Chapter 01 – Section 01

Chapter 01 – Section 01 Variables and Expressions

To translate verbal expressions into mathematical expressions and vice versa. 1-1 VARIABLES AND EXPRESSIONS OBJECTIVES

This section is the basics of the basics.

Terms to become familiar with:

variables – symbol used to express an unspecified number

algebraic expressions – one or more numbers and variables along with one or more arithmetic operations

factors – quantities that are being multiplied

product – the result of factors being multiplied

EXAMPLE 1 α : Write an algebraic expression for each verbal expression. a. three times a number x subtracted from 24 b. 5 greater than half of a number t EX1 β 1-1 VARIABLES AND EXPRESSIONS

EXAMPLE 1 β : Write an algebraic expression for each verbal expression. a. m increased by 5 b. the difference of x and 9 c. 7 times the product of x and t 1-1 VARIABLES AND EXPRESSIONS

EXAMPLE 2 α : Write a verbal expression for each algebraic expression. a. (3 + b) ÷ y b. 5y + 10x 1-1 VARIABLES AND EXPRESSIONS EX2 β

EXAMPLE 2 β : Write a verbal expression for each algebraic expression. a. 9t b. 8 + a c. 7 – 3y 1-1 VARIABLES AND EXPRESSIONS

More terms you will need to become familiar with:

power – an expression with a superscript representing a number multiplied by itself a certain number of times

Examples of powers: 5 4 and x 3

base – the number or variable that is multiplied

exponent – the superscript number that signifies the number of times multiplication should occur

4 5 = 4 * 4 * 4 * 4 * 4

1-1 VARIABLES AND EXPRESSIONS four is multiplied by itself five times { = 1024

EXAMPLE 3 α : Write a power that represents the number of smallest squares in the large square. 1-1 VARIABLES AND EXPRESSIONS EX3 β Count the number of squares along one side. There are 8 squares in each row. Count the number of squares along the other side. There are 8 squares in each column. To find the number of smallest squares, you would multiply 8 * 8. 8 * 8 can be written as a power by 1) writing the base, 8, once 2) writing the number of times multiplied, 2, once superscripted Answer: 8 2

EXAMPLE 3 β : Write a power that represents the number of smallest squares in the large square. 1-1 VARIABLES AND EXPRESSIONS

EXAMPLE 4 α : Evaluate 3 4 . 1-1 VARIABLES AND EXPRESSIONS EX4 β Method 1 Write the problem out in long form. 3 * 3 * 3 * 3 Multiply in small steps. 3 * 3 = 9 9 * 3 = 27 27 * 3 = 81 Method 2 Use your calculator. Hit the “3” key. Hit the power key – “^” or “y x ”. Hit the “4” key. Hit the “=“ key. Answer: 81.

EXAMPLE 4 β : Evaluate each expression. a. 3 5 b. 5 3 1-1 VARIABLES AND EXPRESSIONS

HOMEWORK PAGE 8 #15 – 39 odd 1-1 VARIABLES AND EXPRESSIONS