Skip to Content
OpenStax Logo
Prealgebra 2e

2.1 Use the Language of Algebra

Prealgebra 2e2.1 Use the Language of Algebra
Buy book
  1. Preface
  2. 1 Whole Numbers
    1. Introduction
    2. 1.1 Introduction to Whole Numbers
    3. 1.2 Add Whole Numbers
    4. 1.3 Subtract Whole Numbers
    5. 1.4 Multiply Whole Numbers
    6. 1.5 Divide Whole Numbers
    7. Key Terms
    8. Key Concepts
    9. Exercises
      1. Review Exercises
      2. Practice Test
  3. 2 The Language of Algebra
    1. Introduction to the Language of Algebra
    2. 2.1 Use the Language of Algebra
    3. 2.2 Evaluate, Simplify, and Translate Expressions
    4. 2.3 Solving Equations Using the Subtraction and Addition Properties of Equality
    5. 2.4 Find Multiples and Factors
    6. 2.5 Prime Factorization and the Least Common Multiple
    7. Key Terms
    8. Key Concepts
    9. Exercises
      1. Review Exercises
      2. Practice Test
  4. 3 Integers
    1. Introduction to Integers
    2. 3.1 Introduction to Integers
    3. 3.2 Add Integers
    4. 3.3 Subtract Integers
    5. 3.4 Multiply and Divide Integers
    6. 3.5 Solve Equations Using Integers; The Division Property of Equality
    7. Key Terms
    8. Key Concepts
    9. Exercises
      1. Review Exercises
      2. Practice Test
  5. 4 Fractions
    1. Introduction to Fractions
    2. 4.1 Visualize Fractions
    3. 4.2 Multiply and Divide Fractions
    4. 4.3 Multiply and Divide Mixed Numbers and Complex Fractions
    5. 4.4 Add and Subtract Fractions with Common Denominators
    6. 4.5 Add and Subtract Fractions with Different Denominators
    7. 4.6 Add and Subtract Mixed Numbers
    8. 4.7 Solve Equations with Fractions
    9. Key Terms
    10. Key Concepts
    11. Exercises
      1. Review Exercises
      2. Practice Test
  6. 5 Decimals
    1. Introduction to Decimals
    2. 5.1 Decimals
    3. 5.2 Decimal Operations
    4. 5.3 Decimals and Fractions
    5. 5.4 Solve Equations with Decimals
    6. 5.5 Averages and Probability
    7. 5.6 Ratios and Rate
    8. 5.7 Simplify and Use Square Roots
    9. Key Terms
    10. Key Concepts
    11. Exercises
      1. Review Exercises
      2. Practice Test
  7. 6 Percents
    1. Introduction to Percents
    2. 6.1 Understand Percent
    3. 6.2 Solve General Applications of Percent
    4. 6.3 Solve Sales Tax, Commission, and Discount Applications
    5. 6.4 Solve Simple Interest Applications
    6. 6.5 Solve Proportions and their Applications
    7. Key Terms
    8. Key Concepts
    9. Exercises
      1. Review Exercises
      2. Practice Test
  8. 7 The Properties of Real Numbers
    1. Introduction to the Properties of Real Numbers
    2. 7.1 Rational and Irrational Numbers
    3. 7.2 Commutative and Associative Properties
    4. 7.3 Distributive Property
    5. 7.4 Properties of Identity, Inverses, and Zero
    6. 7.5 Systems of Measurement
    7. Key Terms
    8. Key Concepts
    9. Exercises
      1. Review Exercises
      2. Practice Test
  9. 8 Solving Linear Equations
    1. Introduction to Solving Linear Equations
    2. 8.1 Solve Equations Using the Subtraction and Addition Properties of Equality
    3. 8.2 Solve Equations Using the Division and Multiplication Properties of Equality
    4. 8.3 Solve Equations with Variables and Constants on Both Sides
    5. 8.4 Solve Equations with Fraction or Decimal Coefficients
    6. Key Terms
    7. Key Concepts
    8. Exercises
      1. Review Exercises
      2. Practice Test
  10. 9 Math Models and Geometry
    1. Introduction
    2. 9.1 Use a Problem Solving Strategy
    3. 9.2 Solve Money Applications
    4. 9.3 Use Properties of Angles, Triangles, and the Pythagorean Theorem
    5. 9.4 Use Properties of Rectangles, Triangles, and Trapezoids
    6. 9.5 Solve Geometry Applications: Circles and Irregular Figures
    7. 9.6 Solve Geometry Applications: Volume and Surface Area
    8. 9.7 Solve a Formula for a Specific Variable
    9. Key Terms
    10. Key Concepts
    11. Exercises
      1. Review Exercises
      2. Practice Test
  11. 10 Polynomials
    1. Introduction to Polynomials
    2. 10.1 Add and Subtract Polynomials
    3. 10.2 Use Multiplication Properties of Exponents
    4. 10.3 Multiply Polynomials
    5. 10.4 Divide Monomials
    6. 10.5 Integer Exponents and Scientific Notation
    7. 10.6 Introduction to Factoring Polynomials
    8. Key Terms
    9. Key Concepts
    10. Exercises
      1. Review Exercises
      2. Practice Test
  12. 11 Graphs
    1. Graphs
    2. 11.1 Use the Rectangular Coordinate System
    3. 11.2 Graphing Linear Equations
    4. 11.3 Graphing with Intercepts
    5. 11.4 Understand Slope of a Line
    6. Key Terms
    7. Key Concepts
    8. Exercises
      1. Review Exercises
      2. Practice Test
  13. A | Cumulative Review
  14. B | Powers and Roots Tables
  15. C | Geometric Formulas
  16. Answer Key
    1. Chapter 1
    2. Chapter 2
    3. Chapter 3
    4. Chapter 4
    5. Chapter 5
    6. Chapter 6
    7. Chapter 7
    8. Chapter 8
    9. Chapter 9
    10. Chapter 10
    11. Chapter 11
  17. Index

Learning Objectives

By the end of this section, you will be able to:
  • Use variables and algebraic symbols
  • Identify expressions and equations
  • Simplify expressions with exponents
  • Simplify expressions using the order of operations
Be Prepared 2.1

Before you get started, take this readiness quiz.

Add:43+69.Add:43+69.
If you missed this problem, review Example 1.19.

Be Prepared 2.2

Multiply:(896)201.Multiply:(896)201.
If you missed this problem, review Example 1.48.

Be Prepared 2.3

Divide:7,263÷9.Divide:7,263÷9.
If you missed this problem, review Example 1.64.

Use Variables and Algebraic Symbols

Greg and Alex have the same birthday, but they were born in different years. This year Greg is 2020 years old and Alex is 23,23, so Alex is 33 years older than Greg. When Greg was 12,12, Alex was 15.15. When Greg is 35,35, Alex will be 38.38. No matter what Greg’s age is, Alex’s age will always be 33 years more, right?

In the language of algebra, we say that Greg’s age and Alex’s age are variable and the three is a constant. The ages change, or vary, so age is a variable. The 33 years between them always stays the same, so the age difference is the constant.

In algebra, letters of the alphabet are used to represent variables. Suppose we call Greg’s age g.g. Then we could use g+3g+3 to represent Alex’s age. See Table 2.1.

Greg’s age Alex’s age
1212 1515
2020 2323
3535 3838
gg g+3g+3
Table 2.1

Letters are used to represent variables. Letters often used for variables are x,y,a,b,andc.x,y,a,b,andc.

Variables and Constants

A variable is a letter that represents a number or quantity whose value may change.

A constant is a number whose value always stays the same.

To write algebraically, we need some symbols as well as numbers and variables. There are several types of symbols we will be using. In Whole Numbers, we introduced the symbols for the four basic arithmetic operations: addition, subtraction, multiplication, and division. We will summarize them here, along with words we use for the operations and the result.

Operation Notation Say: The result is…
Addition a+ba+b aplusbaplusb the sum of aa and bb
Subtraction abab aminusbaminusb the difference of aa and bb
Multiplication a·b,(a)(b),(a)b,a(b)a·b,(a)(b),(a)b,a(b) atimesbatimesb The product of aa and bb
Division a÷b,a/b,ab,baa÷b,a/b,ab,ba aa divided by bb The quotient of aa and bb

In algebra, the cross symbol, ×,×, is not used to show multiplication because that symbol may cause confusion. Does 3xy3xy mean 3×y3×y (three times yy) or 3·x·y3·x·y (three times xtimesyxtimesy)? To make it clear, use • or parentheses for multiplication.

We perform these operations on two numbers. When translating from symbolic form to words, or from words to symbolic form, pay attention to the words of or and to help you find the numbers.

  • The sum of 55 and 33 means add 55 plus 3,3, which we write as 5+3.5+3.
  • The difference of 99 and 22 means subtract 99 minus 2,2, which we write as 92.92.
  • The product of 44 and 88 means multiply 44 times 8,8, which we can write as 4·8.4·8.
  • The quotient of 2020 and 55 means divide 2020 by 5,5, which we can write as 20÷5.20÷5.

Example 2.1

Translate from algebra to words:

  1. 12+1412+14
  2. (30)(5)(30)(5)
  3. 64÷864÷8
  4. xyxy
Try It 2.1

Translate from algebra to words.

  1. 18+1118+11
  2. (27)(9)(27)(9)
  3. 84÷784÷7
  4. pqpq
Try It 2.2

Translate from algebra to words.

  1. 47194719
  2. 72÷972÷9
  3. m+nm+n
  4. (13)(7)(13)(7)

When two quantities have the same value, we say they are equal and connect them with an equal sign.

Equality Symbol

a=bis readais equal toba=bis readais equal tob

The symbol == is called the equal sign.

An inequality is used in algebra to compare two quantities that may have different values. The number line can help you understand inequalities. Remember that on the number line the numbers get larger as they go from left to right. So if we know that bb is greater than a,a, it means that bb is to the right of aa on the number line. We use the symbols “<”“<” and “>”“>” for inequalities.

Inequality

a<ba<b is read aa is less than bb

aa is to the left of bb on the number line

The figure shows a horizontal number line that begins with the letter a on the left then the letter b to its right.

a>ba>b is read aa is greater than bb

aa is to the right of bb on the number line

The figure shows a horizontal number line that begins with the letter b on the left then the letter a to its right.

The expressions a<banda>ba<banda>b can be read from left-to-right or right-to-left, though in English we usually read from left-to-right. In general,

a<bis equivalent tob>a.For example,7<11is equivalent to11>7.a>bis equivalent tob<a.For example,17>4is equivalent to4<17.a<bis equivalent tob>a.For example,7<11is equivalent to11>7.a>bis equivalent tob<a.For example,17>4is equivalent to4<17.

When we write an inequality symbol with a line under it, such as ab,ab, it means a<ba<b or a=b.a=b. We read this aa is less than or equal to b.b. Also, if we put a slash through an equal sign, ≠,≠, it means not equal.

We summarize the symbols of equality and inequality in Table 2.2.

Algebraic Notation Say
a=ba=b aa is equal to bb
abab aa is not equal to bb
a<ba<b aa is less than bb
a>ba>b aa is greater than bb
abab aa is less than or equal to bb
abab aa is greater than or equal to bb
Table 2.2

Symbols << and >>

The symbols << and >> each have a smaller side and a larger side.

smaller side << larger side
larger side >> smaller side

The smaller side of the symbol faces the smaller number and the larger faces the larger number.

Example 2.2

Translate from algebra to words:

  1. 20352035
  2. 1115311153
  3. 9>10÷29>10÷2
  4. x+2<10x+2<10
Try It 2.3

Translate from algebra to words.

  1. 14271427
  2. 19281928
  3. 12>4÷212>4÷2
  4. x7<1x7<1
Try It 2.4

Translate from algebra to words.

  1. 19151915
  2. 7=1257=125
  3. 15÷3<815÷3<8
  4. y-3>6y-3>6

Example 2.3

The information in Figure 2.2 compares the fuel economy in miles-per-gallon (mpg) of several cars. Write the appropriate symbol =,<,or>=,<,or> in each expression to compare the fuel economy of the cars.

This table has two rows and six columns. The first column is a header column and it labels each row The first row is labeled “Car” and the second “Fuel economy (mpg)”. To the right of the ‘Car’ row are the labels: “Prius”, “Mini Cooper”, “Toyota Corolla”, “Versa”, “Honda Fit”. Each of these columns contains an image of the labeled car model. To the right of the “Fuel economy (mpg)” row are the algebraic equations: the letter p, the equals symbol, the number forty-eight; the letter m, the equals symbol, the number twenty-seven; the letter c, the equals symbol, the number twenty-eight; the letter v, the equals symbol, the number twenty-six; and the letter f, the equals symbol, the number twenty-seven.
Figure 2.2 (credit: modification of work by Bernard Goldbach, Wikimedia Commons)
  1. MPG of Prius_____ MPG of Mini Cooper
  2. MPG of Versa_____ MPG of Fit
  3. MPG of Mini Cooper_____ MPG of Fit
  4. MPG of Corolla_____ MPG of Versa
  5. MPG of Corolla_____ MPG of Prius
Try It 2.5

Use Figure 2.2 to fill in the appropriate symbol,=,<,or>.symbol,=,<,or>.

  1. MPG of Prius_____MPG of Versa
  2. MPG of Mini Cooper_____ MPG of Corolla
Try It 2.6

Use Figure 2.2 to fill in the appropriate symbol,=,<,or>.symbol,=,<,or>.

  1. MPG of Fit_____ MPG of Prius
  2. MPG of Corolla _____ MPG of Fit

Grouping symbols in algebra are much like the commas, colons, and other punctuation marks in written language. They indicate which expressions are to be kept together and separate from other expressions. Table 2.3 lists three of the most commonly used grouping symbols in algebra.

Common Grouping Symbols
parentheses ()()
brackets [][]
braces {}{}
Table 2.3

Here are some examples of expressions that include grouping symbols. We will simplify expressions like these later in this section.

8(148)213[2+4(98)]24÷{132[1(65)+4]}8(148)213[2+4(98)]24÷{132[1(65)+4]}

Identify Expressions and Equations

What is the difference in English between a phrase and a sentence? A phrase expresses a single thought that is incomplete by itself, but a sentence makes a complete statement. “Running very fast” is a phrase, but “The football player was running very fast” is a sentence. A sentence has a subject and a verb.

In algebra, we have expressions and equations. An expression is like a phrase. Here are some examples of expressions and how they relate to word phrases:

Expression Words Phrase
3+53+5 3plus53plus5 the sum of three and five
n1n1 nn minus one the difference of nn and one
6·76·7 6times76times7 the product of six and seven
xyxy xx divided by yy the quotient of xx and yy

Notice that the phrases do not form a complete sentence because the phrase does not have a verb. An equation is two expressions linked with an equal sign. When you read the words the symbols represent in an equation, you have a complete sentence in English. The equal sign gives the verb. Here are some examples of equations:

Equation Sentence
3+5=83+5=8 The sum of three and five is equal to eight.
n1=14n1=14 nn minus one equals fourteen.
6·7=426·7=42 The product of six and seven is equal to forty-two.
x=53x=53 xx is equal to fifty-three.
y+9=2y3y+9=2y3 yy plus nine is equal to two yy minus three.

Expressions and Equations

An expression is a number, a variable, or a combination of numbers and variables and operation symbols.

An equation is made up of two expressions connected by an equal sign.

Example 2.4

Determine if each is an expression or an equation:

  1. 166=10166=10
  2. 4·2+14·2+1
  3. x÷25x÷25
  4. y+8=40y+8=40
Try It 2.7

Determine if each is an expression or an equation:

  1. 23+6=2923+6=29
  2. 7·377·37
Try It 2.8

Determine if each is an expression or an equation:

  1. y÷14y÷14
  2. x6=21x6=21

Simplify Expressions with Exponents

To simplify a numerical expression means to do all the math possible. For example, to simplify 4·2+14·2+1 we’d first multiply 4·24·2 to get 88 and then add the 11 to get 9.9. A good habit to develop is to work down the page, writing each step of the process below the previous step. The example just described would look like this:

4·2+14·2+1
8+18+1
99

Suppose we have the expression 2·2·2·2·2·2·2·2·2.2·2·2·2·2·2·2·2·2. We could write this more compactly using exponential notation. Exponential notation is used in algebra to represent a quantity multiplied by itself several times. We write 2·2·22·2·2 as 2323 and 2·2·2·2·2·2·2·2·22·2·2·2·2·2·2·2·2 as 29.29. In expressions such as 23,23, the 22 is called the base and the 33 is called the exponent. The exponent tells us how many factors of the base we have to multiply.

The image shows the number two with the number three, in superscript, to the right of the two. The number two is labeled as “base” and the number three is labeled as “exponent”.
means multiply three factors of 2means multiply three factors of 2

We say 2323 is in exponential notation and 2·2·22·2·2 is in expanded notation.

Exponential Notation

For any expression an,aan,a is a factor multiplied by itself nn times if nn is a positive integer.

anmeans multiplynfactors ofaanmeans multiplynfactors ofa
At the top of the image is the letter a with the letter n, in superscript, to the right of the a. The letter a is labeled as “base” and the letter n is labeled as “exponent”. Below this is the letter a with the letter n, in superscript, to the right of the a set equal to n factors of a.

The expression anan is read aa to the nthnth power.

For powers of n=2n=2 and n=3,n=3, we have special names.

a2is read as"asquared"a3is read as"acubed"a2is read as"asquared"a3is read as"acubed"

Table 2.4 lists some examples of expressions written in exponential notation.

Exponential Notation In Words
7272 77 to the second power, or 77 squared
5353 55 to the third power, or 55 cubed
9494 99 to the fourth power
125125 1212 to the fifth power
Table 2.4

Example 2.5

Write each expression in exponential form:

  1. 16·16·16·16·16·16·1616·16·16·16·16·16·16
  2. 9·9·9·9·99·9·9·9·9
  3. x·x·x·xx·x·x·x
  4. a·a·a·a·a·a·a·aa·a·a·a·a·a·a·a
Try It 2.9

Write each expression in exponential form:

41·41·41·41·4141·41·41·41·41

Try It 2.10

Write each expression in exponential form:

7·7·7·7·7·7·7·7·77·7·7·7·7·7·7·7·7

Example 2.6

Write each exponential expression in expanded form:

  1. 8686
  2. x5x5
Try It 2.11

Write each exponential expression in expanded form:

  1. 4848
  2. a7a7
Try It 2.12

Write each exponential expression in expanded form:

  1. 8888
  2. b6b6

To simplify an exponential expression without using a calculator, we write it in expanded form and then multiply the factors.

Example 2.7

Simplify: 34.34.

Try It 2.13

Simplify:

  1. 5353
  2. 1717
Try It 2.14

Simplify:

  1. 7272
  2. 0505

Simplify Expressions Using the Order of Operations

We’ve introduced most of the symbols and notation used in algebra, but now we need to clarify the order of operations. Otherwise, expressions may have different meanings, and they may result in different values.

For example, consider the expression:

4+3·74+3·7
Some students say it simplifies to 49.Some students say it simplifies to 25.4+3·7Since4+3gives 7.7·7And7·7is 49.494+3·7Since3·7is 21.4+21And21+4makes 25.25Some students say it simplifies to 49.Some students say it simplifies to 25.4+3·7Since4+3gives 7.7·7And7·7is 49.494+3·7Since3·7is 21.4+21And21+4makes 25.25

Imagine the confusion that could result if every problem had several different correct answers. The same expression should give the same result. So mathematicians established some guidelines called the order of operations, which outlines the order in which parts of an expression must be simplified.

Order of Operations

When simplifying mathematical expressions perform the operations in the following order:

1. Parentheses and other Grouping Symbols

  • Simplify all expressions inside the parentheses or other grouping symbols, working on the innermost parentheses first.

2. Exponents

  • Simplify all expressions with exponents.

3. Multiplication and Division

  • Perform all multiplication and division in order from left to right. These operations have equal priority.

4. Addition and Subtraction

  • Perform all addition and subtraction in order from left to right. These operations have equal priority.

Students often ask, “How will I remember the order?” Here is a way to help you remember: Take the first letter of each key word and substitute the silly phrase. Please Excuse My Dear Aunt Sally.

Order of Operations
Please Parentheses
Excuse Exponents
My Dear Multiplication and Division
Aunt Sally Addition and Subtraction

It’s good that ‘My Dear’ goes together, as this reminds us that multiplication and division have equal priority. We do not always do multiplication before division or always do division before multiplication. We do them in order from left to right.

Similarly, ‘Aunt Sally’ goes together and so reminds us that addition and subtraction also have equal priority and we do them in order from left to right.

Manipulative Mathematics

Doing the Manipulative Mathematics activity Game of 24 will give you practice using the order of operations.

Example 2.8

Simplify the expressions:

  1. 4+3·74+3·7
  2. (4+3)·7(4+3)·7
Try It 2.15

Simplify the expressions:

  1. 125·2125·2
  2. (125)·2(125)·2
Try It 2.16

Simplify the expressions:

  1. 8+3·98+3·9
  2. (8+3)·9(8+3)·9

Example 2.9

Simplify:

  1. 18÷9·218÷9·2
  2. 18·9÷218·9÷2
Try It 2.17

Simplify:

42÷7·342÷7·3

Try It 2.18

Simplify:

12·3÷412·3÷4

Example 2.10

Simplify: 18÷6+4(52).18÷6+4(52).

Try It 2.19

Simplify:

30÷5+10(32)30÷5+10(32)

Try It 2.20

Simplify:

70÷10+4(62)70÷10+4(62)

When there are multiple grouping symbols, we simplify the innermost parentheses first and work outward.

Example 2.11

Simplify:5+23+3[ 63(42) ].Simplify:5+23+3[ 63(42) ].

Try It 2.21

Simplify:

9+53[ 4(9+3) ]9+53[ 4(9+3) ]

Try It 2.22

Simplify:

722[4(5+1) ]722[4(5+1) ]

Example 2.12

Simplify: 23+34÷352.23+34÷352.

Try It 2.23

Simplify:

32+24÷2+4332+24÷2+43

Try It 2.24

Simplify:

6253÷5+826253÷5+82

Section 2.1 Exercises

Practice Makes Perfect

Use Variables and Algebraic Symbols

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

1.

169169

2.

257257

3.

5·65·6

4.

3·93·9

5.

28÷428÷4

6.

45÷545÷5

7.

x+8x+8

8.

x+11x+11

9.

(2)(7)(2)(7)

10.

(4)(8)(4)(8)

11.

14<2114<21

12.

17<3517<35

13.

36193619

14.

42274227

15.

3n=243n=24

16.

6n=366n=36

17.

y1>6y1>6

18.

y4>8y4>8

19.

218÷6218÷6

20.

320÷4320÷4

21.

a7·4a7·4

22.

a1·12a1·12

Identify Expressions and Equations

In the following exercises, determine if each is an expression or an equation.

23.

9·6=549·6=54

24.

7·9=637·9=63

25.

5·4+35·4+3

26.

6·3+56·3+5

27.

x+7x+7

28.

x+9x+9

29.

y5=25y5=25

30.

y8=32y8=32

Simplify Expressions with Exponents

In the following exercises, write in exponential form.

31.

3·3·3·3·3·3·33·3·3·3·3·3·3

32.

4·4·4·4·4·44·4·4·4·4·4

33.

x·x·x·x·xx·x·x·x·x

34.

y·y·y·y·y·yy·y·y·y·y·y

In the following exercises, write in expanded form.

35.

5353

36.

8383

37.

2828

38.

105105

Simplify Expressions Using the Order of Operations

In the following exercises, simplify.

39.
  1. 3+8·53+8·5
  2. (3+8)·5(3+8)·5
40.
  1. 2+6·32+6·3
  2. (2+6)·3(2+6)·3
41.

2312÷(95)2312÷(95)

42.

3218÷(115)3218÷(115)

43.

3·8+5·23·8+5·2

44.

4·7+3·54·7+3·5

45.

2+8(6+1)2+8(6+1)

46.

4+6(3+6)4+6(3+6)

47.

4·12/84·12/8

48.

2·36/62·36/6

49.

6+10/2+26+10/2+2

50.

9+12/3+49+12/3+4

51.

(6+10)÷(2+2)(6+10)÷(2+2)

52.

(9+12)÷(3+4)(9+12)÷(3+4)

53.

20÷4+6·520÷4+6·5

54.

33÷3+8·233÷3+8·2

55.

20÷(4+6)·520÷(4+6)·5

56.

33÷(3+8)·233÷(3+8)·2

57.

42+5242+52

58.

32+7232+72

59.

(4+5)2(4+5)2

60.

(3+7)2(3+7)2

61.

3(1+9·6)423(1+9·6)42

62.

5(2+8·4)725(2+8·4)72

63.

2[1+3(102)]2[1+3(102)]

64.

5[2+4(32)]5[2+4(32)]

Everyday Math

65.

Basketball In the 2014 NBA playoffs, the San Antonio Spurs beat the Miami Heat. The table below shows the heights of the starters on each team. Use this table to fill in the appropriate symbol (=,<,>).(=,<,>).

Spurs Height Heat Height
Tim Duncan 83″83″ Rashard Lewis 82″82″
Boris Diaw 80″80″ LeBron James 80″80″
Kawhi Leonard 79″79″ Chris Bosh 83″83″
Tony Parker 74″74″ Dwyane Wade 76″76″
Danny Green 78″78″ Ray Allen 77″77″
  1. Height of Tim Duncan____Height of Rashard Lewis
  2. Height of Boris Diaw____Height of LeBron James
  3. Height of Kawhi Leonard____Height of Chris Bosh
  4. Height of Tony Parker____Height of Dwyane Wade
  5. Height of Danny Green____Height of Ray Allen
66.

Elevation In Colorado there are more than 5050 mountains with an elevation of over 14,000feet.14,000feet. The table shows the ten tallest. Use this table to fill in the appropriate inequality symbol.

Mountain Elevation
Mt. Elbert 14,433′14,433′
Mt. Massive 14,421′14,421′
Mt. Harvard 14,420′14,420′
Blanca Peak 14,345′14,345′
La Plata Peak 14,336′14,336′
Uncompahgre Peak 14,309′14,309′
Crestone Peak 14,294′14,294′
Mt. Lincoln 14,286′14,286′
Grays Peak 14,270′14,270′
Mt. Antero 14,269′14,269′
  1. Elevation of La Plata Peak____Elevation of Mt. Antero
  2. Elevation of Blanca Peak____Elevation of Mt. Elbert
  3. Elevation of Gray’s Peak____Elevation of Mt. Lincoln
  4. Elevation of Mt. Massive____Elevation of Crestone Peak
  5. Elevation of Mt. Harvard____Elevation of Uncompahgre Peak

Writing Exercises

67.

Explain the difference between an expression and an equation.

68.

Why is it important to use the order of operations to simplify an expression?

Self Check

After completing the exercises, use this checklist to evaluate your mastery of the objectives of this section.

.

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. Whom 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.

Citation/Attribution

Want to cite, share, or modify this book? This book is Creative Commons Attribution License 4.0 and you must attribute OpenStax.

Attribution information
  • If you are redistributing all or part of this book in a print format, then you must include on every physical page the following attribution:
    Access for free at https://openstax.org/books/prealgebra-2e/pages/1-introduction
  • If you are redistributing all or part of this book in a digital format, then you must include on every digital page view the following attribution:
    Access for free at https://openstax.org/books/prealgebra-2e/pages/1-introduction
Citation information

© Mar 3, 2020 OpenStax. Textbook content produced by OpenStax is licensed under a Creative Commons Attribution License 4.0 license. The OpenStax name, OpenStax logo, OpenStax book covers, OpenStax CNX name, and OpenStax CNX logo are not subject to the Creative Commons license and may not be reproduced without the prior and express written consent of Rice University.