# Algebraic Expressions PowerPoint

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

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

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

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Write an algebraic expression for each word phrase. Additional Example 1: Translating Word Phrases into Math Expressions 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 3 increased by the difference of p and 5 3 + ( p – 5 ) 3 + ( p – 5)

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

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

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

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

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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. Additional Example 3: Writing and Evaluating Expressions in Word Problems \$10 • n Combine n equal amounts of \$10. 10 n Cost in dollars 20 10( 20 ) \$200 21 10( 21 ) \$210 22 10( 22 ) \$220 23 10( 23 ) \$230 Evaluate for n = 20, 21, 22, and 23. n 10 n Cost

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

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Write a word problem that can be evaluated by the algebraic expression 27 + t , and evaluate the expression for t = 1.76. Additional Example 4: Writing a Word Problem from a Math Expression 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.

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Write a word problem that can be evaluated by the algebraic expression 43 – d , and evaluate the expression for d = 10.24. Check It Out! Example 4 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.