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.

[latex]0,\frac{2}{3},5,8.1,125[/latex]

  1. 0, 5, 125
  2. 0, 5, 125

[latex]0,\frac{7}{10},3,20.5,300[/latex]

[latex]0,\frac{4}{9},3.9,50,221[/latex]

  1. 50, 221
  2. 0, 50, 221

[latex]0,\frac{3}{5},10,303,422.6[/latex]

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

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.

[latex]579,601[/latex]

  1. 9
  2. 6
  3. 0
  4. 7
  5. 5
  1. thousands
  2. hundreds
  3. tens
  4. ten thousands
  5. hundred thousands

[latex]398,127[/latex]

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

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

  1. 8
  2. 6
  3. 4
  4. 7
  5. 0
  1. hundred thousands
  2. millions
  3. thousands
  4. tens
  5. ten thousands

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

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

Use Place Value to Name Whole Numbers
In the following exercises, name each number in words.

[latex]1,078[/latex]

One thousand, seventy-eight

[latex]5,902[/latex]

[latex]364,510[/latex]

Three hundred sixty-four thousand, five hundred ten

[latex]146,023[/latex]

[latex]5,846,103[/latex]

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

[latex]1,458,398[/latex]

[latex]37,889,005[/latex]

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

[latex]62,008,465[/latex]

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

Fourteen thousand, four hundred ten

The height of Mount Adams is [latex]12,276[/latex] feet.

Seventy years is [latex]613,200[/latex] hours.

Six hundred thirteen thousand, two hundred

One year is [latex]525,600[/latex] minutes.

The U.S. Census estimate of the population of Miami-Dade county was [latex]2,617,176[/latex].

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

The population of Chicago was [latex]2,718,782[/latex].

There are projected to be [latex]23,867,000[/latex] college and university students in the US in five years.

Twenty three million, eight hundred sixty-seven thousand

About twelve years ago there were [latex]20,665,415[/latex] registered automobiles in California.

The population of China is expected to reach [latex]1,377,583,156[/latex] in [latex]2016[/latex].

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

The population of India is estimated at [latex]1,267,401,849[/latex] as of July [latex]1,2014[/latex].

Use Place Value to Write Whole Numbers
In the following exercises, write each number as a whole number using digits.

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. [latex]386[/latex]
  2. [latex]2,931[/latex]
  1. 390
  2. 2,930

Round to the nearest ten:

  1. [latex]792[/latex]
  2. [latex]5,647[/latex]
  3. 790
  4. 5,650

Round to the nearest hundred:

  1. [latex]13,748[/latex]
  2. [latex]391,794[/latex]
  1. 13,700
  2. 391,800

Round to the nearest hundred:

  1. [latex]28,166[/latex]
  2. [latex]481,628[/latex]

 

  1. 28,200
  2. 481,700

Round to the nearest ten:

  1. [latex]1,492[/latex]
  2. [latex]1,497[/latex]
  1. 1,490
  2. 1,500

Round to the nearest thousand:

  1. [latex]2,391[/latex]
  2. [latex]2,795[/latex]

 

  1. 2,000
  2. 3,000

Round to the nearest hundred:

  1. [latex]63,994[/latex]
  2. [latex]63,949[/latex]

 

  1. [latex]64,000[/latex]
  2. [latex]63,900[/latex]

Round to the nearest thousand:

  1. [latex]163,584[/latex]
  2. [latex]163,246[/latex]

 

  1. 164,000
  2. 163,000

Everyday Math

Writing a Check Jorge bought a car for [latex]\text{$24,493}[/latex]. 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 [latex]\text{$18,549}[/latex]. She wrote a check to the contractor. Write the amount paid in words.

Buying a Car Jorge bought a car for [latex]\text{$24,493}[/latex]. 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 [latex]\text{$18,549}[/latex]. 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 [latex]1,355,692,544[/latex] in [latex]2014[/latex]. Round the population to the nearest:

  1. billion people
  2. hundred-million people
  3. million people
  1. [latex]1,000,000,000[/latex]
  2. [latex]1,400,000,000[/latex]
  3. [latex]1,356,000,000[/latex]

Astronomy The average distance between Earth and the sun is [latex]149,597,888[/latex] 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.

[latex]5+2[/latex]

five plus two; the sum of 5 and 2.

[latex]6+3[/latex]

[latex]13+18[/latex]

thirteen plus eighteen; the sum of 13 and 18.

[latex]15+16[/latex]

[latex]214+642[/latex]

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

[latex]438+113[/latex]

Model Addition of Whole Numbers
In the following exercises, model the addition.

[latex]2+4[/latex]

No Alt Text
[latex]2+4=6[/latex]

[latex]5+3[/latex]

[latex]8+4[/latex]

No Alt Text
[latex]8+4=12[/latex]

[latex]5+9[/latex]

[latex]14+75[/latex]

No Alt Text
[latex]14+75=89[/latex]

[latex]15+63[/latex]

[latex]16+25[/latex]

No Alt Text
[latex]16+25=41[/latex]

[latex]14+27[/latex]

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. [latex]0+13[/latex]
  2. [latex]13+0[/latex]
  1. 13
  2. 13
  1. [latex]0+5,280[/latex]
  2. [latex]5,280+0[/latex]
  1. [latex]8+3[/latex]
  2. [latex]3+8[/latex]
  1. [latex]11[/latex]
  2. [latex]11[/latex]
  1. [latex]7+5[/latex]
  2. [latex]5+7[/latex]

[latex]45+33[/latex]

[latex]78[/latex]

[latex]37+22[/latex]

[latex]71+28[/latex]

[latex]99[/latex]

[latex]43+53[/latex]

[latex]26+59[/latex]

[latex]85[/latex]

[latex]38+17[/latex]

[latex]64+78[/latex]

[latex]142[/latex]

[latex]92+39[/latex]

[latex]168+325[/latex]

[latex]493[/latex]

[latex]247+149[/latex]

[latex]584+277[/latex]

[latex]861[/latex]

[latex]175+648[/latex]

[latex]832+199[/latex]

[latex]1,031[/latex]

[latex]775+369[/latex]

[latex]6,358+492[/latex]

[latex]6,850[/latex]

[latex]9,184+578[/latex]

[latex]3,740+18,593[/latex]

[latex]22,333[/latex]

[latex]6,118+15,990[/latex]

[latex]485,012+619,848[/latex]

[latex]1,104,860[/latex]

[latex]368,911+857,289[/latex]

[latex]24,731+592+3,868[/latex]

[latex]29,191[/latex]

[latex]28,925+817+4,593[/latex]

[latex]8,015+76,946+16,570[/latex]

[latex]101,531[/latex]

[latex]6,291+54,107+28,635[/latex]

Translate Word Phrases to Math Notation
In the following exercises, translate each phrase into math notation and then simplify.

the sum of [latex]13[/latex] and [latex]18[/latex]

[latex]13+18=31[/latex]

the sum of [latex]12[/latex] and [latex]19[/latex]

the sum of [latex]90[/latex] and [latex]65[/latex]

[latex]90+65=155[/latex]

the sum of [latex]70[/latex] and [latex]38[/latex]

[latex]33[/latex] increased by [latex]49[/latex]

[latex]33+49=82[/latex]

[latex]68[/latex] increased by [latex]25[/latex]

[latex]250[/latex] more than [latex]599[/latex]

[latex]250+599=849[/latex]

[latex]115[/latex] more than [latex]286[/latex]

the total of [latex]628[/latex] and [latex]77[/latex]

[latex]628+77=705[/latex]

the total of [latex]593[/latex] and [latex]79[/latex]

[latex]1,482[/latex] added to [latex]915[/latex]

[latex]915+1,482=2,397[/latex]

[latex]2,719[/latex] added to [latex]682[/latex]

Add Whole Numbers in Applications
In the following exercises, solve the problem.

Home remodeling Sophia remodeled her kitchen and bought a new range, microwave, and dishwasher. The range cost [latex]\text{$1,100}[/latex], the microwave cost [latex]\text{$250}[/latex], and the dishwasher cost [latex]\text{$525}[/latex]. 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 [latex]\text{$299}[/latex], the helmet cost [latex]\text{$35}[/latex], and the glove cost [latex]\text{$68}[/latex]. What was the total cost of Aiden’s sports equipment?

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

Ethan rode 138 miles.

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

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

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 [latex]175,192,148,169,205,181[/latex], and [latex]\text{225}[/latex] pounds. What was the total weight of the seven men?

Salary Last year Natalie’s salary was [latex]\text{$82,572}[/latex]. Two years ago, her salary was [latex]\text{$79,316}[/latex], and three years ago it was [latex]\text{$75,298}[/latex]. 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 [latex]\text{$292,540},\text{$505,875}[/latex], and [latex]$423,699[/latex]. 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 [latex]\text{16-ounce}[/latex] drink for lunch. On the restaurant’s nutrition chart, she saw that each item had the following number of calories:
Grilled chicken salad – [latex]320[/latex] calories

Ranch dressing – [latex]170[/latex] calories

[latex]\text{16-ounce}[/latex] drink – [latex]150[/latex] 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 [latex]\text{12-oz}[/latex] chocolate shake for dinner. The restaurant’s nutrition chart lists the following calories for each item:
Grilled chicken sandwich – [latex]420[/latex] calories

Small fries – [latex]230[/latex] calories

[latex]\text{12-oz}[/latex] chocolate shake – [latex]580[/latex] calories
What was the total number of calories of Fred’s dinner?

Test scores A students needs a total of [latex]400[/latex] points on five tests to pass a course. The student scored [latex]82,91,75,88,\text{and}70[/latex]. Did the student pass the course?

Yes, he scored 406 points.

Elevators The maximum weight capacity of an elevator is [latex]1150[/latex] pounds. Six men are in the elevator. Their weights are [latex]210,145,183,230,159,\text{and}164[/latex] 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.

[latex]15 - 9[/latex]

fifteen minus nine; the difference of fifteen and nine

[latex]18 - 16[/latex]

[latex]42 - 35[/latex]

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

[latex]83 - 64[/latex]

[latex]675 - 350[/latex]

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

[latex]790 - 525[/latex]

Model Subtraction of Whole Numbers
In the following exercises, model the subtraction.

[latex]5 - 2[/latex]

No Alt Text

[latex]8 - 4[/latex]

[latex]6 - 3[/latex]

No Alt Text

[latex]7 - 5[/latex]

[latex]18 - 5[/latex]

No Alt Text

[latex]19 - 8[/latex]

[latex]17 - 8[/latex]

No Alt Text

[latex]17 - 9[/latex]

[latex]35 - 13[/latex]

No Alt Text

[latex]32 - 11[/latex]

[latex]61 - 47[/latex]

No Alt Text

[latex]55 - 36[/latex]

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

[latex]9 - 4[/latex]

5

[latex]9 - 3[/latex]

[latex]8 - 0[/latex]

8

[latex]2 - 0[/latex]

[latex]38 - 16[/latex]

22

[latex]45 - 21[/latex]

[latex]85 - 52[/latex]

33

[latex]99 - 47[/latex]

[latex]493 - 370[/latex]

123

[latex]268 - 106[/latex]

[latex]5,946 - 4,625[/latex]

1,321

[latex]7,775 - 3,251[/latex]

[latex]75 - 47[/latex]

28

[latex]63 - 59[/latex]

[latex]461 - 239[/latex]

222

[latex]486 - 257[/latex]

[latex]525 - 179[/latex]

346

[latex]542 - 288[/latex]

[latex]6,318 - 2,799[/latex]

3,519

[latex]8,153 - 3,978[/latex]

[latex]2,150 - 964[/latex]

1,186

[latex]4,245 - 899[/latex]

[latex]43,650 - 8,982[/latex]

34,668

[latex]35,162 - 7,885[/latex]

Translate Word Phrases to Algebraic Expressions
In the following exercises, translate and simplify.

The difference of [latex]10[/latex] and [latex]3[/latex]

10 − 3; 7

The difference of [latex]12[/latex] and [latex]8[/latex]

The difference of [latex]15[/latex] and [latex]4[/latex]

15 − 4; 11

The difference of [latex]18[/latex] and [latex]7[/latex]

Subtract [latex]6[/latex] from [latex]9[/latex]

9 − 6; 3

Subtract [latex]8[/latex] from [latex]9[/latex]

Subtract [latex]28[/latex] from [latex]75[/latex]

75 − 28; 47

Subtract [latex]59[/latex] from [latex]81[/latex]

[latex]45[/latex] decreased by [latex]20[/latex]

45 − 20; 25

[latex]37[/latex] decreased by [latex]24[/latex]

[latex]92[/latex] decreased by [latex]67[/latex]

92 − 67; 25

[latex]75[/latex] decreased by [latex]49[/latex]

[latex]12[/latex] less than [latex]16[/latex]

16 − 12; 4

[latex]15[/latex] less than [latex]19[/latex]

[latex]38[/latex] less than [latex]61[/latex]

61 − 38; 23

[latex]47[/latex] less than [latex]62[/latex]

Mixed Practice
In the following exercises, simplify.

[latex]76 - 47[/latex]

29

[latex]91 - 53[/latex]

[latex]256 - 184[/latex]

72

[latex]305 - 262[/latex]

[latex]719+341[/latex]

1,060

[latex]647+528[/latex]

[latex]2,015 - 1,993[/latex]

22

[latex]2,020 - 1,984[/latex]

In the following exercises, translate and simplify.

Seventy more than thirty-five

75 + 35; 110

Sixty more than ninety-three

[latex]13[/latex] less than [latex]41[/latex]

41 − 13; 28

[latex]28[/latex] less than [latex]36[/latex]

The difference of [latex]100[/latex] and [latex]76[/latex]

100 − 76; 24

The difference of [latex]1,000[/latex] and [latex]945[/latex]

Subtract Whole Numbers in Applications
In the following exercises, solve.

Temperature The high temperature on June [latex]2[/latex] in Las Vegas was [latex]80[/latex] degrees and the low temperature was [latex]63[/latex] 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 [latex]1[/latex] in Phoenix was [latex]97[/latex] degrees and the low was [latex]73[/latex] degrees. What was the difference between the high and low temperatures?

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

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

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

Shopping A mountain bike is on sale for [latex]\text{$399}[/latex]. Its regular price is [latex]\text{$650}[/latex]. 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 [latex]\text{$755}[/latex]. Its regular price is [latex]\text{$1,600}[/latex]. What is the difference between the regular price and the sale price?

Savings John wants to buy a laptop that costs [latex]\text{$840}[/latex]. He has [latex]\text{$685}[/latex] 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 [latex]\text{$1,125}[/latex] in his checking account. He spent [latex]\text{$892}[/latex]. How much money does he have left?

Everyday Math

Road trip Noah was driving from Philadelphia to Cincinnati, a distance of [latex]502[/latex] miles. He drove [latex]115[/latex] miles, stopped for gas, and then drove another [latex]230[/latex] miles before lunch. How many more miles did he have to travel?

157 miles

Test Scores Sara needs [latex]350[/latex] points to pass her course. She scored [latex]75,50,70,\text{and}80[/latex] 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.

[latex]4\times 7[/latex]

four times seven; the product of four and seven

[latex]8\times 6[/latex]

[latex]5\cdot 12[/latex]

five times twelve; the product of five and twelve

[latex]3\cdot 9[/latex]

[latex]\left(10\right)\left(25\right)[/latex]

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

[latex]\left(20\right)\left(15\right)[/latex]

[latex]42\left(33\right)[/latex]

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

[latex]39\left(64\right)[/latex]

Model Multiplication of Whole Numbers
In the following exercises, model the multiplication.

[latex]3\times 6[/latex]

No Alt Text

[latex]4\times 5[/latex]

[latex]5\times 9[/latex]

No Alt Text

[latex]3\times 9[/latex]

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.

[latex]0\cdot 15[/latex]

0

[latex]0\cdot 41[/latex]

[latex]\left(99\right)0[/latex]

0

[latex]\left(77\right)0[/latex]

[latex]1\cdot 43[/latex]

43

[latex]1\cdot 34[/latex]

[latex]\left(28\right)1[/latex]

28

[latex]\left(65\right)1[/latex]

[latex]1\left(240,055\right)[/latex]

240,055

[latex]1\left(189,206\right)[/latex]

  1. [latex]7\cdot 6[/latex]
  2. [latex]6\cdot 7[/latex]
  1. 42
  2. 42

[latex]8\times 9[/latex]
[latex]9\times 8[/latex]

[latex]\left(79\right)\left(5\right)[/latex]

395

[latex]\left(58\right)\left(4\right)[/latex]

[latex]275\cdot 6[/latex]

1,650

[latex]638\cdot 5[/latex]

[latex]3,421\times 7[/latex]

23,947

[latex]9,143\times 3[/latex]

[latex]52\left(38\right)[/latex]

1,976

[latex]37\left(45\right)[/latex]

[latex]96\cdot 73[/latex]

7,008

[latex]89\cdot 56[/latex]

[latex]27\times 85[/latex]

2,295

[latex]53\times 98[/latex]

[latex]23\cdot 10[/latex]

230

[latex]19\cdot 10[/latex]

[latex]\left(100\right)\left(36\right)[/latex]

360

[latex]\left(100\right)\left(25\right)[/latex]

[latex]1,000\left(88\right)[/latex]

88,000

[latex]1,000\left(46\right)[/latex]

[latex]50\times 1,000,000[/latex]

50,000,000

[latex]30\times 1,000,000[/latex]

[latex]247\times 139[/latex]

34,333

[latex]156\times 328[/latex]

[latex]586\left(721\right)[/latex]

422,506

[latex]472\left(855\right)[/latex]

[latex]915\cdot 879[/latex]

804,285

[latex]968\cdot 926[/latex]

[latex]\left(104\right)\left(256\right)[/latex]

26,624

[latex]\left(103\right)\left(497\right)[/latex]

[latex]348\left(705\right)[/latex]

245,340

[latex]485\left(602\right)[/latex]

[latex]2,719\times 543[/latex]

1,476,417

[latex]3,581\times 724[/latex]

Translate Word Phrases to Math Notation
In the following exercises, translate and simplify.

the product of [latex]18[/latex] and [latex]33[/latex]

18 · 33; 594

the product of [latex]15[/latex] and [latex]22[/latex]

fifty-one times sixty-seven

51(67); 3,417

forty-eight times seventy-one

twice [latex]249[/latex]

2(249); 498

twice [latex]589[/latex]

ten times three hundred seventy-five

10(375); 3,750

ten times two hundred fifty-five

Mixed Practice
In the following exercises, simplify.

[latex]38\times 37[/latex]

1,406

[latex]86\times 29[/latex]

[latex]415 - 267[/latex]

148

[latex]341 - 285[/latex]

[latex]6,251+4,749[/latex]

11,000

[latex]3,816+8,184[/latex]

[latex]\left(56\right)\left(204\right)[/latex]

11,424

[latex]\left(77\right)\left(801\right)[/latex]

[latex]947\cdot 0[/latex]

0

[latex]947+0[/latex]

[latex]15,382+1[/latex]

15,383

[latex]15,382\cdot 1[/latex]

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 [latex]\text{$}12[/latex] per share. How much money did Javier’s portfolio gain?

Javier’s portfolio gained $3,600.

Salary Carlton got a [latex]\text{$}200[/latex] 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.

[latex]54\div 9[/latex]

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

[latex]\frac{56}{7}[/latex]

[latex]\frac{32}{8}[/latex]

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

[latex]6\overline{)42}[/latex]

[latex]48\div 6[/latex]

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

[latex]\frac{63}{9}[/latex]

[latex]7\overline{)63}[/latex]

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

[latex]72\div 8[/latex]

Model Division of Whole Numbers
In the following exercises, model the division.

[latex]15\div 5[/latex]

No Alt Text

[latex]10\div 5[/latex]

[latex]\frac{14}{7}[/latex]

No Alt Text

[latex]\frac{18}{6}[/latex]

[latex]4\overline{)20}[/latex]

No Alt Text

[latex]3\overline{)15}[/latex]

[latex]24\div 6[/latex]

No Alt Text

[latex]16\div 4[/latex]

Divide Whole Numbers
In the following exercises, divide. Then check by multiplying.

[latex]18\div 2[/latex]

9

[latex]14\div 2[/latex]

[latex]\frac{27}{3}[/latex]

9

[latex]\frac{30}{3}[/latex]

[latex]4\overline{)28}[/latex]

7

[latex]4\overline{)36}[/latex]

[latex]\frac{45}{5}[/latex]

9

[latex]\frac{35}{5}[/latex]

[latex]72/8[/latex]

9

[latex]8\overline{)64}[/latex]

[latex]\frac{35}{7}[/latex]

5

[latex]42\div 7[/latex]

[latex]15\overline{)15}[/latex]

1

[latex]12\overline{)12}[/latex]

[latex]43\div 43[/latex]

1

[latex]37\div 37[/latex]

[latex]\frac{23}{1}[/latex]

23

[latex]\frac{29}{1}[/latex]

[latex]19\div 1[/latex]

19

[latex]17\div 1[/latex]

[latex]0\div 4[/latex]

0

[latex]0\div 8[/latex]

[latex]\frac{5}{0}[/latex]

undefined

[latex]\frac{9}{0}[/latex]

[latex]\frac{26}{0}[/latex]

undefined

[latex]\frac{32}{0}[/latex]

[latex]12\overline{)0}[/latex]

0

[latex]16\overline{)0}[/latex]

[latex]72\div 3[/latex]

24

[latex]57\div 3[/latex]

[latex]\frac{96}{8}[/latex]

12

[latex]\frac{78}{6}[/latex]

[latex]5\overline{)465}[/latex]

93

[latex]4\overline{)528}[/latex]

[latex]924\div 7[/latex]

132

[latex]861\div 7[/latex]

[latex]\frac{5,226}{6}[/latex]

871

[latex]\frac{3,776}{8}[/latex]

[latex]4\overline{)31,324}[/latex]

7,831

[latex]5\overline{)46,855}[/latex]

[latex]7,209\div 3[/latex]

2,403

[latex]4,806\div 3[/latex]

[latex]5,406\div 6[/latex]

901

[latex]3,208\div 4[/latex]

[latex]4\overline{)2,816}[/latex]

704

[latex]6\overline{)3,624}[/latex]

[latex]\frac{91,881}{9}[/latex]

10,209

[latex]\frac{83,256}{8}[/latex]

[latex]2,470\div 7[/latex]

352 R6

[latex]3,741\div 7[/latex]

[latex]8\overline{)55,305}[/latex]

6,913 R1

[latex]9\overline{)51,492}[/latex]

[latex]\frac{431,174}{5}[/latex]

86,234 R4

[latex]\frac{297,277}{4}[/latex]

[latex]130,016\div 3[/latex]

43,338 R2

[latex]105,609\div 2[/latex]

[latex]15\overline{)5,735}[/latex]

382 R5

[latex]\frac{4,933}{21}[/latex]

[latex]56,883\div 67[/latex]

849

[latex]43,725/75[/latex]

[latex]\frac{30,144}{314}[/latex]

96

[latex]26,145\div 415[/latex]

[latex]273\overline{)542,195}[/latex]

1,986 R17

[latex]816,243\div 462[/latex]

Mixed Practice
In the following exercises, simplify.

[latex]15\left(204\right)[/latex]

3,060

[latex]74\cdot 391[/latex]

[latex]256 - 184[/latex]

72

[latex]305 - 262[/latex]

[latex]719+341[/latex]

1,060

[latex]647+528[/latex]

[latex]25\overline{)875}[/latex]

35

[latex]1104\div 23[/latex]

Translate Word Phrases to Algebraic Expressions
In the following exercises, translate and simplify.

the quotient of [latex]45[/latex] and [latex]15[/latex]

45 ÷ 15; 3

the quotient of [latex]64[/latex] and [latex]16[/latex]

the quotient of [latex]288[/latex] and [latex]24[/latex]

288 ÷ 24; 12

the quotient of [latex]256[/latex] and [latex]32[/latex]

Divide Whole Numbers in Applications
In the following exercises, solve.

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

Ric can fill 32 bags.

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

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

There are 25 groups.

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

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

Marta can wrap 16 cakes from 1 roll.

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

Mixed Practice
In the following exercises, solve.

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

The difference is 28 miles per gallon.

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

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

They will need 5 vans for the field trip

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

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

Bill hiked 50 miles

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

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

LaVonne treated 48 patients last week.

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

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 [latex]300[/latex] by [latex]8[/latex] and said his answer was [latex]37[/latex] with a remainder of [latex]4[/latex]. How can you check to make sure he is correct?

Everyday Math

Contact lenses Jenna puts in a new pair of contact lenses every [latex]14[/latex] days. How many pairs of contact lenses does she need for [latex]365[/latex] 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 [latex]25[/latex] days. How many bags of cat food does Lara need for [latex]365[/latex] 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.

[latex]0,2,99[/latex]

  1. 2, 99
  2.  0, 2, 99

[latex]0,3,25[/latex]

[latex]0,4,90[/latex]

  1. 4, 90
  2. 0, 4, 90

[latex]0,1,75[/latex]

Model Whole Numbers
In the following exercises, model each number using [latex]\text{base - 10}[/latex] 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.

[latex]472,981[/latex]

  1. [latex]8[/latex]
  2. [latex]4[/latex]
  3. [latex]1[/latex]
  4. [latex]7[/latex]
  5. [latex]2[/latex]
  1. tens
  2. hundred thousands
  3. ones
  4. thousands
  5. ten thousands

[latex]12,403,295[/latex]

  1. [latex]4[/latex]
  2. [latex]0[/latex]
  3. [latex]1[/latex]
  4. [latex]9[/latex]
  5. [latex]3[/latex]

Use Place Value to Name Whole Numbers
In the following exercises, name each number in words.

[latex]5,280[/latex]

Five thousand two hundred eighty

[latex]204,614[/latex]

[latex]5,012,582[/latex]

Five million twelve thousand five hundred eighty-two

[latex]31,640,976[/latex]

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.

[latex]412[/latex]

410

[latex]648[/latex]

[latex]3,556[/latex]

3,560

[latex]2,734[/latex]

In the following exercises, round to the nearest hundred.

[latex]38,975[/latex]

39,000

[latex]26,849[/latex]

[latex]81,486[/latex]

81,500

[latex]75,992[/latex]

Add Whole Numbers

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

[latex]4+3[/latex]

four plus three; the sum of four and three

[latex]25+18[/latex]

[latex]571+629[/latex]

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

[latex]10,085+3,492[/latex]

Model Addition of Whole Numbers
In the following exercises, model the addition.

[latex]6+7[/latex]

No Alt Text

[latex]38+14[/latex]

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. [latex]0+19[/latex] 2. [latex]19+0[/latex]

1.  19
2.  19

1.  [latex]0+480[/latex] 2. [latex]480+0[/latex]

  1. [latex]7+6[/latex] 2. [latex]6+7[/latex]

1. 13
2. 13

  1. [latex]23+18[/latex] 2. [latex]18+23[/latex]

[latex]44+35[/latex]

82

[latex]63+29[/latex]

[latex]96+58[/latex]

154

[latex]375+591[/latex]

[latex]7,281+12,546[/latex]

19,827

[latex]5,280+16,324+9,731[/latex]

Translate Word Phrases to Math Notation
In the following exercises, translate each phrase into math notation and then simplify.

the sum of [latex]30[/latex] and [latex]12[/latex]

30 + 12; 42

[latex]11[/latex] increased by [latex]8[/latex]

[latex]25[/latex] more than [latex]39[/latex]

39 + 25; 64

total of [latex]15[/latex] and [latex]50[/latex]

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 [latex]\text{$24,}[/latex] the tie cost [latex]\text{$14,}[/latex] and the slacks cost [latex]\text{$38.}[/latex] What was Nathan’s total cost?

$76

Running Jackson ran [latex]4[/latex] miles on Monday, [latex]12[/latex] miles on Tuesday, [latex]1[/latex] mile on Wednesday, [latex]8[/latex] miles on Thursday, and [latex]5[/latex] 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.

[latex]14 - 5[/latex]

fourteen minus five; the difference of fourteen and five

[latex]40 - 15[/latex]

[latex]351 - 249[/latex]

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

[latex]5,724 - 2,918[/latex]

Model Subtraction of Whole Numbers
In the following exercises, model the subtraction.

[latex]18 - 4[/latex]

No Alt Text

[latex]41 - 29[/latex]

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

[latex]8 - 5[/latex]

3

[latex]12 - 7[/latex]

[latex]23 - 9[/latex]

14

[latex]46 - 21[/latex]

[latex]82 - 59[/latex]

23

[latex]110 - 87[/latex]

[latex]539 - 217[/latex]

322

[latex]415 - 296[/latex]

[latex]1,020 - 640[/latex]

380

[latex]8,355 - 3,947[/latex]

[latex]10,000 - 15[/latex]

9,985

[latex]54,925 - 35,647[/latex]

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 [latex]86[/latex] degrees Fahrenheit and the low temperature was [latex]28[/latex] 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 [latex]\text{$2,485.}[/latex] She has [latex]\text{$948}[/latex] 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.

[latex]8\times 5[/latex]

eight times five the product of eight and five

[latex]6\cdot 14[/latex]

[latex]\left(10\right)\left(95\right)[/latex]

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

[latex]54\left(72\right)[/latex]

Model Multiplication of Whole Numbers
In the following exercises, model the multiplication.

[latex]2\times 4[/latex]

No Alt Text

[latex]3\times 8[/latex]

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.

[latex]0\cdot 14[/latex]

0

[latex]\left(256\right)0[/latex]

[latex]1\cdot 99[/latex]

99

[latex]\left(4,789\right)1[/latex]

ⓐ [latex]7\cdot 4[/latex] ⓑ [latex]4\cdot 7[/latex]

  1. ⓐ 28
  2. ⓑ 28

[latex]\left(25\right)\left(6\right)[/latex]

[latex]9,261\times 3[/latex]

27,783

[latex]48\cdot 76[/latex]

[latex]64\cdot 10[/latex]

640

[latex]1,000\left(22\right)[/latex]

[latex]162\times 493[/latex]

79,866

[latex]\left(601\right)\left(943\right)[/latex]

[latex]3,624\times 517[/latex]

1,873,608

[latex]10,538\cdot 22[/latex]

Translate Word Phrases to Math Notation
In the following exercises, translate and simplify.

the product of [latex]15[/latex] and [latex]28[/latex]

15(28); 420

ninety-four times thirty-three

twice [latex]575[/latex]

2(575); 1,150

ten times two hundred sixty-four

Multiply Whole Numbers in Applications
In the following exercises, solve.

Gardening Geniece bought [latex]8[/latex] packs of marigolds to plant in her yard. Each pack has [latex]6[/latex] 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 [latex]4[/latex] cups of rice, how many cups of water does she need?

Multiplex There are twelve theaters at the multiplex and each theater has [latex]150[/latex] 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, [latex]30[/latex] feet by [latex]24[/latex] feet. What is the area of the roof?

Divide Whole Numbers

Use Division Notation
Translate from math notation to words.

[latex]54\div 9[/latex]

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

[latex]42/7[/latex]

[latex]\frac{72}{8}[/latex]

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

[latex]6\overline{)48}[/latex]

Model Division of Whole Numbers
In the following exercises, model.

[latex]8\div 2[/latex]

No Alt Text

[latex]3\overline{)12}[/latex]

Divide Whole Numbers
In the following exercises, divide. Then check by multiplying.

[latex]14\div 2[/latex]

7

[latex]\frac{32}{8}[/latex]

[latex]52\div 4[/latex]

13

[latex]26\overline{)26}[/latex]

[latex]\frac{97}{1}[/latex]

97

[latex]0\div 52[/latex]

[latex]100\div 0[/latex]

undefined

[latex]\frac{355}{5}[/latex]

[latex]3828\div 6[/latex]

638

[latex]31\overline{)1,519}[/latex]

[latex]\frac{7505}{25}[/latex]

300 R5

[latex]5,166\div 42[/latex]

Translate Word Phrases to Math Notation
In the following exercises, translate and simplify.

the quotient of [latex]64[/latex] and [latex]16[/latex]

64 ÷ 16; 4

the quotient of [latex]572[/latex] and [latex]52[/latex]

Divide Whole Numbers in Applications
In the following exercises, solve.

Ribbon One spool of ribbon is [latex]27[/latex] feet. Lizbeth uses [latex]3[/latex] 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 [latex]128[/latex] ounces. How many [latex]4[/latex] 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.

[latex]0,4,87[/latex]

  1. 4, 87
  2. 0, 4, 8

Find the place value of the given digits in the number [latex]549,362[/latex].

  1. [latex]9[/latex]
  2. [latex]6[/latex]
  3. [latex]2[/latex]
  4. [latex]5[/latex]

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 [latex]25,849[/latex] to the nearest hundred.

Simplify.

[latex]45+23[/latex]

68

[latex]65 - 42[/latex]

[latex]85\div 5[/latex]

17

[latex]1,000\times 8[/latex]

[latex]90 - 58[/latex]

32

[latex]73+89[/latex]

[latex]\left(0\right)\left(12,675\right)[/latex]

0

[latex]634+255[/latex]

[latex]\frac{0}{9}[/latex]

0

[latex]8\overline{)128}[/latex]

[latex]145 - 79[/latex]

66

[latex]299+836[/latex]

[latex]7\cdot 475[/latex]

3,325

[latex]8,528+704[/latex]

[latex]35\left(14\right)[/latex]

490

[latex]\frac{26}{0}[/latex]

[latex]733 - 291[/latex]

442

[latex]4,916 - 1,538[/latex]

[latex]495\div 45[/latex]

11

[latex]52\times 983[/latex]

Translate each phrase to math notation and then simplify.

The sum of [latex]16[/latex] and [latex]58[/latex]

16 + 58; 74

The product of [latex]9[/latex] and [latex]15[/latex]

The difference of [latex]32[/latex] and [latex]18[/latex]

32 − 18; 14

The quotient of [latex]63[/latex] and [latex]21[/latex]

Twice [latex]524[/latex]

2(524); 1,048

[latex]29[/latex] more than [latex]32[/latex]

[latex]50[/latex] less than [latex]300[/latex]

300 − 50; 250

In the following exercises, solve.

LaVelle buys a jumbo bag of [latex]84[/latex] candies to make favor bags for her son’s party. If she wants to make [latex]12[/latex] bags, how many candies should she put in each bag?

Last month, Stan’s take-home pay was [latex]\text{$3,816}[/latex] and his expenses were [latex]\text{$3,472.}[/latex] 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 [latex]22[/latex] children enrolled. The school has [latex]24[/latex] classes. How many children are enrolled at Greenville School?

Clayton walked [latex]12[/latex] blocks to his mother’s house, [latex]6[/latex] blocks to the gym, and [latex]9[/latex] blocks to the grocery store before walking the last [latex]3[/latex] blocks home. What was the total number of blocks that Clayton walked?

Clayton walked 30 blocks.