{)26} 971\frac{97}{1} 97 0÷520\div 52 100÷0100\div 0 undefined 3555\frac{355}{5} 3828÷63828\div 6 638 31)1,51931\overline{)1,519} 750525\frac{7505}{25} 300 R5 5,166÷425,166\div 42 Translate Word Phrases to Math Notation In the following exercises, translate and simplify. the quotient of 6464 and 1616 64 ÷ 16; 4 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? 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
  1. counting numbers
  2. whole numbers.
0,4,870,4,87
  1. 4, 87
  2. 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
  2. fifty-five thousand two hundred eight
  1. 613
  2. 55,208
Round 25,84925,849 to the nearest hundred. Simplify. 45+2345+23 68 654265 - 42 85÷585\div 5 17 1,000×81,000\times 8 905890 - 58 32 73+8973+89 (0)(12,675)\left(0\right)\left(12,675\right) 0 634+255634+255 09\frac{0}{9} 0 8)1288\overline{)128} 14579145 - 79 66 299+836299+836 74757\cdot 475 3,325 8,528+7048,528+704 35(14)35\left(14\right) 490 260\frac{26}{0} 733291733 - 291 442 4,9161,5384,916 - 1,538 495÷45495\div 45 11 52×98352\times 983 Translate each phrase to math notation and then simplify. The sum of 1616 and 5858 16 + 58; 74 The product of 99 and 1515 The difference of 3232 and 1818 32 − 18; 14 The quotient of 6363 and 2121 Twice 524524 2(524); 1,048 29[/latex]morethan[latex]3229[/latex] more than [latex]32 50[/latex]lessthan[latex]30050[/latex] less than [latex]300 300 − 50; 250 In the following exercises, solve. 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? Last month, Stan’s take-home pay was \text{$3,816} and his expenses were \text{$3,472.} How much of his take-home pay did Stan have left after he paid his expenses? Stan had $344 left. Each class at Greenville School has 2222 children enrolled. The school has 2424 classes. How many children are enrolled at Greenville School? 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? Clayton walked 30 blocks.    

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