Pre Test Translate each word into a mathematical operation. + 1) increase + 6) plus − 2) decrease − 7) difference ÷ 3) more than + 8) quotient + 4) less than − 9) sum • 5) product • 10) times Write and answer the following problems. 11) Simplify. −42 12) Write 2y • 2y • 2y in exponential form.

1-1 Variables and Expressions You would be wise to listen carefully and take notes! Be smart -correct your odd homework problems after you complete them! Algebra 1 Glencoe McGraw-Hill Linda Stamper

In algebra, variables are symbols used to represent unspecified numbers or values. Any letter may be used as a variable. An expression that represents a particular number is called a numerical expression. Example: 3 + 2 An algebraic expression consists of one or more constants and variables along with one or more arithmetic operations. constants - numbers variables - letters operations - addition, subtraction, multiplication and division Example of an algebraic expression: 3x + 2

In algebraic expressions, a raised dot or parentheses are often used to indicate multiplication as the symbol x can be easily mistaken for the variable x. Here are some ways to represent the product of x and y. Use good form in an answer! In each expression, the quantities being multiplied are called factors, and the result is called the product.

An expression like 43 is called a power. base   exponent or power word form: four to the third power four cubed factor form: 4 • 4 • 4 evaluated form: 64 To evaluate an expression means to find its value. The word power can also refer to the exponent.

Writing Algebraic Expressions In English there is a difference between a phrase and a sentence. Phrases are translated into mathematical expressions. Sentences are translated into equations or inequalities. Phrase The sum of 6 and a number 6 + n Sentence The difference of a number and three is five. n – 3 = 5 Sentence Seven times a number is less than 50. 7n < 50 When choosing a variable for an unknown, it may be helpful to select a letter that relates to the unknown value (for example: let a represent age). If a variable is given use it! Sentences must have a verb! Sentences must have a verb!

Would you say 5 notebooks or notebooks 5? The product of five and a number 5n The product of a number and five Would you say 5 notebooks or notebooks 5? 5n Write your answer in good form - the number comes before a variable in a term involving multiplication.

Use a fraction bar to designate division! Write an algebraic expression for each word phrase. a. The difference of a number and 7 n – 7 b. 32 increased by a number 32 + n c. 25 less than a number 25 n – d. 10 less the product of 5 and a number cubed 10 – 5n3 e. The quotient of a number and six. n 6 Use a fraction bar to designate division!

Did you use a fraction bar to designate division? Example 1 Write the phrase as an algebraic expression. a. 11 greater than a number Did you use a fraction bar to designate division? n + 11 b. a number subtracted from 15 15 – n c. The sum of a number and 30 n + 30 d. Maria’s age minus 27 a – 27 18 n e. The quotient of 18 and a number f. The sum of a number and ten, divided by two.

Example 2 Write the phrase as an algebraic expression. a. eight more than a number n + 8 b. seven less the product of 4 and a number x 7 – 4x c. n cubed divided by 2 d. 9 more than the quotient of b and 5 e. one third the original area of a f. thirteen less than a number n - 13

Write in exponential form (as a power). Example 3 Example 4 Example 5 y • y • y • y 3x • 3x • 3x • 3x 5 • 5 • 5 y4 53 (3x)4 Evaluate. Example 6 Example 7 Example 8 2 • 2 • 2 • 2 5 • 5 • 5 -32 (-3)2 16 125 -9 9 Must have parentheses! A power applies only to what is directly in front of it.

Pre Test Write and answer the following problems in your spiral notebook. 1) Simplify. −42 2) Write 2y • 2y • 2y in exponential form. −16 (2y)3 − 4 • 4 A power applies only to what is directly in front of it. The 2y must be in parentheses!

Homework 1-A2 Pages 8–9, #13–29,46–54.