1. Objective The student will be able to: translate verbal expressions into math expressions and vice versa.

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. VOCABULARY A numerical expression is a mathematical phrase with only numbers and operation symbols (+, -, x, ÷). Example: 8 + 5 - 2 An algebraic expression is a mathematical phrase that contains a variable and operation symbols. A variable is a symbol (usually a letter) that stands for a number. Algebraic expression: 5y + 2

4. Evaluating Algebraic Expressions Replace the variable with the value that you are given. Now we have a numerical expression. Solve using order of operations.

5. Example: Evaluate 2b-8 for b=11 2b-8 Substitute the 11 for the variable. 2(11)-8 Multiplying comes before subtracting. 22 - 8 14

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

7. 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?

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

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

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

11. 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

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

13. Which of the following expressions represents 7 times a number decreased by 13? 1.7x + 13 2.7x - 13 3.13 - 7x 4.13 + 7x Answer Now

14. Which one of the following expressions represents 28 less than three times a number? 1.28 - 3x 2.3x - 28 3.28 + 3x 4.3x + 28 Answer Now

15. 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)

16. 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 9 4.9 less than twice a number

17. Which of the following expressions represents the sum of 16 and five times a number? Answer Now 1.5x - 16 2.16x + 5 3.16 + 5x 4.16 - 5x

18. 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

19. 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

20. 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

21. Which of the following expressions represents four less than the cube of a number? Answer Now 1.4 – x 3 2.4 – 3x 3.3x – 4 4.x 3 – 4

22. Evaluate. 2 1 22 2 2 = 4 2323 2 2 2 = 8 2n 7 We can’t evaluate because we don’t know what n equals to!!

23. 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!

24. Translate each verbal expressions into an algebraic expression: (a)the sum of 8 and y (b) 4 less than x (c) a number decreased by one (d) The difference between x and y (e) One half of a (f) Nine less than the total of 9 and a number 8 + y x - 4 n - 1 x - y ½ a (9 + n)- 9

25. Write an algebraic expression to describe Jerry’s age. Use the following information: Jerry is 4 years younger than his brother Steve. First, we have to know how old Steve is. We do not have an age for Steve, soFirst, we have to know how old Steve is. We do not have an age for Steve, so we will use a variable: Let s = Steve’s age Now that we have determined Steve’s age (s), we can use it to determine Jerry’s age. Jerry is 4 years younger than Steve. j = s - 4

26. If Steve is 22 years old, then how old is Jerry? j = s – 4 j = 22 - 4 j = 18 Jerry is 18 years old.