The document discusses variable expressions and algebraic terms. It provides examples of expressions containing variables, numbers, and arithmetic operations. It defines terms like variables, expressions, and explains different ways to write multiplication and division. Phrases used for addition, subtraction, multiplication and division operations are listed. Examples of writing expressions for word problems are given and key concepts like exponents/powers are explained.

1. Translating variable expressions

2. 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.

3. An algebraic expression contains: 1) one or more numbers or variables, and 2) one or more arithmetic operations. Examples: x - 3 3 • 2n

4. In expressions, there are many different ways to write multiplication. 1) ab 2) a • b 3) a(b) or (a)b 4) (a)(b) 5) a x b We are not going to use the multiplication symbol any more. Why?

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

6. Throughout this year, you will hear many words that mean addition, subtraction, multiplication, and division. Complete the table with as many as you know.

7. Here are some phrases you may have listed. The terms with * are ones that are often used.

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

9. 3) 11 less than 4 times a number. 4 n - 11 4) two more than 6 times a number. 6 n + 2 5) the quotient of a number and 12.

10. Which of the following expressions represents 7 times a number decreased by 13? 7x + 13 7x - 13 13 - 7x 13 + 7x Answer Now

11. Which one of the following expressions represents 28 less than three times a number? 28 - 3x 3x - 28 28 + 3x 3x + 28 Answer Now

12. Write a verbal expression for: 1) 8 + a . The ratio of m to r Do you have a different way of writing these? The sum of 8 and a 2)

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

14. Which of the following expressions represents the sum of 16 and five times a number? 5x - 16 16x + 5 16 + 5x 16 - 5x Answer Now

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

16. How is it said? 2 1 Two to the first power 2 2 Two to the second power or two squared 2 3 Two to the third power or two cubed 2n 7 Two times n to the seventh power

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

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

19. Evaluate. 2 1 2 2 2 2 • 2 = 4 2 3 2 • 2 • 2 = 8 2n 7 We can’t evaluate because we don’t know what n equals to!!

20. Is 3 5 the same as 5 3 ? Evaluate each and find out! 3 5 = 3 • 3 • 3 • 3 • 3 = 243 5 3 = 5 • 5 • 5 = 125 243 ≠ 125 They are not the same!