Name:_______________________________ 3.2 Writing Expressions and Equations To translate statements into expressions and equations: 1) Identify __KEY__ __WORDS____ that indicate the operation. 2) Write the numbers/variables in the correct order. The SUM of _____5_______ and ______8______: _____5 + 8_____ The DIFFERENCE of ___n_____ and ____3______ : _____n – 3______ The PRODUCT of ____4______ and ____b – 1____: __4(b – 1)___ The QUOTIENT of ___4_____ and ____ b – 1_____: 4 ÷ (b – 1) or Write each verbal phrase as an algebraic expression. 1. the sum of 8 and t 8 + t 2. the quotient of g and 15 3. the product of 5 and b 5b 4. the difference of 32 and x 32 – x SWITCH THE LESS THAN the first number subtracted ORDER OF from the second! THE TERMS! MORE THAN 5. Eight more than x _x +8_ 6. Six less than p __p – 6___ Write the phrase five dollars less than Jennifer earned as an algebraic expression. Key Words five dollars less than Jennifer earned Variable Let d represent # of $ Jennifer earned Expression d – 5 6. 14 less than f f – 14 7. p more than 10 10 + p 8. 3 more runs than Pirates scored P + 3 9. 12 less than some number n – 12 10. Arthur is 8 years younger than Tanya 11. Kelly’s test score is 6 points higher than Mike’s IS, equals, is equal to Substitute with equal sign. 7. 5 more than a number is 6. 8. The product of 7 and b is equal to 63. n + 5 = 6 7b = 63 9. The sum of r and 45 is 79. 10. The quotient of x and 7 is equal to 13. r + 45 = 79 = 13 TWICE = DOUBLE = 2 times a number = multiply by 2 Addition Phrases Expression Subtraction Phrases Expression 8 more than a number The difference of r and 6 The sum of 8 and a number x + 8 r decreased by 6 r - 6 x increased by 8 6 less than a number the total of x and 8 6 subtracted from a number Multiplication Phrases Expression Division Phrases Expression Twice a number The quotient of z and 3 The product of 2 and n 2n A number divided by 3 2 multiplied by a number The ratio of z and 3 2 times a number Practice: Underline key words. Write each phrase as an algebraic expression or equation. 11. Seven less than a number is 15 n – 7 = 15 12. The total of 5 and c 5 + c 13. 7 less than m m – 7 14. The sum of a number and 16 is 23 n + 16 = 23 15. the score increased by 8 points s + 8 16. The quotient of w and 10 is equal to 7 =7 18. 17 more than some number is 57 n – 17 = 57 19. $12 less than the original price is $48 p–12=48 20. twice as many points as Bob has 2B 21. (– 65) is 5 times a product of 5 and a number -65 = 5(5n) Translate each expression or equation into a word expression or statement. 22) 9y the product of 9 and number y________________ 23) x – 8 = 14 _8 less than a number is 14.__ 24) = 24 __the quotient of y and 12 is 24___ Writing Two-Step Expressions and Equations Six less than twice a number x is four Two less than the quotient of 15 and a number 2x – 6 = 4 – 2 = 15 Nine times a number decreased by four ← 4 is subtracted at the very end 9n – 4 YOU MUST USE PARENTHESES for · or ÷ Five times the sum of six and some number THE (SUM) or (DIFFERENCE)! 5 (6 + n) Twice the difference of y and three The quotient of 7 and d decreased by 9 2 ( y – 3) – 9 The sum of 5 and product of 7 and x The difference of 9 and the quotient of s and –4 5 + 7x 9 – The product of 4 and the difference of x and 3 The product of the difference of x and 3 and 4 4( x – 3) (x – 3)4 7. Five less than twice a number is 7. __2n – 5 = 7____ 8. One less than the product of four and a number is 11. __4n – 1 = 11_ 9. Ten more than the quotient of a number and 3 is 12. + 10 = 12__________ 10. The sum of 9 and the quotient of x and 7 is 11. _9 + _= 11_________ 11. The product of 2 and the sum of 5 and t is 8. ___2(5 + t) = 8___ 12. Ten less than the quotient of a number and −2 is three ___ – 10 = 3_______ 13. 7(b + 2) _The product of 7 and the sum of b and 2_ 14. 2c – 5 __5 less than twice a number_________ .