Translate each verbal model into an equation. (Answers may vary, depending on the

A _____ is the result of an addition. A _____ is the result of a subtraction. A ______ is the result of a multiplication. A _____ is the result of a division.

______are letters (or symbols) that stand for numbers.

A number, such as 8, is called a ______ because it does not change.

Variables and numbers can be combined with the operations of addition, subtraction, multiplication, and division to create algebraic ______.

An is a mathematical sentence that contains an = symbol. An algebraic ______ does not.

An equation such as c  10m, which expresses a relationship between two or more variables, is called a ______ .

The _____ axis of a graph extends left and right and the vertical axis extends up and down.

The word ______ comes from the title of a book written by an Arabian mathematician around A.D. 800.

Classify each item as an algebraic expression or an equation. a. m  18  23 b. m  18

Classify each item as an algebraic expression or an equation. a. 30x b. 30x = 600

Classify each item as an algebraic expression or an equation. a. c 7 5 b. c 7 5  7c c

Classify each item as an algebraic expression or an equation. a.  r 2 3 b. 2 3 r

What arithmetic operations does the expression 12  9t 25 contain? What variable does it contain?

What arithmetic operations does the equation 4y 14  5(6) contain? What variable does it contain?

Construct a line graph using the data in the following table. Hours Pay worked (dollars) 1 20 2 40 3 60 4 80 5 100 20 40 60 80 100 12

Use the data in the graph to complete the table. Depth Minutes (feet) 0 5 10 15 20 100 200 300 400 500 60

The  symbol means ___ _____ ___ ____.

The ( ) symbols are called _______ .

Write the multiplication 5 x 6 using a raised dot and then using parentheses.

Give four verbs that can be represented by an equal symbol = .

Write each expression without using a multiplication symbol or parentheses. 4 x P

Write each expression without using a multiplication symbol or parentheses. P r t 

Write each expression without using a multiplication symbol or parentheses. 2(w)

Write each expression without using a multiplication symbol or parentheses. (x)(y)

Write each division using a fraction bar. 32 x 3

Write each division using a fraction bar. 3090

Write each division using a fraction bar. 555 h

Write each division using a fraction bar. h 15

Use the given line graphs to answer the following questions. See Example 1. Accounting. Explain what the dashed lines in the graph below help us find. 0 20 30 40 50 60 0 20 30 10 Age of machinery (years) Value ($ thousands)

Use the given line graphs to answer the following questions. See Example 1. Accounting. What is the value of 35-year-old machinery? 0 20 30 40 50 60 0 20 30 10 Age of machinery (years) Value ($ thousands)

Use the given line graphs to answer the following questions. See Example 1. Business. Refer to the graph below. Find the income received from 30 customers. 0 200 300 400 500 600 0 4 20 0 60 Number of customers Income (dollars) 80 100

Use the given line graphs to answer the following questions. See Example 1. Refer to the graph below. Find the income received from 70 customers. 0 200 300 400 500 600 0 4 20 0 60 Number of customers Income (dollars) 80 100

Express each statement using one of the words sum, product, difference, or quotient. See Example 2. 8(2) = 16

Express each statement using one of the words sum, product, difference, or quotient. See Example 2. 45 12  540

Express each statement using one of the words sum, product, difference, or quotient. See Example 2. 11 - 9 = 2

Express each statement using one of the words sum, product, difference, or quotient. See Example 2. 65 + 89 = 154

Express each statement using one of the words sum, product, difference, or quotient. See Example 2. x + 2 = 10

Express each statement using one of the words sum, product, difference, or quotient. See Example 2. 16 - t = 4

Express each statement using one of the words sum, product, difference, or quotient. See Example 2. 66 11  6

Express each statement using one of the words sum, product, difference, or quotient. See Example 2. 12 3  4

Translate each verbal model into an equation. (Answers may vary, depending on the variables chosen.) See Example 3. The sale price is $100 minus the discount.

Translate each verbal model into an equation. (Answers may vary, depending on the variables chosen.) See Example 3. The cost of dining out equals the cost of the meal plus $7 for parking.

Translate each verbal model into an equation. (Answers may vary, depending on the variables chosen.) See Example 3. 7 times the age of a dog in years gives the dogs equivalent human age.

Translate each verbal model into an equation. (Answers may vary, depending on the variables chosen.) See Example 3. The number of centuries is the number of years divided by 100.

Translate each verbal model into an equation. (Answers may vary, depending on the variables chosen.) See Example 3. The amount of sand that should be used is the product of 3 and the amount of cement used.

Translate each verbal model into an equation. (Answers may vary, depending on the variables chosen.) See Example 3. The number of waiters needed is the quotient of the number of customers and 10.

Translate each verbal model into an equation. (Answers may vary, depending on the variables chosen.) See Example 3. The weight of the truck is the sum of the weight of the engine and 1,200.

Translate each verbal model into an equation. (Answers may vary, depending on the variables chosen.) See Example 3. The number of classes still open is the difference of 150 and the number of classes that are closed.

Translate each verbal model into an equation. (Answers may vary, depending on the variables chosen.) See Example 3. The profit is the difference of the revenue and 600.

Translate each verbal model into an equation. (Answers may vary, depending on the variables chosen.) See Example 3. The distance is the product of the rate and 3.

Translate each verbal model into an equation. (Answers may vary, depending on the variables chosen.) See Example 3. The quotient of the number of laps run and 4 gives the number of miles run.

Translate each verbal model into an equation. (Answers may vary, depending on the variables chosen.) See Example 3. The sum of the tax and 35 gives the total cost.

Use the formula to complete each table. See Examples 4 and 5. d  360  L Lunch time School day (minutes) (minutes) 30 40 45 L d

Use the formula to complete each table. See Examples 4 and 5. b  1,024k Kilobytes Bytes 1 5 10 bk

Use the formula to complete each table. See Examples 4 and 5. t  1,500 d Take-home Deductions pay 200 300 400 d t

Use the formula to complete each table. See Examples 4 and 5. w  s 12 Inches of Inches of snow water 12 24 72 s w

Use the data in the table to complete the formula. d  e Eggs Dozens 24 2 36 3 48 4

Use the data in the table to complete the formula. p  c Canoes Paddles 6 12 7 14 8 16 c p

Use the data in the table to complete the formula. I  c Couples Individuals 20 40 100 200 200 400 c I

Use the data in the table to complete the formula. t  p Players Teams 5 1 10 2 15 3

Exercise. The number of calories that a 125-pound adult burns doing general house cleaning chores is three times the number of minutes spent cleaning. a. Write a verbal model using the word product that describes the relationship between calories burned and minutes cleaning. b. Write a formula using the variables c and m that describes the relationship between calories burned and minutes cleaning. c. Use your answer to part b to complete the following table. m 10 20 30 40 50 60 c d. Use the data from the table to construct a line graph. Scale the horizontal axis in units of 10 minutes. Scale the vertical axis in units of 30 calories.

Traffic Safety. As the railroad crossing guard drops, the measure of angle 1 (written ) increases while the measure of decreases. At any instant the sum of the measures of the two angles is . Complete the table. Then use the data to construct a line graph. Scale each axis in units of . Angle 2 Angle 1 Angle 2 (degrees) (degrees) 0 15 30 45 60 75 90

Many students misuse the word equation when discussing mathematics. What is an equation? Give an example.

Explain the difference between an algebraic expression and an equation. Give an example of each.

In this section, four methods for describing numerical relationships were discussed: tables, verbal models (words), graphs, and equations. Which method do you think is the most useful? Explain why.

In your own words, define horizontal and vertical.

Complete the formula.  s  s t 18 55 33 100 47 142

Suppose and . Complete the following formula: h  g

A factor is a number being ______.

Numbers that have only 1 and themselves as factors, such as 23, 37, and 41, are called ______ numbers.

When we write 60 as , we say that we have written 60 in ______ form.

The _______ of the fraction is 3, and the ______ is 4.

Two fractions that represent the same number, such as and , are called ______ fractions.

2 3 is the ______ of 3 2, because their product is 1.

The ______ common denominator for a set of fractions is the smallest number each denominator will divide exactly.

The ______ number 7 1 3 represents the sum of a whole number and a fraction: 7  1 3

Complete each fact about fractions. Assume there are no divisions by 0. a. a a  b. a 1  a c. a b c d  d. a b c d  a e. a d  b d  f. a d b d  a

What two equivalent fractions are shown?

Complete each statement. a. To simplify a fraction, we remove factors equal to in the form of , , or , and so on. b. To build a fraction, we multiply it by in the form of , , or , and so on

What is the LCD for fractions having denominators of: a. 3 and 7? b. 4 and 6?

a. Multiply by a form of 1 to build an equivalent fraction with denominator 30. 5 6 b. Remove common factors to simplify . 12 42  2 3 2 3  12

a. Write 2 15 16 as an improper fraction. b. Write 49 12 as a mixed number.

Find the prime factorization of each number. See Example 1. 75

Find the prime factorization of each number. See Example 1. 20

Find the prime factorization of each number. See Example 1. 28

Find the prime factorization of each number. See Example 1. 54

Find the prime factorization of each number. See Example 1. 81

Find the prime factorization of each number. See Example 1. 125

Find the prime factorization of each number. See Example 1. 117

Find the prime factorization of each number. See Example 1. 147

Find the prime factorization of each number. See Example 1. 220

Find the prime factorization of each number. See Example 1. 270

Find the prime factorization of each number. See Example 1. 1,254

Find the prime factorization of each number. See Example 1. 1,144

Multiply. See Example 2. 5 6 1 8

Multiply. See Example 2. 2 3 1 5

Multiply. See Example 2. 7 11 3 5

Multiply. See Example 2. 13 9 2 3

Divide. See Example 3. 3 4 2 5

Divide. See Example 3. 7 8 6 13

Divide. See Example 3. 6 5 5 7

Divide. See Example 3. 4 3 3 2

Build each fraction or whole number to an equivalent fraction with the indicated denominator. See Example 4. 1 3, denominator 9

Build each fraction or whole number to an equivalent fraction with the indicated denominator. See Example 4. 3 8, denominator 24

Build each fraction or whole number to an equivalent fraction with the indicated denominator. See Example 4. 4 9, denominator 54

Build each fraction or whole number to an equivalent fraction with the indicated denominator. See Example 4. 9 16, denominator 64

Build each fraction or whole number to an equivalent fraction with the indicated denominator. See Example 4. 7, denominator 5

Build each fraction or whole number to an equivalent fraction with the indicated denominator. See Example 4. 12, denominator 3

Build each fraction or whole number to an equivalent fraction with the indicated denominator. See Example 4. 5, denominator 7

Build each fraction or whole number to an equivalent fraction with the indicated denominator. See Example 4. 6, denominator 8

Simplify each fraction, if possible. See Examples 5 and 6. 6 18

Simplify each fraction, if possible. See Examples 5 and 6. 6 9

Simplify each fraction, if possible. See Examples 5 and 6. 24 28

Simplify each fraction, if possible. See Examples 5 and 6. 35 14

Simplify each fraction, if possible. See Examples 5 and 6. 15 40

Simplify each fraction, if possible. See Examples 5 and 6. 22 77

Simplify each fraction, if possible. See Examples 5 and 6. 33 56

Simplify each fraction, if possible. See Examples 5 and 6. 26 21

Simplify each fraction, if possible. See Examples 5 and 6. 26 39

Simplify each fraction, if possible. See Examples 5 and 6. 72 64

Simplify each fraction, if possible. See Examples 5 and 6. 36 225

Simplify each fraction, if possible. See Examples 5 and 6. 175 490

Perform the operations and, if possible, simplify. See Objective 6 and Example 7. 3 5  3 5

Perform the operations and, if possible, simplify. See Objective 6 and Example 7. 4 9 1 9

Perform the operations and, if possible, simplify. See Objective 6 and Example 7. 6 7 2 7

Perform the operations and, if possible, simplify. See Objective 6 and Example 7. 5 13  6 13

Perform the operations and, if possible, simplify. See Objective 6 and Example 7. 1 6  1 24

Perform the operations and, if possible, simplify. See Objective 6 and Example 7. 17 25 2 5

Perform the operations and, if possible, simplify. See Objective 6 and Example 7. 7 10 1 14

Perform the operations and, if possible, simplify. See Objective 6 and Example 7. 9 8 5 6

Perform the operations and, if possible, simplify. See Objective 6 and Example 7. 2 15  7 9

Perform the operations and, if possible, simplify. See Objective 6 and Example 7. 7 25  3 10

Perform the operations and, if possible, simplify. See Objective 6 and Example 7. 13 28 1 21

Perform the operations and, if possible, simplify. See Objective 6 and Example 7. 13 24 3 40

Perform the operations and, if possible, simplify. See Example 8. 16a b 3 2 b

Perform the operations and, if possible, simplify. See Example 8. 30a 5 6

Perform the operations and, if possible, simplify. See Example 8. 18 2 9

Perform the operations and, if possible, simplify. See Example 8. 14 3 7

Perform the operations and, if possible, simplify. See Example 8. 2 3  5 18 1 6

Perform the operations and, if possible, simplify. See Example 8. 3 5  7 20 7 10

Perform the operations and, if possible, simplify. See Example 8. 5 12  1 3 2 5

Perform the operations and, if possible, simplify. See Example 8. 7 15  1 5 4 9

Perform the operations and, if possible, simplify. See Examples 9 and 10. 4 2 3 7

Perform the operations and, if possible, simplify. See Examples 9 and 10. 7 1 3 28

Perform the operations and, if possible, simplify. See Examples 9 and 10. 8 3 1 5

Perform the operations and, if possible, simplify. See Examples 9 and 10. 15 3 1 3

Perform the operations and, if possible, simplify. See Examples 9 and 10. 8 2 9 7 2 3

Perform the operations and, if possible, simplify. See Examples 9 and 10. 3 4 5 3 1 10

Perform the operations and, if possible, simplify. See Examples 9 and 10. 3 3 16  2 5 24

Perform the operations and, if possible, simplify. See Examples 9 and 10. 15 5 6  11 5 8

Perform the operations and, if possible, simplify. 3 5  2 3

Perform the operations and, if possible, simplify. 4 3  7 2

Perform the operations and, if possible, simplify. 21a b 10 3 b

Perform the operations and, if possible, simplify. 28a 4 7

Perform the operations and, if possible, simplify. 6 2 7 24

Perform the operations and, if possible, simplify. 3 1 2 1 5

Perform the operations and, if possible, simplify. 2 3 1 4  1 12

Perform the operations and, if possible, simplify. 3 7 2 5  2 35 2

Perform the operations and, if possible, simplify. 21 35 3 14

Perform the operations and, if possible, simplify. 23 25 46 5

Perform the operations and, if possible, simplify. 4 3 a 6 5 b

Perform the operations and, if possible, simplify. 21 8 a 2 15b

Perform the operations and, if possible, simplify. 4 63  1 45

Perform the operations and, if possible, simplify. 5 18  1 99

Perform the operations and, if possible, simplify. 3 3 4

Perform the operations and, if possible, simplify. 4 7 3

Perform the operations and, if possible, simplify. 1 5 3 5

Perform the operations and, if possible, simplify. 3 4 5 7

Perform the operations and, if possible, simplify. 3 1 3 1 5 6

Perform the operations and, if possible, simplify. 2 1 2 1 5 8

Perform the operations and, if possible, simplify. 11 21 8 21

Perform the operations and, if possible, simplify. 19 35 12 35

Perform the operations and, if possible, simplify. 7 30  1 50 19 75

Perform the operations and, if possible, simplify. 11 12 7 15 9 20 7

Perform the operations and, if possible, simplify. 1 31 32 7 1 9

Perform the operations and, if possible, simplify. 3 1 16 4 4 7

Perform the operations and, if possible, simplify. a. 4 9  3 7 b. 4 9 3 7 c.4 9 3 7 d. 4 9 3 7

Perform the operations and, if possible, simplify. a. 4 1 8  1 5 6 b. 4 1 8 1 5 6 c. 4 1 8 1 5 6 d. 4 1 8 1 5 6

Forestry. A ranger cut down a tree and measured the widths of the outer two growth rings. a. What was the growth over this 2-year period? b. What is the difference in the widths of the rings? 5 32 1 16 in. in.

Hardware. To secure the bracket to the stock, a bolt and a nut are used. How long should the threaded part of the bolt be? 5 8 5 16 Bolt head Bolt extends in. past nut. in. thick 3 4 4 in. pine 7 8 1 in. nut

Each year, the Transportation Security Administration (TSA) screens more than 500 million pieces of luggage. On many flights, airlines do not accept luggage whose total dimension (length  width  height) exceeds 62 inches. What is the total dimension figure for the suitcase shown below? 7 8 Length:28 in. 1 2 Width: 11 in. 3 4 Height: 22 in.

Cooking. How much butter is left in a 101 2-pound tub of butter if 43 4 pounds are used to make a wedding cake?

Frames. How many inches of molding are needed to make the square picture frame? 10 in. 1 8

Decorating. The materials used to make a pillow are shown below. Examine the inventory list to decide how many pillows can be manufactured in one production run with the materials in stock. 7 8 yd corduroy fabric 2 3 lb cotton filling 9 10 yd lace trim Materials in stock Lace trim 135 yd Corduroy fabric 154 yd Cotton filling 98 lb

Explain the error made below in simplifying 15 45 15 45  3 5 3 3 5  0 3  0 1

To multiply two fractions, must they have like denominators? Explain.

What are equivalent fractions? Give an example.

Explain the error in the following addition. 4 3  3 2  4  3 3  2  7 5

_____ are letters (or symbols) that stand for numbers.

A number, such as 10, is called a _____ because it does not change.

Which is larger: 11 12 or 8 9?

If the circle represents a whole, find the missing value. 1 2 1 4 1 5

The set of _____ numbers is {0, 1, 2, 3, 4, 5, . . .}.

The set of _____ numbers is {1, 2, 3, 4, 5, . . .} .

The figure 2 1 0 1 2 is called a _____ _____ .

The set of ______ is {. . . , 2, 1, 0, 1, 2, . . .}.

Positive and negative numbers are called ______ numbers.

4 3 2 1 0 1 2 3 4 Zero

The symbols < and > are ______ symbols.

A ______ number is any number that can be expressed as a fraction with an integer numerator and a nonzero integer denominator.

0.25 is called a _____ decimal and 0.333 . . . is called a _____ decimal.

An ______ number cannot be expressed as a quotient of two integers.

An irrational number is a nonterminating, nonrepeating ______ .

The _____ ______ of a number is the distance on the number line between the number and 0.

Represent each situation using a signed number. a. A loss of $15 million b. A building foundation 5 16 inch above grade

Show that each of the following numbers is a rational number by expressing it as a fraction with an integer numerator and a nonzero integer denominator: 6, 9, 7 8, 3 0.3 1 2 6 2.83.

Give the opposite of each number. a. 20 b. 16.

What two numbers are a distance of 8 away from 5 on the number line?

What two numbers are a distance of 5 away from on the number line?

Refer to the number line below. Use an inequality symbol, < or >, to make each statement true. a. a b b. b a c. b 0 and 0 d. a 0 0 b 0 a 0 b

22 is read the ____ ____ of 2.

15 0 is read the ____ ____ of .

The symbol means ___ _______ ____ ____.

The symbols { } are called ______ .

The symbol is a letter from the _____ alphabet.

To find the decimal equivalent for 2 3 , we perform the following long division: 2

4 5  5  4

Write each repeating decimal using an overbar. a. 0.666 . . . b. 0.2444 . . . c. 0.717171 . . . d. 0.456456456 . . .

Place check marks in the table to show the set or sets to which each number belongs. For example, the check shows that is irrational. See Example 1. 22 4 5  5  4 2 3 p { } 0 15 0 15 22 a 0 b b a 0 a 0 0 b 0 a b b a   9 5 0 0.17 Real Irrational Rational Integer Whole Natural 9 22 p 1 4 7

Which numbers in the following set are natural numbers, whole numbers, integers, rational numbers, irrational numbers, real numbers? 567, 4 13, 5.9, 112 3, 22, 0, 3, p6 7

Determine whether each statement is true or false. See Example 1. Every whole number is an integer.

Determine whether each statement is true or false. See Example 1. Every integer is a natural number.

Determine whether each statement is true or false. See Example 1. Every integer is a whole number.

Determine whether each statement is true or false. See Example 1. Every real number is either a rational number or an irrational number

Determine whether each statement is true or false. See Example 1. . Irrational numbers are real numbers.

Determine whether each statement is true or false. See Example 1. Every whole number is a rational number

Determine whether each statement is true or false. See Example 1. Every rational number can be written as a fraction (ratio) of two integers.

Determine whether each statement is true or false. See Example 1. Every rational number is a whole number.

Use one of the symbols < or > to make each statement true. See Example 2. 0 -4

Use one of the symbols < or > to make each statement true. See Example 2. 0 32

Use one of the symbols < or > to make each statement true. See Example 2. 917 971

Use one of the symbols < or > to make each statement true. See Example 2. 898 889

Use one of the symbols < or > to make each statement true. See Example 2. -2 -3

Use one of the symbols < or > to make each statement true. See Example 2. -5 -4

Use one of the symbols < or > to make each statement true. See Example 2. 5 8 3 8

Use one of the symbols < or > to make each statement true. See Example 2. 192 3 191 3 19

Use one of the symbols < or > to make each statement true. See Example 2. 2 3 3 5

Use one of the symbols < or > to make each statement true. See Example 2. 3 4 5 6

Use one of the symbols < or > to make each statement true. See Example 2. -6.19 -5.8

Use one of the symbols < or > to make each statement true. See Example 2. -2.27 -5.25

Write each fraction as a decimal. If the result is a repeating decimal, use an overbar. See Objective 2. 5 8

Write each fraction as a decimal. If the result is a repeating decimal, use an overbar. See Objective 2. 3 32

Write each fraction as a decimal. If the result is a repeating decimal, use an overbar. See Objective 2. 1 30

Write each fraction as a decimal. If the result is a repeating decimal, use an overbar. See Objective 2. 7 9

Write each fraction as a decimal. If the result is a repeating decimal, use an overbar. See Objective 2. 1 60

Write each fraction as a decimal. If the result is a repeating decimal, use an overbar. See Objective 2. 5 11

Write each fraction as a decimal. If the result is a repeating decimal, use an overbar. See Objective 2. 21 50

Write each fraction as a decimal. If the result is a repeating decimal, use an overbar. See Objective 2. 2 125

Graph each set of numbers on a number line. See Example 3. 5p, 4.25, 11 2, 0.333 p , 22, 35 8 , 36 2

Graph each set of numbers on a number line. See Example 3. 521 8, p, 2.75, 22, 17 4 , 0.666 p , 36 5p

Graph each set of numbers on a number line. See Example 3. The integers between -5 and 2

Graph each set of numbers on a number line. See Example 3. The whole numbers less than 4

Find each absolute value. See Example 4. 0 83 0 0

Find each absolute value. See Example 4. 29 0

Find each absolute value. See Example 4. 0 0 4 3

Find each absolute value. See Example 4. 0 9 16

Find each absolute value. See Example 4. 11 0

Find each absolute value. See Example 4. 0 14 0

Find each absolute value. See Example 4. 0 6.1 0

Find each absolute value. See Example 4. 25.3 0

Insert one of the symbols >, <, or = in the blank to make each statement true. See Examples 2 and 4. 0 3.4 0 3

Insert one of the symbols >, <, or = in the blank to make each statement true. See Examples 2 and 4. 0.08 0.079

Insert one of the symbols >, <, or = in the blank to make each statement true. See Examples 2 and 4. 1.1 0 1.2

Insert one of the symbols >, <, or = in the blank to make each statement true. See Examples 2 and 4. 5.5 51 2 0

Insert one of the symbols >, <, or = in the blank to make each statement true. See Examples 2 and 4. 0 15 2 0 7.5

Insert one of the symbols >, <, or = in the blank to make each statement true. See Examples 2 and 4. 22 3 0 0 15 7 3

Insert one of the symbols >, <, or = in the blank to make each statement true. See Examples 2 and 4. 99 100 0.99

Insert one of the symbols >, <, or = in the blank to make each statement true. See Examples 2 and 4. 2 0 0 2 0

Insert one of the symbols >, <, or = in the blank to make each statement true. See Examples 2 and 4. 0.3 0.333 . . .

Insert one of the symbols >, <, or = in the blank to make each statement true. See Examples 2 and 4. 0.666 0.6 0

Insert one of the symbols >, <, or = in the blank to make each statement true. See Examples 2 and 4. 1 15 16

Insert one of the symbols >, <, or = in the blank to make each statement true. See Examples 2 and 4. 22 p

Drafting. Which dimensions of the aluminum bracket shown below are natural numbers, whole numbers, integers, rational numbers, irrational numbers, and real numbers? 9 in. 1.765 in. 89 in. Arc length 2 in. Arc length 3 in. 3 in. 15 16 1 8 in.

History. Refer to the time line shown below. a. What basic unit was used to scale the time line? b. What symbolism is used to represent zero? c. Which numbers could be thought of as positive and which as negative? d. Express the dates for the Maya civilization using positive and negative numbers. MAYA CIVILIZATION 500 B.C. B.C./A.D. A.D. 500 A.D. 1000 A.D. 1500 A.D. 2000 A.D. 1697 A.D. 1441 Last Maya city conquered by the Spanish Mayapn falls to invaders A.D. 900 A.D. 1400 Maya culture declines A.D. 300 A.D. 900 Classic period of Maya culture 500 B.C. Maya culture begi

iPhones. You can get a more accurate reading of an iPhones signal strength by dialing *3001#12345#*. Field test mode is then activated and the standard signal strength bars (in the upper left corner of the display) are replaced by a negative number. The closer the negative number is to zero, the stronger the signal. Which iPhone shown below is receiving the strongest signal? 57 UMTS Cell Environment MM Info GSM Cell Environment 71 UMTS Cell Environment MM Info GSM Cell Environment 49 UMTS Cell Environment MM Info GSM Cell Environment 68 UMTS Cell Environment MM Info GSM Cell Environment (i) (ii) (iii) (iv)

Drafting. On an architects scale, the edge marked 16 divides each inch into 16 equal parts. Find the decimal form for each fractional part of one inch that is highlighted on the scale. 16 0

Trade. Each year from 1994 through 2009, the United States imported more goods and services from Japan than it exported to Japan. This caused trade deficits, which are represented by negative numbers on the following graph. a. In which year was the deficit the worst? Express that deficit using a signed number. b. In which year was the deficit the smallest? Express that deficit using a signed number. 10 $ billions 10 20 30 40 50 60 70 80 90 100 NET TRADE BALANCE, U.S. JAPAN '95 '97 '99 '01 '03 '05 '07 '09

U.S. Budget. A budget deficit is a negative number that indicates the government spent more money than it took in that year. A budget surplus is a positive number that indicates the government took in more money than it spent that year. a. Refer to the graph in the next column that shows the U.S. Federal Budget Deficit/Surplus for the years 1980 through 2009. For how many of those years was there a budget surplus? b. Consider the years in which there was a budget deficit. For how many of those years was it smaller than $300 billion? 1,414 200 100 100 0 200 $ billions 400 Fe

Explain the difference between a rational and an irrational number.

Can two different numbers have the same absolute value? Explain.

Explain how to find the decimal equivalent of a fraction.

What is a real number?

Pi Day (or Pi Approximation Day) is an unofficial holiday held to celebrate . Why do you think Pi Day is observed each year on March 14?

Explain why is not the simplest way to represent 0.1333....

Simplify: 24 54

Multiply: 3 41 8 52

Divide: 52 3  25 9

Add: 3 10 2 15

How many integers have an absolute value that is less than 1,000?

Is 0.10100100010000 . . . a repeating decimal? Explain.

Find a rational number between each pair of numbers. 1 8 and 1 9

Find a rational number between each pair of numbers. 1.71 and 1.72

In the addition statement -2 + 5 = 3 , the result, 3, is called the _____ .

Two numbers that are the same distance from 0 on a number line, but on opposite sides of it, are called _____ or additive _____ .

The ______ property of addition states that changing the order when adding does not affect the answer. The ______ property of addition states that changing the grouping when adding does not affect the answer.

Since any number added to 0 remains the same (is identical), the number 0 is called ______ the element for addition.

For each pair of numbers, which one has the larger absolute value? a. 6 or 5 b. 8.9 or - 9.2

Determine whether each statement is true or false. a. The sum of a number and its opposite is always 0. b. The sum of two negative numbers is always negative. c. The sum of two numbers with different signs is always negative.

For each addition, just determine the sign of the answer. a. 39.6 + (-64.9) b. -18.9 + 19.8

Complete each property of addition. Then give its name. a. a + (-a) = b. a + 0 = c. a + b = b + d. ( a + b ) + c = a+

Use the commutative property of addition to complete each statement. a. -5 + 1 = b. 15 + (-80.5) = c. -20 + (4 + 20) = -20 + ( ) d. (2.1 + 3) + 6 = ( ) + 6

Use the associative property of addition to complete each statement. a. (-6 + 2) + 8 = b. -7 + (7 + 3) =

What properties were used in Step 1 and Step 2 of the solution? (99 + 4) + 1 = (4 + 99) + 1 Step 1 = 4 + (99 + 1) Step 2 = 4 + 100 = 104

Consider: - 3 + 6 + (-9) + 8 + (-4) a. Add all the positives in the expression. b. Add all of the negatives. c. Add the results from parts a and b.

a. Express the commutative property of addition using the variables x and y. b. Express the associative property of addition using the variables x, y, and z.

Fill in the blank: We read - a as the _____ of a.

Add. See Example 1. 8 (1) 3

Add. See Example 1. 3 (2)a

Add. See Example 1. 5 (12) 4

Add. See Example 1. 4 (14) 8

Add. See Example 1. 29 (45) 23

Add. See Example 1. 23 (31) 5

Add. See Example 1. 4.2 (6.1) 5.1

Add. See Example 1. 5.1 (5.1) 29

Add. See Example 1. b 3 4 a 2 3 b

Add. See Example 1. 1 5 a 3 4 b

Add. See Example 1. b 1 4 a 1 10b

Add. See Example 1. 3 8 a 1 3 b 1 4

Add. See Example 2. 7 4 9

Add. See Example 2. 9 7

Add. See Example 2. 50 (11) 27

Add. See Example 2. 27 (30) 7

Add. See Example 2. 15.84 (15.84) 9.

Add. See Example 2. 9.19 (9.19) 5

Add. See Example 2. 6.25 8.5 21

Add. See Example 2. 21.37 (12.1) 1

Add. See Example 2. 7 15 3 15

Add. See Example 2. 8 11 3 11

Add. See Example 2. 1 2 a 1 8 b

Add. See Example 2. 5 6 a 1 4 b 1

Add. See Examples 3 and 5. 8 (5) 13 17

Add. See Examples 3 and 5. 17 (12) (23) 38

Add. See Examples 3 and 5. 21 (27) (9) 32

Add. See Examples 3 and 5. 32 12 17 8

Add. See Examples 3 and 5. 27 (3) (13) 22 21 (

Add. See Examples 3 and 5. 53 (27) (32) (7) 27 (

Add. See Examples 3 and 5. 60 70 (10) (10) 205 53 (2

Add. See Examples 3 and 5. 100 200 (300) (100) 200 60 70

Apply the associative property of addition to find the sum. See Example 4. 99 (99 215) 67

Apply the associative property of addition to find the sum. See Example 4. 67 (67 127) 10

Apply the associative property of addition to find the sum. See Example 4. (112 56) (56) (67

Apply the associative property of addition to find the sum. See Example 4. (67 5) (5) 99

Apply the associative property of addition to find the sum. See Example 4. 1 8 a 7 8 2 3 b (

Apply the associative property of addition to find the sum. See Example 4. a 1 2 9 16b 7 16 1

Apply the associative property of addition to find the sum. See Example 4. (12.4 1.9) 1.1 87

Apply the associative property of addition to find the sum. See Example 4. 87.6 (2.4 1.7) a

Add. See Example 6. 1 9 1 5 8

Add. See Example 6. 5 8 (5)(12

Add. See Example 6. 8 11 (11) 8 1 1 9

Add. See Example 6. 2 15 (15) 8 (2) 8 11

Add. 9 81 (2) 11

Add. 11 (21) (13) 2

Add. 0 (6.6) 0

Add. 0 (2.14) 9

Add. 9 16 7 16

Add. 3 4 1 4

Add. 6 (8) 4

Add. 4 (3) 3

Add. 167 167 25

Add. 25 25 6

Add. 20 (16) 10 13

Add. 13 (16) 4 167

Add. 19.35 (20.21) 1.53 33.

Add. 33.12 (35.7) 2.98 20

Add. 7 5 (10) 7 3 6

Add. 3 6 (9) (6) 19.35

Add. 19.2 (41.3) 57

Add. 57.93 (93.27) 7

Add. 2,345 (178) 4,

Add. 4,061 5,000 1

Add. 2.1 6.5 (8.2) 2.1 2,34

Add. 0.9 0.5 (0.2) (0.9) 2.1

Add. 3 (6) (3) 74 4 (3

Add. 4 (3) (4) 5 0.9

Add. 1 4 a 2 7 b 3

Add. 3 32 a 1 2 b 1 4

Add. 0.2 (0.3) (0.4) 0.9

Add. 0.9 (1.9) (2.9) 3

Add. a. 12 15 b. 12 15 c. 12 (15) d. 12 (15)

Add. . a. 432 67 b. 432 67 c. 432 (67) d. 432 (67)

Add. a. 1 2 2 9 b. 1 2 2 9 c. 2 1 2 1 2 9 2 1 d. 1 2 1 2 9 2 1

Add. a. 0.87 0.29 b. 0.87 0.29 c. 0.87 (0.29) d. 0.87 (0.29)

Military Science. During a battle, an army retreated 1,500 meters, regrouped, and advanced 2,400 meters. The next day, it advanced another 1,250 meters. Find the armys net gain.

Health. Find the point total for the six risk factors (in blue) on the medical questionnaire. Then use the table at the bottom of the form to determine the patients risk of contracting heart disease in the next 10 years. Age 35 Points 4 Reading 280 Points 3 Total Cholesterol Cholesterol HDL 62 Points 3 Systolic/Diastolic 124/100 Points 3 Blood Pressure Diabetic Yes Points 4 Total Points 2 or less 1 to 1 2 to 3 4 Risk 1% 2% 3% 4% Total 5 6 7 8 Risk 4% 6% 6% 7%

Golf. The leaderboard below shows the top four finishers from the 2009 PGA Championship Golf Tournament. Scores for each round are compared to par, the standard number of strokes necessary to complete the course. A score of , for example, indicates that the golfer used two strokes less than par to complete the course. A score of 5 indicates five strokes more than par. Determine the tournament total for each golfer. Y.E. Yang Tiger Woods Lee Westwood Rory McIlroy +1 5 2 1 2 2 0 +1 5 1 +1 1 2 +3 2 2 1 2 Round 3 4 Total

Submarines. A submarine was cruising at a depth of 1,250 feet. The captain gave the order to climb 550 feet. Compared to sea level, find the new depth of the sub.

Credit Cards. Refer to the monthly statement. What is the new balance? Previous Balance Billing Date Date Payment Due Credit Line New Purchases, Fees, Advances & Debts Payments & Credits New Balance 3,660.66 1,408.78 3,826.58 04/21/11 05/16/11 9,100

Politics. The following proposal to limit campaign contributions was on the ballot in a state election, and it passed. What will be the net fiscal impact on the state government? 212 Campaign Spending Limits YES NO Limits contributions to $200 in state campaigns. Fiscal impact: Costs of $4.5 million for implemen tation and enforcement. Increases state revenue by $6.7 million by eliminating tax deductions for lobbying.

Movie Losses. According to the Numbers Box Office Data website, the movie Stealth, released in 2005 by Sony Pictures, cost about $176,350,000 to produce, promote, and distribute. It reportedly earned back just $76,700,000 worldwide. Express the dollar loss suffered by Sony as a signed number.

Stocks. The last entry on the line for June 12 indicates that one share of Walt Disney Co. stock lost $0.81 in value that day. How much did the value of a share of Disney stock rise or fall over the 5-day period from June 12 through June 16? June 12 June 13 June 14 June 15 June 16 43.88 43.88 43.88 43.88 43.88 23.38 23.38 23.38 23.38 23.38 Disney Disney Disney Disney Disney .21 .21 .21 .21 0.5 0.5 0.5 0.5 87 86 87 89 43 15 50 28 15 40.75 40.19 41.00 41.81 41.19 .81 .56 +.81 +.81 .63

Chemistry. An atom is composed of protons (with a charge of ), neutrons (with no charge), and electrons (with a charge of ). Two simple models of atoms are shown. What is the overall charge of each atom? Electron Proton (a) (b)

Physics. In the illustration, arrows show the two forces acting on a lamp hanging from a ceiling. What is the sum of the forces? The force applied by the chain is upward: 12 units. The force of gravity is downward: 12 units.

The Big Easy. The city of New Orleans lies, on average, 6 feet below sea level. What is the elevation of the top of an 85-foot tall building in New Orleans?

Electronics. A closed circuit contains two batteries and three resistors. The sum of the voltages in the loop must be 0. Is it? 11 volts 10 volts 22 volts 8 volts 15 volts

Accounting. The 2009 quarterly profits and losses of the Bank of America are shown in the table. Losses are denoted using parentheses. Calculate the companys total net income for 2009. Net income Quarter ($ million) 1st 4,247 2nd 3,224 3rd (1,001) 4th (194)

Politics. Six months before an election, the incumbent trailed the challenger by 18 points. To overtake her opponent, the incumbent decided to use a four-part strategy. Each part of the plan is shown below, with the expected point gain. With these gains, will the incumbent overtake the challenger on election day? TV ads pts Union endorsement pts Voter mailing 3 pts Telephone calls 1 pts 10 2 WR

Explain why the sum of two positive numbers is always positive and the sum of two negative numbers is always negative.

Explain why the sum of a negative number and a positive number is sometimes positive, sometimes negative, and sometimes zero.

True or false: Every real number can be expressed as a decimal.

Multiply: 1 3 1 3

What two numbers are a distance of 6 away from - 3 on the number line?

Graph: 52.5, 22, 11 3 , 0.333 . . . , 0.756 3

A set is said to be closed under addition if the sum of any two of its members is also a member of the set. Is the set { -1, 0, 1 } a closed set under addition? Explain.

Think of two numbers. First, add the absolute value of the two numbers, and write your answer. Second, add the two numbers, take the absolute value of that sum, and write that answer. Do the two answers agree? Can you find two numbers that produce different answers? When do you get answers that agree, and when dont you?

______ finds the difference between two numbers.

In the subtraction -2 - 5 = -7, the result of is called the ______.

The difference between the maximum and the minimum value of a collection of measurements is called the ______ of the values.

To find the ______ in a quantity, subtract the earlier value from the later value.

Find the opposite (additive inverse) of each number. a. 12 b. 1 5 c. 2.71 d. 0

Complete each statement. a. a - b = a + To subtract two numbers, add the first number to the ______ of the number to be subtracted. b. - (-a) = The opposite of the opposite of a number is that _____ .

Apply the rule for subtraction and fill in the blanks. 1 - (-9) = 1 =

Use addition to check this subtraction: 15 - (- 8) = 7. Is the result correct?

Write each subtraction in the following expression as addition of the opposite. -10 -8 + (-23) + 5 - (-34)

For each subtraction, just determine the sign of the answer. a. 8.76 - 12.91 b. 8.76 - (-12.91)

Circle any minus signs in each expression. a. -6 - (-4) b. 7 + (-3) - 5 - (-2)

In each case, determine what number is being subtracted. a. 5 - 8 b. -5 - (-8)

Write each phrase using symbols. Then find its value. a. One minus negative seven b. The opposite of negative two c. The opposite of the absolute value of negative three d. Subtract 6 from 2

Write each expression in words. a. - (-m) b. -2 - (-3) c. x - (-y)

Simplify each expression. See Example 1. (55) (2

Simplify each expression. See Example 1. (27.2)x

Simplify each expression. See Example 1. (x) (t

Simplify each expression. See Example 1. (t)(

Simplify each expression. See Example 1. 0 25 0 0

Simplify each expression. See Example 1. 0 100 0(

Simplify each expression. See Example 1. ` ` 3 16 `

Simplify each expression. See Example 1. ` 4 3 `

Subtract. See Example 2. 4 7 1

Subtract. See Example 2. 1 6

Subtract. See Example 2. 6 4 3

Subtract. See Example 2. 3 4 4

Subtract. See Example 2. 8 (3) 17

Subtract. See Example 2. 17 (21)6

Subtract. See Example 2. 0 6 0

Subtract. See Example 2. 0 9

Subtract. See Example 2. 1 (3) 32.

Subtract. See Example 2. 1 (7) 0

Subtract. See Example 2. 20 (20) 30

Subtract. See Example 2. 30 (30)1

Subtract. See Example 2. 2 (7) 9

Subtract. See Example 2. 9 (1) 20

Subtract. See Example 2. 0 (12) 0

Subtract. See Example 2. 0 12

Subtract. See Example 2. 1.4 5.5 1.

Subtract. See Example 2. 1.3 4.7 0

Subtract. See Example 2. 1.5 0.81 1.

Subtract. See Example 2. 1.57 (0.8) 1.

Subtract. See Example 2. 1 8 3 8

Subtract. See Example 2. 3 4 1 4 1

Subtract. See Example 2. 1 3 3 4

Subtract. See Example 2. 1 6 5 8

Perform the indicated operation. See Example 3. Subtract -5 from 17.

Perform the indicated operation. See Example 3. Subtract 45 from - 50.

Perform the indicated operation. See Example 3. Subtract 12 from -13.

Perform the indicated operation. See Example 3. Subtract -11 from -12.

Perform the operations. See Example 4. 6 8 (1) 10 4 5

Perform the operations. See Example 4. 4 5 (3) 13 13 1

Perform the operations. See Example 4. 61 (62) (64) 60 93 (

Perform the operations. See Example 4. 93 (92) (94) 95 6 8

Perform the operations. 244 (12) 35

Perform the operations. 354 (29) 6

Perform the operations. 20 (30) 50 40 24 (

Perform the operations. 24 (28) 48 44 244

Perform the operations. 1.2 0.9 2.

Perform the operations. 2.52 1.72 2

Perform the operations. 1 8 a5 7 b

Perform the operations. 5 8 a2 9 b

Perform the operations. 62 71 (37) 99 17 3

Perform the operations. 17 32 (85) 51 5 8

Perform the operations. Subtract 47.5 from 0.

Perform the operations. Subtract 30.3 from 0.

Perform the operations. Subtract -137 from 12.

Perform the operations. Subtract 512 from -47.

Perform the operations. 1,903 (1,732) 300

Perform the operations. 300 (11) 13

Perform the operations. 2.83 (1.8) 4.

Perform the operations. 4.75 (1.9) 1

Perform the operations. 5 6 3 4

Perform the operations. 3 7 2 5 5

Perform the operations. 8 9 10 1

Perform the operations. 1 2 3 3

Perform the operations. 44 44 33

Perform the operations. 33 33 8

Perform the operations. 0.9 0.2 0.

Perform the operations. 0.3 0.2 4

Perform the operations. 25 (50) 75 33

Perform the operations. 33 (22) 44 0.9

Perform the operations. 6.3 9.8 2

Perform the operations. 2.1 9.4

Perform the operations. 9 16 a1 4 b

Perform the operations. 1 2 a1 4 b 9

Perform the operations. 0 (1) 0

Perform the operations. 0 (8) 1

Perform the operations. 2 15 3

Perform the operations. 3 14

Perform the operations. a. 50 (3) 50 b. 50 (3) 2

Perform the operations. a. 1 16 1 4 b. 1 16 1 4

Perform the operations. a. 5 9 a1 6 b 1 b. 5 9 a1 6 b 5 9

Perform the operations. a. 2.96 (1.78) b b. 2.96 (1.78) 5

The Empire State. New York states record high temperature of was set in 1926, and the record low of was set in 1979. What is the range of these temperature extremes?

Eyesight. Nearsightedness, the condition where near objects are clear and far objects are blurry, is measured using negative numbers. Farsightedness, the condition where far objects are clear and near objects are blurry, is measured using positive numbers. Find the range in the measurements shown. Nearsighted: 2.5 Farsighted: +4.35

Law Enforcement. A burglar scored on a lie detector test, a score that indicates deception. However, on a second test, he scored , a score that is inconclusive. Find the change in the scores.

Racing. To improve handling, drivers often adjust the angle of the wheels of their car. When the wheel leans out, the degree measure is considered positive. When the wheel leans in, the degree measure is considered negative. Find the change in the position of the wheel shown below. Previous position Tires lean outward +3.5 New position Tires lean inward

Determine the change in the number of passengers using each airport in 2009 compared with 2008. Top 2 Destination Airports in the U.S. (Number of passengers) Orlando Int'l Airport Florida Ft Lauderdale Airport Florida Source: Bureau of Transportation Statistics 2009 2008 1,296,000 1,411,000 2009 2008 1,148,000 1,198,000

U.S. Jobs. The table lists the three occupations that are predicted to have the largest job declines from 2008 to 2018. Complete the column labeled Change. Number of jobs Occupation 2008 2018 Change Farmers/ranchers 985,900 906,700 Sewing machine operators 212,400 140,900 Order clerks 245,700 181,500

Geography. The elevation of Death Valley, California, is 282 feet below sea level. The elevation of the Dead Sea in Israel is 1,312 feet below sea level. Find the difference in their elevations.

Card Games. Gonzalo won the second round of a card game and earned 50 points. Matt and Hydecki had to deduct the value of each of the cards left in their hands from their score on the first round. Use this information to update the score sheet below. (Face cards are counted as 10 points, aces as 1 point, and all others have the value of the number printed on the card.) Matt Hydecki Running point total Round 1 Round 2 Matt Gonzalo Hydecki 2 15 50 20

Worlds Coldest Ice Cream. Dippin Dots is an ice cream snack that was invented by Curt Jones in 1987. The tiny multicolored beads are created by flash freezing ice cream mix in liquid nitrogen at a temperature of 355F. When they come out of the processor, they are stored at a temperature of 40F. Find the change in temperature of Dippin Dots from production to storage. (Source: fundinguniverse.com) 1

History. Plato, a famous Greek philosopher, died in 347 B.C. at the age of 81. When was he born?

NASCAR. Complete the table below to determine how many points the third and fourth place finishers were behind the leader. 46 CHAPTER 1 An Introduction to Algebra from Campus to Careers Lead Transportation Security Officer Determine the change in the number of passengers using each airport in 2009 compared with 2008. Top 2 Destination Airports in the U.S. (Number of passengers) Orlando Int'l Airport Florida Ft Lauderdale Airport Florida Source: Bureau of Transportation Statistics 2009 2008 1,296,000 1,411,000 2009 2008 1,148,000 1,198,000 99. Number of jobs Occupation 2008 2018 Change Farmers/ranchers 985,900 906,700 Sewing machine operators 212,400 140,900 Order clerks 245,700 181,500 Running point total Round 1 Round 2 Matt Gonzalo Hydecki 2 15 50 2009 Final Driver Standings Points Points behind Rank Driver leader 1 Jimmie Johnson 6,652 . . . 2 Mark Martin 6,511 141 3 Jeff Gordon 6,473 4 Kurt Busch 6,446 Ca

Gauges. With the engine off, the ammeter on a car reads 0. If the headlights, which draw a current of 7 amps, and the radio, which draws a current of 6 amps, are both turned on, what will be the new reading? 20 15 10 5 5 10 15 20

Explain what it means when we say that subtraction is not commutative.

Why is addition of signed numbers taught before subtraction of signed numbers?

Explain why we know that the answer to is negative without having to do any computation.

Is the following statement true or false? Explain. Having a debt of $100 forgiven is equivalent to gaining $100.

Find the prime factorization of 30.

Write the set of integers.

True or false: -4 > -5?

Use the associative property of addition to simplify the calculation: -18 + (18 + 89)

Suppose is positive and is negative. Determine whether each statement is true or false. a. x y  0 y b. y x  0 c. x 0  0 d. 0 y 0  0

Find: 1 2 3 4 5 6 . . . 99 100 0 x 0

The answer to a multiplication problem is called a _____ . The answer to a division problem is called a ______ .

The _____ property of multiplication states that changing the order when multiplying does not affect the answer

The _____ property of multiplication states that changing the grouping when multiplying does not affect the answer

Division of a nonzero number by 0 is ______ .

a. The product or quotient of two numbers with like signs is _____. b. The product or quotient of two numbers with unlike signs is _____.

a. The product of an even number of negative numbers is _____ . b. The product of an odd number of negative numbers is _____ .

a. 9 3  3 O because . = b. 0 8  0 because . =

Complete each property of multiplication. a. a b  b (a b. (ab)c  c. 0 a  d. 1 e. aa 1 a  f.1 a b  0

Complete each property of division. a. a 1  b. a a  a a  d. a 0 is

Which property justifies each statement? a. 5(2 17)  (5 2)17 a b. 5a1 5 b  1 5( c. 5 2  2(5) 5a1 d. 5(1)  55 e. 5 0  0 5

For each multiplication or division, just determine the sign of the answer a. 19 37 a51 75b b. 45.568 2.56 1 c. 8.2(4.1)(6)(9.3)(1.5) 45.5

Use multiplication to check this division: 29.4 7  4.1 Is the answer correct? 29.4 7

Complete each statement using the given property. a. Commutative property of multiplication b. Associative property of multiplication c. Inverse property of multiplication d. Multiplication property of 1 14. (20)  20 5a b  1 2(6 9)  8  5 Let

Complete the table. Opposite Reciprocal Number (additive inverse) (multiplicative inverse) 2 1.75 4 5

Let POS stand for a positive number and NEG stand for a negative number. Determine the sign of each result, if possible. a. POS NEG b. POS + NEG c. POS - NEG d. POS NEG

Let POS stand for a positive number and NEG stand for a negative number. Determine the sign of each result, if possible. a. NEG NEG b. NEG + NEG c. NEG - NEG d. NEG NEG

Write each sentence using symbols. The product of negative four and negative five is twenty.

Write each sentence using symbols. The quotient of sixteen and negative eight is negative two.

Multiply. See Example 1. 4(1) 6(

Multiply. See Example 1. 6(1)

Multiply. See Example 1. 2 8 3

Multiply. See Example 1. 3 4 4

Multiply. See Example 1. 12(5) (

Multiply. See Example 1. (9)(11) 2

Multiply. See Example 1. 3(22) 8

Multiply. See Example 1. 8 9 1

Multiply. See Example 1. 1.2(0.4) (

Multiply. See Example 1. (3.6)(0.9)

Multiply. See Example 1. 1 3 a 3 4 b 1

Multiply. See Example 1. a 3 4 b a4 5 b 1

Multiply. See Example 2. (1)(7) (2

Multiply. See Example 2. (2)(5) a

Multiply. See Example 2. (6)(9) 34

Multiply. See Example 2. (8)(7) (1

Multiply. See Example 2. 3(3) 1(1

Multiply. See Example 2. 1(1) 91

Multiply. See Example 2. 63(7) 4

Multiply. See Example 2. 43(6)

Multiply. See Example 2. 0.6(4) 0.

Multiply. See Example 2. 0.7(8) 6

Multiply. See Example 2. a b 7 8 b a 2 21b 0.

Multiply. See Example 2. a 5 6 b a 2 15 a b 7 8

Multiply. See Example 3. 3.3(4)(5) (2

Multiply. See Example 3. (2.2)(4)(5) a

Multiply. See Example 3. 2(3)(4)(5)(6) 9(7)(

Multiply. See Example 3. 9(7)(5)(3)(1) 3.3(

Multiply. See Example 3. (41)(3)(7)(1) 56(

Multiply. See Example 3. 56(3)(4)(1) 2(

Multiply. See Example 3. (6)(6)(6) (5)

Multiply. See Example 3. (5)(5)(5) (41

Find the reciprocal of each number. Then find the product of the given number and its reciprocal. See Example 4. 7 9

Find the reciprocal of each number. Then find the product of the given number and its reciprocal. See Example 4. 8 9

Find the reciprocal of each number. Then find the product of the given number and its reciprocal. See Example 4. -1

Find the reciprocal of each number. Then find the product of the given number and its reciprocal. See Example 4. 1 8

Divide. See Example 5. 30  (3) 12

Divide. See Example 5. 12  (2) 1

Divide. See Example 5. 6  (2) 36

Divide. See Example 5. 36  (9) 3

Divide. See Example 5. 85 5

Divide. See Example 5. 84 7

Divide. See Example 5. 110 110 8

Divide. See Example 5. 200 200 1

Divide. See Example 5. 10.8 1.2

Divide. See Example 5. 13.5 1.5 1

Divide. See Example 5. 0.5 100

Divide. See Example 5. 1.7 10

Divide. See Example 5. 1 3  4 5

Divide. See Example 5. 2 3  7 8

Divide. See Example 5. 9 16  a 3 20b

Divide. See Example 5. 4 5  a 8 25

Perform the operations. 0 150

Perform the operations. 0 12

Perform the operations. 17 0

Perform the operations. 225 0

Perform the operations. 24 6

Perform the operations. 78 6

Perform the operations. 17 17

Perform the operations. 24 24

Perform the operations. (2)(2)(2)(2) (3)(

Perform the operations. (3)(3)(3)(3) 24

Perform the operations. 3(4)(0) 15

Perform the operations. 15(0)(22)

Perform the operations. 23.5 5

Perform the operations. 337.8 6

Perform the operations. 5.2 100 1.

Perform the operations. 1.17 1,000 3

Perform the operations. 2 a 1 3 b a 1 4 b 5.

Perform the operations. 3 a 1 5 b a 1 7 b 1

Perform the operations. 550 50

Perform the operations. 440 20

Perform the operations. 3 b 8 2 a 1 4 b

Perform the operations.3 4 15 1 10

Perform the operations. 7.2 (2.1)(2)

Perform the operations. 4.6 (5.4)(2)

Perform the operations. 1 2 a 3 4 b

Perform the operations. 1 3 a 5 16b 1

Perform the operations. 16 25  64 15

Perform the operations. 15 16  25 8

Perform the operations. 24.24 0.8 1

Perform the operations. 55.02 0.7 2

Perform the operations. 1 b 1 4 a 3 4 b 5

Perform the operations. 1 1 8 a 3 8 1 b 1

Perform the operations. a. 2.7  (0.9) 2 b. 2.7 (0.9)1 c. 2.7(0.9) d. 2.7 0.9 2

Perform the operations. a. 5 3  a 9 25b 2 b.5 3 a 9 25 b 5 c. 5 3 a 9 25b d. 5 3  a 9 25 b 5

Use the associative property of multiplication to find each product. b 1 2 (2 67)

Use the associative property of multiplication to find each product. a 5 16 1 7 b7 1

Use the associative property of multiplication to find each product. 0.2(10 3) 1.5(

Use the associative property of multiplication to find each product. 1.5(100 4) a

Real Estate. Over a 5-year period, the value of a $200,000 lot fell at a uniform rate to $160,000. What signed number indicates the amount of depreciation per year?

Tourism. The ocean liner Queen Mary cost $22,500,000 to build in 1936. The ship was purchased by the city of Long Beach, California, in 1967 for $3,450,000. It now serves as a convention center. What signed number indicates the annual average depreciation of the ship over the 31-year period from 1936 to 1967? Round to the nearest dollar.

Fluid Flow. In a lab, the temperature of a fluid was decreased 6 per hour for 12 hours. What signed number indicates the change in temperature?

Stress on the Job. A health care provider for a company estimates that 75 hours per week are lost by employees suffering from stress-related illness. In one year, how many hours are lost? Use a signed number to answer.

Weight Loss. As a result of a diet, Tom has been steadily losing 41 2 pounds per month. a. Which expression below can be used to determine how much heavier Tom was 8 months ago? i.4 (8) 1 2 8 41 ii.41 2 4 (8) 1 2 iii. 4 2 8 1 2(8) 4 iv.41 4 2 8 1 b. How much heavier was Tom 8 months ago?

Astronomy. The temperature on Pluto gets as low as F. This is twice as low as the lowest temperature reached on Jupiter. What is the lowest temperature on Jupiter?

Car Radiators. The instructions on a container of antifreeze state, A 50/50 mixture of antifreeze and water protects against freeze-ups down to F, while a 60/40 mix protects against freeze-ups down to one and one-half times that temperature. To what temperature does the 60/40 mixture protect?

Accounting. For 2010, the net income of Rite Aid Corporation (the drugstore chain) was about $508 million. The previous year, the companys net income was even worse, by a factor of about 5.75. What signed number represents Rite Aids net income in 2009? (Source: moneycentral .msn.com)

Airlines. In the 2009 income statement for Delta Air Lines below, numbers within parentheses represent a loss. Complete the statement given these facts. The second quarter loss was about 6.4 times the first quarter loss. The fourth quarter loss was about 5 times the second quarter loss. The third quarter loss was about of the fourth quarter loss. DELTA INCOME STATEMENT 2009 All amounts in millions of dollars Source: dailyfinance.com 1st Qtr (25) 2nd Qtr (?) 3rd Qtr (?) 4th Qtr (?)

Computers. The formula A1*B1*C1 in cell D1 of the spreadsheet instructs the computer to multiply the values in cells A1, B1, and C1 and to print the result in place of the formula in cell D1. (The symbol * represents multiplication.) What value will be printed in the cell D1? What values will be printed in cells D2 and D3? File Edit View Insert Format Window 4 22 60 5 30 20 17 14 34 = A1*B1*C1 = A2*B2*C2 = A3*B3*C3 Tools Data 1 ABCD 2 3 4 5 . . .

Physics. An oscilloscope displays electrical signals as wavy lines on a screen. By switching the magnification dial to , for example, the height of the peak and the depth of the valley of a graph will be doubled. Use signed numbers to indicate the height and depth of the display for each setting of the dial. a. normal b. c. d. INTENS. FOCUS MAGNIFICATION NORM X 2 X .5 X 1.5 5 5 10 15 10 15 Peak Valley 1.5 2 0.5 2

Light. Water acts as a selective filter of light. In the illustration, we see that red light waves penetrate water only to a depth of about 5 meters. How many times deeper does a. yellow light penetrate than red light? b. green light penetrate than orange light? c. blue light penetrate than yellow light? Surface of water Depth (meters) 10 20 30 40 50 60 70 80 Red Orange Yellow Green Blue Violet

Explain why16 0 is undefined.

The commutative property states that changing the order when multiplying does not change the answer. Are the following activities commutative? Explain. a. Washing a load of clothes; drying a load of clothes b. Putting on your left sock; putting on your right sock

What is wrong with the following statement? A negative and a positive is a negative.

If we multiply two different numbers and the answer is 0, what must be true about one of the numbers? Explain your answer.

Add: 3  (4)  (5)  4  3 16

Write 3 (5) 3 as addition of the opposite.

Find 1 2  1 4  1 3. Answer in decimal form.

Which integers have an absolute value equal to 45?

If the product of five numbers is negative, how many of them could be negative? Explain.

Suppose is a positive number and is a negative number. Determine whether the given expression is positive or negative. a. b. c. d. 1 b a a a b a(b) a b

In the exponential expression 75, 7 is the _____ , and 5 is the ____ . 75 is the fifth _____ of seven.

102 can be read as ten , and 103 can be read as ten _____.

An ______ is used to represent repeated multiplication.

To _____ the expression2(1  42) means to find its value.

The rule for the _____ of operations guarantees that an evaluation of a numerical expression will result in a single answer.

To find the arithmetic ______ or average of a set of values, divide the sum of the values by the number of values.

To evaluate each expression, what operation should be performed first? a. 24 - 4 + 2 b. 32 8.4 c. 8 - (3 + 5)2 d. 65.33

To evaluate , what operation should be performed first in the numerator? In the denominator?

a. Give the name of each grouping symbol: , , , , and . b. In the expression , which grouping symbols are innermost, and which are outermost?

What operation is indicated?

a. In the expression (-5)2, what is the base? b. In the expression -52 , what is the base?

Write each expression using symbols. Then evaluate it. a. Negative two squared b. The opposite of the square of two

Complete the evaluation of each expression.

Complete the evaluation of each expression. 46 23 3(5) 4  46

Write each product using exponents. See Example 1. 8 8 8 (4

Write each product using exponents. See Example 1. (4)(4)(4)(4) 

Write each product using exponents. See Example 1. 7 7 7 12 12 5 5

Write each product using exponents. See Example 1. 5 5 5 5 5 7 7 7 8 8 8

Write each product using exponents. See Example 1. x x x b

Write each product using exponents. See Example 1. b b b b 7

Write each product using exponents. See Example 1. r r r r s s m m

Write each product using exponents. See Example 1. m m m n n n n x x

Evaluate each expression. See Example 2. 72

Evaluate each expression. See Example 2. 92

Evaluate each expression. See Example 2. 63

Evaluate each expression. See Example 2. 64

Evaluate each expression. See Example 2. (5)4

Evaluate each expression. See Example 2. (5)3 (

Evaluate each expression. See Example 2. (0.1)2 (

Evaluate each expression. See Example 2. (0.8)2 (

Evaluate each expression. See Example 2. a 1 4 b 3

Evaluate each expression. See Example 2. a 1 3 b 4

Evaluate each expression. See Example 2. a 2 3 b 3

Evaluate each expression. See Example 2. a 3 4 b 3

Evaluate each expression. See Example 3. (6)2 and 62

Evaluate each expression. See Example 3. (4)2 6 and 42 (

Evaluate each expression. See Example 3. (8)2 and 82 (

Evaluate each expression. See Example 3. (9)2 8 and 92 (

Evaluate each expression. See Example 4. 3 5 4 4

Evaluate each expression. See Example 4. 4 6  5 9

Evaluate each expression. See Example 4. 32 16  4  2 6

Evaluate each expression. See Example 4. 60 20  10  5

Evaluate each expression. See Example 4. 3 5 4  2 2 5 6  3 32

Evaluate each expression. See Example 4. 23 3 5 4  2 2

Evaluate each expression. See Example 4. 12  3 2 1

Evaluate each expression. See Example 4. 18  6 3

Evaluate each expression. See Example 4. 22 15  3 33

Evaluate each expression. See Example 4. 33 8  10 1

Evaluate each expression. See Example 4. 2(9) 2(5)(10) 6(

Evaluate each expression. See Example 4. 6(7) 3(4)(2) 22

Evaluate each expression. See Example 5. 4(6  5) 3

Evaluate each expression. See Example 5. 3(5 4)

Evaluate each expression. See Example 5. (9 3)(9 9)2 4

Evaluate each expression. See Example 5. (8 6)(6 6)2 (9 3

Evaluate each expression. See Example 5. (1 32 4)22 (8

Evaluate each expression. See Example 5. 1(28 52 2)32 (1

Evaluate each expression. See Example 5.  5(10  2 5) 1 14

Evaluate each expression. See Example 5. 14  3(7 5 3) 1

Evaluate each expression. See Example 6. (1)9 [72 (2)2 ] 1 

Evaluate each expression. See Example 6. [92 (8)2 ](1)10 (1)9

Evaluate each expression. See Example 6. 64 6[15  2(3  8)] 4

Evaluate each expression. See Example 6. 4 2[26  2(5 3)] [

Evaluate each expression. See Example 6. 2[2  42 (8 9)]2 6

Evaluate each expression. See Example 6. 3[5  32 (4 5)]2 2[2

Evaluate each expression. See Example 6. 3  2[1 (4 5)] 4 

Evaluate each expression. See Example 6. 4  2[7 (3 9)] 3[

Evaluate each expression. See Example 7. 2 5 7  (7) 3 

Evaluate each expression. See Example 7. 3 (1) 2  (2) 2 5

Evaluate each expression. See Example 7. 2 25 60  (4) 54 (4)(5) 3 (1

Evaluate each expression. See Example 7. (6 5)8 1 (9)(3) 4 2 2

Evaluate each expression. See Example 7. 2(4 2 2) 3(3)(2) (6

Evaluate each expression. See Example 7. 3(32  2 22 ) (5 8)(7 9) 2(4

Evaluate each expression. See Example 7. 72 (2 2 4) 102 (9 10  22 ) 3(32

Evaluate each expression. See Example 7. 132 52 3(5 32 ) 72

Evaluate each expression. See Example 8. 10 2 0 4 8 0 45

Evaluate each expression. See Example 8. 45 5 0 1 8 0 1

Evaluate each expression. See Example 8. 0 7 2 ) 0 3 (4 7) 0 10

Evaluate each expression. See Example 8. 0 9 5(1 23 0

Evaluate each expression. See Example 8. 3  5)2  0 2 0 2(5 8) 0

Evaluate each expression. See Example 8. 25 0 8(5) 24 29 (3

Evaluate each expression. See Example 8. 6 4 0  2 0 4 0 226 63 0

Evaluate each expression. See Example 8. 4 0 9 7 0  0 7 0 63 211 0

Evaluate each expression. See Example 8. (2 3 22 ) 5 4

Evaluate each expression. See Example 8. (3 5 2 6)4 (2

Evaluate each expression. See Example 8. 2 52  4 32 (

Evaluate each expression. See Example 8. 5 33 4 23 2

Evaluate each expression. See Example 8. 2(1)  3(3) 1 2  3(1) 3 5 33

Evaluate each expression. See Example 8. 4(3)2 2  3(3) 1 2

Evaluate each expression. See Example 8. 8 3[5 ] 2 (7 3)2 ] 4(3

Evaluate each expression. See Example 8. 3 [33  (3 1)3 8

Evaluate each expression. [6(5) 5(5)]3 (4) 3

Evaluate each expression. 2 34 (6  5)3 [6(5)

Evaluate each expression. 6[(130 4 ) 1] 3 ) 2] 5

Evaluate each expression. 91 5[(150 33 8

Evaluate each expression. 2a  1 15 5 b 6 2  9 11

Evaluate each expression. a 25 5 b 36 9 2a

Evaluate each expression. 5(2) 0 6  5 0 3 0 2  1 0 6a 2

Evaluate each expression. 6(3)3 5(2) 0 6  5 0 3 0

Evaluate each expression. 18 [2  (1 6)] 16 (4)2 6(3

Evaluate each expression. 6 [6(1) 88] 4 22 18

Evaluate each expression. 0 5 7 0 2 0 30 6

Evaluate each expression. 2  0 3 22 82 12 0 5

Evaluate each expression. (3) b(1) 3 a 4 2 b(1) 2 

Evaluate each expression. (2)3 a 6 2 (3) b(1) 3 a

Evaluate each expression. 2 a 1 8 b  a 1 4 b 2 (

Evaluate each expression. 1 9 a 1 4 b  a 1 6 b 2 1

Evaluate each expression. 52 10  5 25 5 3 1 1 9

Evaluate each expression. (62 24 2)  5 4 3 52

Evaluate each expression. a b 40 13 24 3(2  5)  2 b (62

Evaluate each expression. a 82 10 2(3)(4) 5(3) a b 40

Evaluate each expression. a. (7 4)(2) (7 b. (7 4) 2a

Evaluate each expression. a. 2 33 b. (2 3)3 2

Evaluate each expression. a. 100  5 2 10 b. 100  (5 2) (

Evaluate each expression. a. 8  3[2 (6  1)] ( b. (8  3)[2 (6  1)]

Light. As light energy passes through the first unit of area, 1 yard away from the bulb, it spreads out. How much area does that light energy cover 2 yards, 3 yards, and 4 yards from the bulb? Express each answer using exponents. 1 yd 2 yd 3 yd 4 yd 1

Chain Letters. A woman sent two friends a letter with the following request: Please send a copy of this letter to two of your friends. Assume that all those receiving letters responded and that everyone in the chain received just one letter. Complete the table and then determine how many letters will be circulated in the 10th level. Level Number of letters circulated 1st 2nd 3rd 4th  2  2  2 2  21

To determine the average afternoon wait time in security lines at an airport, officials monitored four passengers, each at a different gate. The time that each passenger entered a security line and the time the same passenger cleared the checkpoint was recorded, as shown below. Find the average (mean) wait time for these passengers. 117 Time Time entered cleared Passenger at Gate A 3:05 pm 3:21 pm Passenger at Gate B 3:03 pm 3:13 pm Passenger at Gate C 3:01 pm 3:09 pm Passenger at Gate D 3:02 pm 3:16 pm

Energy Usage. Find the average number of therms of natural gas used per month. Acct 45-009 Janice C. Milton 2012 Energy Audit 23 N. State St. Apt. B Tri-City Gas Co. Salem, OR J F MAM J J A S OND Therms used 50 40 30 20 10 39 41 37 34 22 23 16 16 34 41 34 41

Cash Awards. A contest is to be part of a promotional kickoff for a new childrens cereal. The prizes to be awarded are shown. a. How much money will be awarded in the promotion? b. What is the average cash prize? YouTube Video Contest Grand prize: Disney World vacation plus $2,500 Four 1st place prizes of $500 Thirty-five 2nd place prizes of $150 Eighty-five 3rd place prizes of $25

Surveys. Some students were asked to rate their college cafeteria food on a scale from 1 to 5. The responses are shown on the tally sheet. Find the average rating. 1 Poor Fair Excellent 23 45

Wrapping Gifts. How much ribbon is needed to wrap the package if 15 inches of ribbon are needed to make the bow? 9 in. 16 in. 4 in

Scrabble. Write an expression to determine the number of points received for playing the word QUARTZY and then evaluate it. (The number on each tile gives the point value of the letter.) Q10 U1 A1 R1 T1 Z10 Y4

Explain the difference between 23 and 32.

Why is the order of operations rule necessary?

Explain the error. What is the correct answer? 40  4 2  40  8

Explain the error. What is the correct answer? 5  3(2 6)  5  3(4) 6

What numbers are a distance of 6 away from on a number line?

Fill in the blank with or : 0.3 1 3

Using each of the numbers 2, 3, and 4 only once, what is the greatest value that the following expression can have? 12 1

Insert a pair of parentheses into 4 32 4 2 12 so that it has a value of 40.

Translate the set of instructions to an expression and then evaluate it. Subtract the sum of - 9 and 8 from the product of the cube of -3 and the opposite of 4.

Translate the set of instructions to an expression and then evaluate it. Increase the square of the reciprocal of -2 by the difference of -0.25 and -1.

Variables and/or numbers can be combined with the operations of arithmetic to create algebraic ______.

A ____ is a product or quotient of numbers and/or variables. Examples are: 8x ,t 3 2 , and -cd3 .

Addition symbols separate algebraic expressions into parts called _____.

A term, such as 27, that consists of a single number is called a _____ term.

The _____ of the term 10x is 10.

To _____ 4x - 3 for x = 5 , we substitute 5 for and perform the necessary calculations.

Complete the table below on the left to determine the number of days in weeks.

Complete the table below on the right to determine the number of minutes in seconds. Number Number of weeks of days 1 2 3 w Number Number of seconds of minutes 60 120 180 s

The knife shown below is 12 inches long. Write an expression that represents the length (in inches) of the blade.

A student inherited $5,000 and deposits dollars in American Savings. Write an expression that represents the number of dollars left to deposit in a City Mutual account. American Savings $x City Mutual $? $5

Solution 2 is poured into solution 1. Write an expression that represents the number of ounces in the mixture. Solution 2 x ounces Solution 1 20 ounces

Peanuts were mixed with c pounds of cashews to make 100 pounds of a mixture. Write an expression that represents the number of pounds of peanuts that were used. ? pounds c pounds

a. Let b= the length of the beam shown below (in feet). Write an expression that represents the length of the pipe. b. Let p= the length of the pipe (in feet). Write an expression that represents the length of the beam. 15 ft

Complete the table. Give each value in cents. 15 ft p b American Savings $x City Mutual $? $5,000 x Number Number of weeks of days 1 2 3 w Number Number of seconds of minutes 60 120 180 s Solution 1 20 ounces Solution 2 x ounces 100 pounds ? pounds c pounds Coin Number Value Total value Nickel 6 Dime Half-dollar x  5 d

Complete each solution. Evaluate each expression for a = 5, x = -2, and y = 4. . 20 25 9(5) 9a a2 9( ) (5)2 a  5 x

Complete each solution. Evaluate each expression for a = 5, x = -2, and y = 4. x  6y ( )  6( ) 676  24 =26

Complete each solution. Evaluate each expression for a = 5, x = -2, and y = 4. Write each term in standard form. a. y8 b. d2c c. What property of multiplication did you use?

Complete each solution. Evaluate each expression for a = 5, x = -2, and y = 4. Fill in the blanks. a. w 2 w b. 2 3 m 3

Consider the expression 3x3  11x2 x  9. a. How many terms does the expression have? b. What is the coefficient of each term?

Complete the following table. Term Coefficient t x 5 1 2 6m 75t w bh

Determine whether the variable is used as a factor or as a term. See Example 2. c + 32

Determine whether the variable is used as a factor or as a term. See Example 2. - 24c + 6

Determine whether the variable is used as a factor or as a term. See Example 2. 5c

Determine whether the variable is used as a factor or as a term. See Example 2. a + b + c

Translate each phrase to an algebraic expression. If no variable is given, use as the variable. See Example 3. The sum of the length l and 15

Translate each phrase to an algebraic expression. If no variable is given, use as the variable. See Example 3. The difference of a number and 10

Translate each phrase to an algebraic expression. If no variable is given, use as the variable. See Example 3. The product of a number and 50

Translate each phrase to an algebraic expression. If no variable is given, use as the variable. See Example 3. Three-fourths of the population p

Translate each phrase to an algebraic expression. If no variable is given, use as the variable. See Example 3. The ratio of the amount won w and lost l

Translate each phrase to an algebraic expression. If no variable is given, use as the variable. See Example 3. The tax t added to c

Translate each phrase to an algebraic expression. If no variable is given, use as the variable. See Example 3. P increased by two-thirds of p

Translate each phrase to an algebraic expression. If no variable is given, use as the variable. See Example 3. 21 less than the total height h

Translate each phrase to an algebraic expression. If no variable is given, use as the variable. See Example 3. The square of k, minus 2,005

Translate each phrase to an algebraic expression. If no variable is given, use as the variable. See Example 3. s subtracted from S

Translate each phrase to an algebraic expression. If no variable is given, use as the variable. See Example 3. 1 less than twice the attendance a

Translate each phrase to an algebraic expression. If no variable is given, use as the variable. See Example 3. J reduced by 500

Translate each phrase to an algebraic expression. If no variable is given, use as the variable. See Example 3. 1,000 split n equal ways

Translate each phrase to an algebraic expression. If no variable is given, use as the variable. See Example 3. Exceeds the cost bc y 25,000

Translate each phrase to an algebraic expression. If no variable is given, use as the variable. See Example 3. 90 more than twice the current price p

Translate each phrase to an algebraic expression. If no variable is given, use as the variable. See Example 3. 64 divided by the cube of y

Translate each phrase to an algebraic expression. If no variable is given, use as the variable. See Example 3. 3 times the total of 35, h, and 300

Translate each phrase to an algebraic expression. If no variable is given, use as the variable. See Example 3. Decrease x by -17

Translate each phrase to an algebraic expression. If no variable is given, use as the variable. See Example 3. 680 fewer than the entire population p

Translate each phrase to an algebraic expression. If no variable is given, use as the variable. See Example 3. Triple the number of expected participants

Translate each phrase to an algebraic expression. If no variable is given, use as the variable. See Example 3. The product of d and 4, decreased by 15

Translate each phrase to an algebraic expression. If no variable is given, use as the variable. See Example 3. The quotient of and 6, cubed

Translate each phrase to an algebraic expression. If no variable is given, use as the variable. See Example 3. Twice the sum of 200 and t

Translate each phrase to an algebraic expression. If no variable is given, use as the variable. See Example 3. The square of the quantity 14 less than x