1.1 Variables and Expressions Students will translate verbal expressions into algebraic expressions and vice versa. Key Vocabulary: Variable – symbol used to represent unspecified numbers or values Algebraic expression – consists of one or more numbers and variables along with one or more arithmetic operations Evaluate –to find an expression’s value Designed by Skip Tyler, Edited by Diane Warren

What is the area of a rectangle? Length times Width If the length is 3 meters and the width is 2 meters, what is the area? A = L x W A = 3 x 2 = 6 meters 2 A, L and W are the variables. It is any letter that represents an unknown number.

An algebraic expression contains: 1) one or more numbers or variables, and 2) one or more arithmetic operations. Examples: x n

In expressions, there are many different ways to write multiplication. 1)ab 2)a b 3)a(b) or (a)b 4)(a)(b) We are not going to use the multiplication symbol any more so the times sign will not be confused with the variable x.

Division, on the other hand, is written as: 1) 2) x ÷ 3

Throughout this year, you will hear many words that mean addition, subtraction, multiplication, and division. The table lists some of the most common.

Write an algebraic expression for 1) m increased by 5. m + 5 2) 7 times the product of x and t. 7xt or 7(x)(t) or 7 x t

3) 11 less than 4 times a number. 4n ) two more than 6 times a number. 6n + 2 5) the quotient of a number and 12.

Which of the following expressions represents 7 times a number decreased by 13? 1.7x x x x Answer Now

Which one of the following expressions represents 28 less than three times a number? x 2.3x x 4.3x + 28 Answer Now

Write a verbal expression for: 1) 8 + a. The ratio of m to r There are other possible ways. The sum of 8 and a 2)

Which of the following verbal expressions represents 2x + 9? Answer Now 1.9 increased by twice a number 2.a number increased by nine 3.twice a number decreased by less than twice a number

Which of the following expressions represents the sum of 16 and five times a number? Answer Now 1.5x x x x

base and 3 is called the exponent or power means = 1000 When looking at the expression 10 3, 10 is called the

How is it said? 2 1 Two to the first power2 Two to the second power or two squared 2323 Two to the third power or two cubed 2n 7 Two times n to the seventh power

Which of the following verbal expressions represents x 2 + 2x? Answer Now 1.the sum of a number squared and twice a number 2.the sum of a number and twice the number 3.twice a number less than the number squared 4.the sum of a number and twice the number squared

Which of the following expressions represents four less than the cube of a number? Answer Now 1.4 – x – 3x 3.3x – 4 4.x 3 – 4

Evaluate = = 8 2n 7 We can’t evaluate because we don’t know what n equals to!!

Is 3 5 the same as 5 3 ? Evaluate each and find out! 3 5 = = = = ≠ 125 They are not the same!