<< Chapter < Page Chapter >> Page >
  • Equality Symbol
    • a = b is read as a is equal to b
    • The symbol = is called the equal sign.
  • Inequality
    • a < b is read a is less than b
    • a is to the left of b on the number line
      ..
    • a > b is read a is greater than b
    • a is to the right of b on the number line
      ..
Algebraic Notation Say
a = b a is equal to b
a b a is not equal to b
a < b a is less than b
a > b a is greater than b
a b a is less than or equal to b
a b a is greater than or equal to b
  • Exponential Notation
    • For any expression a n is a factor multiplied by itself n times, if n is a positive integer.
    • a n means multiply n factors of a
      ..
    • The expression of a n is read a to the n th power.

Order of Operations When simplifying mathematical expressions perform the operations in the following order:

  • Parentheses and other Grouping Symbols: Simplify all expressions inside the parentheses or other grouping symbols, working on the innermost parentheses first.
  • Exponents: Simplify all expressions with exponents.
  • Multiplication and Division: Perform all multiplication and division in order from left to right. These operations have equal priority.
  • Addition and Subtraction: Perform all addition and subtraction in order from left to right. These operations have equal priority.

Practice makes perfect

Use Variables and Algebraic Symbols

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

16 9

16 minus 9, the difference of sixteen and nine

Got questions? Get instant answers now!

5 · 6

5 times 6, the product of five and six

Got questions? Get instant answers now!

28 ÷ 4

28 divided by 4, the quotient of twenty-eight and four

Got questions? Get instant answers now!

x + 8

x plus 8, the sum of x and eight

Got questions? Get instant answers now!

( 2 ) ( 7 )

2 times 7, the product of two and seven

Got questions? Get instant answers now!

14 < 21

fourteen is less than twenty-one

Got questions? Get instant answers now!

36 19

thirty-six is greater than or equal to nineteen

Got questions? Get instant answers now!

3 n = 24

3 times n equals 24, the product of three and n equals twenty-four

Got questions? Get instant answers now!

y 1 > 6

y minus 1 is greater than 6, the difference of y and one is greater than six

Got questions? Get instant answers now!

2 18 ÷ 6

2 is less than or equal to 18 divided by 6; 2 is less than or equal to the quotient of eighteen and six

Got questions? Get instant answers now!

a 7 · 4

a is not equal to 7 times 4, a is not equal to the product of seven and four

Got questions? Get instant answers now!

Identify Expressions and Equations

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

Simplify Expressions with Exponents

In the following exercises, write in exponential form.

3 · 3 · 3 · 3 · 3 · 3 · 3

3 7

Got questions? Get instant answers now!

4 · 4 · 4 · 4 · 4 · 4

Got questions? Get instant answers now!

x · x · x · x · x

x 5

Got questions? Get instant answers now!

y · y · y · y · y · y

Got questions? Get instant answers now!

In the following exercises, write in expanded form.

Simplify Expressions Using the Order of Operations

In the following exercises, simplify.

  1. 3 + 8 · 5
  2. (3+8) · 5
  1. 43
  2. 55
Got questions? Get instant answers now!
  1. 2 + 6 · 3
  2. (2+6) · 3
Got questions? Get instant answers now!

2 3 12 ÷ ( 9 5 )

5

Got questions? Get instant answers now!

3 2 18 ÷ ( 11 5 )

Got questions? Get instant answers now!

( 6 + 10 ) ÷ ( 2 + 2 )

4

Got questions? Get instant answers now!

3 ( 1 + 9 · 6 ) 4 2

149

Got questions? Get instant answers now!

5 ( 2 + 8 · 4 ) 7 2

Got questions? Get instant answers now!

2 [ 1 + 3 ( 10 2 ) ]

50

Got questions? Get instant answers now!

Everyday math

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″ Rashard Lewis 82″
Boris Diaw 80″ LeBron James 80″
Kawhi Leonard 79″ Chris Bosh 83″
Tony Parker 74″ Dwyane Wade 76″
Danny Green 78″ Ray Allen 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
Got questions? Get instant answers now!

Elevation In Colorado there are more than 50 mountains with an elevation of over 14,000 feet. The table shows the ten tallest. Use this table to fill in the appropriate inequality symbol.

Mountain Elevation
Mt. Elbert 14,433′
Mt. Massive 14,421′
Mt. Harvard 14,420′
Blanca Peak 14,345′
La Plata Peak 14,336′
Uncompahgre Peak 14,309′
Crestone Peak 14,294′
Mt. Lincoln 14,286′
Grays Peak 14,270′
Mt. Antero 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

Got questions? Get instant answers now!

Writing exercises

Explain the difference between an expression and an equation.

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

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. Who can you ask for help? Your fellow classmates and instructor are good resources. Is there a place on campus where math tutors are available? Can your study skills be improved?

…no—I don’t get it! This is a warning sign and you must not ignore it. You should get help right away or you will quickly be overwhelmed. See your instructor as soon as you can to discuss your situation. Together you can come up with a plan to get you the help you need.

Practice Key Terms 2

Get Jobilize Job Search Mobile App in your pocket Now!

Get it on Google Play Download on the App Store Now




Source:  OpenStax, Prealgebra. OpenStax CNX. Jul 15, 2016 Download for free at http://legacy.cnx.org/content/col11756/1.9
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'Prealgebra' conversation and receive update notifications?

Ask