Study Guide and Intervention

Transcription

1 Study Guide and Intervention An algeraic expression is a comination of variales, numers, and at least one operation. To evaluate an algeraic expression, replace the variale(s) with numers and follow the order of operations. Example 1 ALGEBRA Evaluate each expression if r 6 and s. a. 8s r. 3(r s) 8s r 8 6 Replace r with 6 and s with. 3(r s) 3( 6) Sutract. 4 Replace r with 6 and s with. Evaluate the parentheses. Example a. Assuming no other points, write an expression for a team s total points. Words Variales Expression 3f 6t Exercises three points for field goals and six points for touchdowns Let f numer of field goals and t numer of touchdowns. The total points for the team is 3f 6t.. Find the total score if a team scored two field goals and three touchdowns. 3f 6t FOOTBALL Teams earn three points for field goals and six points for touchdowns. Replace f with and t with 3. Add. The team scored a total of 4 points. ALGEBRA Evaluate each expression if x 10, y 5, and z x y z. x 3. x 4z 4. xy z y 6y x( z) 7. x y 8. (x y) 1 0z z Translate each phrase into an algeraic expression. 9. eight inches taller than Mycala s height 10. twelve more than four times a numer 11. the difference of sixty and a numer 1. three times the numer of tickets sold Glencoe/McGraw-Hill 11 Glencoe Pre-Algera

2 Skills Practice ALGEBRA Evaluate each expression if x 4, y 6, and z x y z. 3x y 3. x z 4. x y 3z 5. 15z 6. 3(x z) 7. xz y 8. yz x ALGEBRA Evaluate each expression if a 7, 9, c, and d a c 10. a (c d) 11. 3a 4d 1. cd 13. (a ) (c d) 14. c(4 d) a 3c a c c 17. a cd 18. a d 19. two inches shorter than Kathryn s height 0. the quotient of some numer and thirteen 1. some numer added to seventeen. six centimeters shorter than the length of the pencil 3. three pounds lighter than Adlai s weight 4. the difference of some numer and eighteen 5. three dollars more than the cost of a ticket 6. eight more than the product of a numer and four 7. half as many pieces of candy 8. twice as long as the length of the string Glencoe/McGraw-Hill 1 Glencoe Pre-Algera

3 Practice ALGEBRA Evaluate each expression if x 1, y 0, and z x y z. 4x y 3. 3x y 4. y 3z 5. x y z 6. yz x 7. (y x) (y z) 8. y z x z 9. 5 x 3y 10. z( y x) 4z ALGEBRA Evaluate each expression if a 3, 6, c 5, and d a c d 1. (a c) 13. a c 14. 6d c c 15. 3(a c) c 17. ac (6c 3d) 19. ( a ) 0. 4[(d a) c] 6( c) 1. six times a numer minus eleven. the product of eight hundred and a numer 3. the quotient of thirty and ten times a numer 4. five times the sum of three and some numer 5. half the distance to the school. 6. RECYCLING In order to encourage recycling, the city is offering five cents for every pound of newspapers collected, twenty-five cents per pound for cans and ten cents per pound for glass ottles or jars. a. Write an expression for the total amount earned from recycling.. If Chen rings in ten pounds of newspapers, eight pounds of cans, and two pounds of glass, how much will he receive? Glencoe/McGraw-Hill 13 Glencoe Pre-Algera

4 Answers () Study Guide and Intervention An algeraic expression is a comination of variales, numers, and at least one operation. To evaluate an algeraic expression, replace the variale(s) with numers and follow the order of operations. Example 1 ALGEBRA Evaluate each expression if r 6 and s. a. 8s r. 3(r 1 s) 8s r 5 8??6 Replace r with 6 and s with. 3(r 1 s) 5 3( 1 6) Replace r with 6 and s with ?8 Evaluate the parentheses. 5 4 Sutract. 5 4 Example a. Assuming no other points, write an expression for a team s total points. Words three points for field goals and six points for touchdowns Variales Let f 5 numer of field goals and t 5 numer of touchdowns. Expression 3f 1 6t The total points for the team is 3f 1 6t.. Find the total score if a team scored two field goals and three touchdowns. 3f 1 6t 5 3? 1 6?3 Replace f with and t with Add. The team scored a total of 4 points. Exercises ALGEBRA Evaluate each expression if x 10, y 5, and z x 1 y z 14. } x y 5. } 1 6 y 0 } 3. x 1 4z 4 4. xy 1 z 51 } 3 6. x( 1 z) x y 0 8. } (x 1 z z y) } 15 Translate each phrase into an algeraic expression. 9. eight inches taller than Mycala s height h twelve more than four times a numer 4n the difference of sixty and a numer 60 n 1. three times the numer of tickets sold 3t Glencoe/McGraw-Hill 11 Glencoe Pre-Algera Skills Practice ALGEBRA Evaluate each expression if x 4, y 6, and z x 1 y 1 z 13. 3x 1 y x z 1 4. x 1 y 3z z (x 1 z) 1 7. xz 4 y 8. yz x 14 ALGEBRA Evaluate each expression if a 7, 9, c, and d a 1 1 c a 1 (c 1 d) a 1 4d cd (a 1 )?(c 1 d) c(4 1 d) } } a 1 3c 10 a 1 c c 17. a cd } } 9 a d 19. two inches shorter than Kathryn s height k 0. the quotient of some numer and thirteen n some numer added to seventeen n 17. six centimeters shorter than the length of the pencil p 6 3. three pounds lighter than Adlai s weight s 3 4. the difference of some numer and eighteen n three dollars more than the cost of a ticket t 3 6. eight more than the product of a numer and four 4n 8 7. half as many pieces of candy } c } 8. twice as long as the length of the string s Glencoe/McGraw-Hill 1 Glencoe Pre-Algera FOOTBALL Teams earn three points for field goals and six points for touchdowns. Answers Glencoe/McGraw-Hill A7 Glencoe Pre-Algera

5 Practice ALGEBRA Evaluate each expression if x 1, y 0, and z x 1 y 1 z 36. 4x y x 1 y y 3z 8 5. x 1 y z yz 1 x 9 7. (y x) 1 (y z) 4 8. } y z } 1 }x z } 8 9. } 5 x } z( y x) 1 4z 48 3 y ALGEBRA Evaluate each expression if a 3, 6, c 5, and d a 1 1 c 1 d 3 1. } (a 1 1 c) } a 1 c d c?c (a 1 1 c) } } 4 5 c 17. ac (6c 3d) } 6 a 1 c) } [(d a) 1 c] six times a numer minus eleven 6n 11. the product of eight hundred and a numer 800n 3. the quotient of thirty and ten times a numer 30 (10n) 4. five times the sum of three and some numer 5(3 n) 5. half the distance to the school. } c } 6. RECYCLING In order to encourage recycling, the city is offering five cents for every pound of newspapers collected, twenty-five cents per pound for cans and ten cents per pound for glass ottles or jars. a. Write an expression for the total amount earned from recycling. 5n 5c 10. If Chen rings in ten pounds of newspapers, eight pounds of cans, and two pounds of glass, how much will he receive? $.70 Glencoe/McGraw-Hill 13 Glencoe Pre-Algera R eading to Learn Mathematics Pre-Activity How are variales used to show relationships? Do the activity at the top of page 17 in your textook. Write your answers elow. a. Suppose the ay-sitter worked 10 hours. How much would he or she earn? $50. What is the relationship etween the numer of hours and the money earned? The amount earned is five times the numer of hours. c. If h represents any numer of hours, what expression could you write to represent the amount of money earned? 5h Reading the Lesson 1 3. See students work. Write a definition and give an example of each new vocaulary word or phrase. Vocaulary Definition Example 1. variale. algeraic expression 3. defining a variale 4. Name three things that make an algeraic expression. variales, numers, and operations 5. Why do you think replacing a variale with a numer is called the Sustitution Property of Equality? If two quantities are equal, then one can e sustituted, or replaced, for the other. Helping You Rememer 6. Variale is a word used in everyday English. a. Find the definition of variale in the dictionary. Write the definition. ale or apt to vary; suject to variation or changes. Explain how the English definition can help you rememer how variale is used in mathematics. See students answers. Glencoe/McGraw-Hill 14 Glencoe Pre-Algera ( ( ) Answers () Glencoe/McGraw-Hill A8 Glencoe Pre-Algera