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. 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. Example 1: Write an algebraic expression for: a) m increased by 5. b) 7 times the sum of x and t. m + 5 7(x + t)

9. c) 11 less than 4 times a number. d) two more than 6 times a number. e) the quotient of a number and 12. 4y - 11 6f + 2 t ÷ 12 or

10. 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

11. 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

12. Example 2: Write a verbal expression for: a) 8 + a. Do you have a different way of writing these? b)

13. Which of the following verbal expressions represents 2x + 9? 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

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

15. base and 3 is called the exponent. 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 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

17. Which of the following verbal expressions represents x 2 + 2x? 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

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

19. EXAMPLE 3 Find a unit rate A car travels 110 miles in 2 hours. Find the unit rate. 110 miles 2 hours = 1 hour 55 miles 2 hours 2 110 miles 2 = The unit rate is 55 miles per hour, or 55 mi/h ANSWER

20. SOLUTION Cell Phones EXAMPLE 4 Solve a multi-step problem Your basic monthly charge for cell phone service is $30, which includes 300 free minutes. You pay a fee for each extra minute you use. One month you paid $3.75 for 15 extra minutes. Find your total bill if you use 22 extra minutes. STEP 1 Calculate the unit rate. 15 3.75 = 0.25 1 = $.25 per minute

21. EXAMPLE 5 Solve a multi-step problem Write a verbal model and then an expression. Let m be the number of extra minutes. STEP 2 30 + 0.25 m

22. EXAMPLE 5 Solve a multi-step problem Evaluate the expression when m = 22. 30 + 0.25(22) = 35.5 ANSWER The total bill is $35.50. STEP 3