Algebraic Expressions Essential Question

1. Algebraic Expressions Essential Question How do verbal expressions translate to algebraic expressions?

2. Warm Up Evaluate each expression for the given values of the variables. Which operation symbol goes with each word? 1. 9y – 13 for y = 4 23 2. 6n + 2p for n = 2 and p = 3 18 1 3. 3x–y for x = 1 and y = 2  4. Sum + 5. Product   6. Quotient 7. Difference

3. a or a 7 7 • a number plus 5 • sum of a number and 5 n + 5 • 5 more than a number • subtract 11 from a number x– 11 • difference of a number and 11 • 11 less than a number • 3 multiplied by a number 3 m or3m • product of 3 and a number • 7 divided into a number • quotient of a number and 7

4. Additional Example 1: Translating Word Phrases into Math Expressions Write an algebraic expression for each word phrase. A. 9 less than a number w 9 less than a number w w– 9 w – 9 B. 3 increased by the difference of p and 5 3increased by the difference ofp and 5 3 + (p –5) 3+ (p – 5)

5. f 6 Check It Out! Example 1 Write an algebraic expression for each word phrase. A. 88 times the difference of h and 4 88 times the differenceofh and 4 88 • (h– 4) 88(h – 4) B. the quotient of a number f and 6 quotient off and 6 f 6

6. Additional Example 2: Translating Math Expressions into Word Phrases Write a word phrase for the algebraic expression 9 – 3c. 9 – 3c 9 – 3 •c 9 minus the product of 3 and c 9 minus the product of 3 and c

7. Check It Out! Example 2 Write a word phrase for the algebraic expression 7 + 19b. 7 + 19b 7 + 19 •b 7 plus the productof 19 and b 7 plus the product of 19 and b

8. To solve a word problem, first interpret the action you need to perform and then choose the correct operation for that action.

9. Additional Example 3: Writing and Evaluating Expressions in Word Problems A restaurant leased its banquet hall for a function. The cost was $10 per person. Write an algebraic expression to determine what the cost would be if n people attended the function. Then evaluate the expression for 20, 21, 22, or 23 people. $10 •n Combine n equal amounts of $10. 10n Cost in dollars 2010(20) $200 Evaluate for n = 20, 21, 22, and 23. 2110(21) $210 2210(22) $220 2310(23) $230

10. Check It Out! Example 3 Gasoline costs $1.99 per n gallons. What will the cost be for 10, 12, 14, and 15 gallons? $1.99 •n Combine n equal amounts of $1.99. 1.99n Cost in dollars 101.99(10) $19.90 Evaluate for n = 10, 12, 14, and 15. 12 1.99(12) $23.88 141.99(14) $27.86 151.99(15) $29.85

11. Additional Example 4: Writing a Word Problem from a Math Expression Write a word problem that can be evaluated by the algebraic expression 27 + t, and evaluate the expression for t = 1.76. Possible answer: Amed bought a new sweater for $27 plus sales tax t. If the tax was $1.76, what was the total cost of the sweater? 27 + t 27 + 1.76 = 28.76 Substitute 1.76 for t. The total cost of the sweater was $28.76.

12. Check It Out! Example 4 Write a word problem that can be evaluated by the algebraic expression 43 – d, and evaluate the expression for d = 10.24. Possible answer: Tina bought a new jacket for $43 minus a store credit. If the store credit was $10.24, what did Tina pay for the jacket? 43 – d 43 – 10.24 = 32.76 Substitute 10.24 for d. Tina paid $32.76 for the jacket.