Name: Expressions and Equations

Transcription

1 Name: Expressions and Equations

2 Lesson 1: Verbal Phrases

3 Write an algebraic expression for each statement. 1) 12 more than a number is 8 2) 21 less than x is 22 3) the difference of x and 19 is equal to 5 4) the quotient of u and 7 is equal to 29 5) the product of a number and 11 is equal to 17 6) 9 more than n is 10 7) 11 less than u is 43 8) d divided by 5 is equal to 10 9) the sum of n and 10 is equal to 24 10) the product of q and 6 is equal to 18

4 11) the quotient of n and 4 is 34 12) 6 more than x is equal to 21 13) the quotient of v and 3 is equal to 49 14) the product of a number and 5 is equal to 5 15) the difference of a number and 5 is equal to 46 16) the sum of a number and 11 is equal to 42 17) the product of a number and 9 is 40 18) 13 less than d is 30 19) n divided by 6 is 47 20) 10 less r is 11

5 Lesson 2: Parts of an Expression

6 Identify the terms, like terms, coefficients, constants, and variable of each expression. 1) 3a a Terms: Like Terms: Coefficients: Constants: Variables: 2) q Terms: Like Terms: Coefficients: Constants: Variables: 3) 2y y Terms: Like Terms: Coefficients: Constants: Variables:

7 4) 13x + 11y - 3x + 3y + 9 Terms: Like Terms: Coefficients: Constants: Variables: 5) 18c c Terms: Like Terms: Coefficients: Constants: Variables: 6) 13a a Terms: Like Terms: Coefficients: Constants: Variables:

8 7) 15p + 7q + 5p - 4q Terms: Like Terms: Coefficients: Constants: Variables: 8) z Terms: Like Terms: Coefficients: Constants: Variables: 9) 12x y + 3x - 2y Terms: Like Terms: Coefficients: Constants: Variables:

9 Review Lesson 1 Verbal Phrases Write an algebraic expression for each statement. 1) 5 more than a number is equal to 50 2) the quotient of x and 36 is 12 3) 14 less than k is equal to 22 4) Sam has twelve bracelets. He makes six new bracelets a day. a). Write an algebraic expression that shows how many bracelets he will have after any number of days. b) How many bracelets will he have after 7 days?

10 Lesson 3: Simplifying Expressions

11 Simplify Each Expression 1. 7n - 3n c + 2c 3. 7e + 2e n n a + a n - 2n f - 2f 9. 6m m 10. 2s + 4s c + 5-3c n n n n 14. 4r r y + 3y - 4-2y t - 7-2t + 7t Write a simplified expression for the perimeter of each shape

12 Review Lesson 1 Verbal Phrases Write an algebraic expression for each statement. 1. the difference of a number and 27 is equal to the difference of x and 13 is equal to George has 13 video games. He plans to buy 2 more every month. a). Write an algebraic expression that shows how many video games he will have after any number of months. b) How many video games will he have after 6 months? Lesson 2 Parts of an Expression Identify the terms, like terms, coefficients, and constants of the expression. 4) 14p + 14q + 3p - 1q Terms: Like Terms: Coefficients: Constants:

13 Lesson 4: Simplifying Expressions Using the Distributive Property Day 1

14 Simplify each expression using the distributive property. 1) 2(10y 13) 2) (5a + 11) 3) 2(4a + 12) + 6a 4) (12a - 16) 5) 10c + 4(4c - 6) 6) 9 + 4(11s - 9) 7) 4(2z + 4) 8) 3(a 12) 9) 3a(2 + 5) ) (10q - 12) 11) 12k + 11(3k - 5) 12) 10(x 4) 3x

15 13) 9(a + 10) ) 3(3-7a) + 3(3a - 9) Write a simplified expression for the area of the square and rectangle. (Area = length x width - 3 points) Review Lesson 1 Verbal Phrases Write an algebraic expression for each statement. 1. the difference of twice c and 14 is The quotient of a number and ten

16 3. Tony makes seven dollars an hour at his job and earns a twenty dollar bonus every week. a). Write an algebraic expression that shows how much money he will earn after one week. b) How much money will Tony earn if he worked twenty hours this week? Lesson 2 Parts of an Expression Identify the terms, like terms, coefficients, and constants of the expression b + 14c - 5b + 3c + 35 Terms: Like terms: Coefficient(s): Constant(s): Lesson 3 Simplifying Expressions Simplify the expression. (Careful this one is tricky!) 5. -3x + (-5) 2y + 4x 6xy + 8

17 Write a simplified expression for the perimeter of the triangle. (combine like terms of the sides) 6. x + 2 3x + 4 4x -15 Perimeter =

18 Lesson 4: Simplifying Expressions Using the Distributive Property Day 2

19 Simplify each expression using the distributive property (-8n - 7) 2. -2(-9 + 9t) 3. -3(6b + 6) 4. -7(8 + 3r) 5. 3(-2 + 3m) 6. 7(-8 + 3w) 7. 2(-w 4w) 8. -6(-4q + 8q) 9. -8(-2-5v) - 8(7v + 2) (g - 1) - (-9 + 6g) (8 + 7b) - 3(-4b - 8) 12. 3(-5 + 8d) -7(4 6d) (7-6j) - 3j(9 + 9) 14. 2(4-4m) - 8(-5m + 9)

20 Review Lesson 1 Verbal Phrases Write an algebraic expression for each statement. 1. Two less than six times a number 2. The quotient of a number and ten less eight 3. Isabel has thirty-three stuffed animals that she made. She makes five new stuffed animals a week. a). Write an algebraic expression that shows how many stuffed animals she will have after any number of weeks. b) How many stuffed animals will she have after one year? (Hint: there are 365 days in a year) Lesson 2 Parts of an Expression Identify the terms, like terms, coefficients, and constants of the expression x y + 4x - 3y Terms: Like terms: Coefficient(s): Constant(s):

21 Lesson 3 Simplifying Expressions Simplify each expression y (-2y) Write a simplified expression for the perimeter of the rectangle (combine like terms of the sides). 6. x 2 2x + 2 Perimeter = Lesson 4 Simplifying Expressions using the Distributive Property Write a simplified expression for the area of the rectangle. (Area of a rectangle = length x width) x + 2 Area =

22 Lesson 5: One-Step Addition and Subtraction Equations

23 Show all steps on both sides of the equation, write your solution and circle it, and show your check step. 1. m 38 = -44 check 2. p - 19 = -44 check 3. n 6 = 7 check 4. x + 32 = 33 check 5. n + 13 = -5 check 6. r 44 = 2 check 7. b 37 = -54 check 8. x 31 = -61 check 9. n + 26 = -23 check 10. a + 39 = 72 check 11. v 6 = 9 check 12. x (-7) = 33 check

24 x = 58 check 14. k + 33 = 17 check Write an equation for each problem and solve it. Show all steps on both sides of the equation, write your solution and circle it, and show your check step. 15. Beth won 45 lollipops playing the bean bag toss. After giving some away she only has 28 remaining. How many did she give away? 16. Krystal wants to buy a hat that costs $29. How much change does she receive if she gives the cashier $100? 17. Asanji is cooking a cake. The recipe calls for 6 cups of sugar. He has already put in 5 cups. How many more cups does he need to put in? 18. Rob is cooking a cake. The recipe calls for 9 cups of flour. He has already put in 3 cups. How many more cups does he need to put in?

25 Review Lesson 1 Verbal Phrases Write an algebraic expression for each statement. 1. the difference of x and 13 is equal to less than n is Jack has fifty-four matchbox cars. His mom buys him two more every week. a). Write an algebraic expression that shows how many matchbox cars he will have after any number of weeks. b) How many matchbox cars will he have after 10 weeks? Lesson 2 Parts of an Expression Identify the terms, like terms, coefficients, and constants of the expression a a Terms: Like terms: Coefficient(s): Constant(s):

26 Lesson 3 Simplifying Expressions Simplify each expression (-3x) x - 4 Write a simplified expression for the perimeter of the rectangle (combine like terms of the sides). 6. x 3x -5 Perimeter = Lesson 4 Simplifying Expressions using the Distributive Property 7. 14a + 5(4a - 3) 8. -8(-5 4y) - 5(5x + 8)

27 Write a simplified expression for the area of the rectangle. (Area of a rectangle = length x width) y - 10 Area =

28 Lesson 6: One-Step Multiplication and Division Equations

29 Show all steps on both sides of the equation, write your solution and circle it, and show your check step. m check 2. 10x = 130 check n = 143 check 4. x 3 10 check x r check check n = 195 check 8. -6x = 54 check 9. x v check check

30 11. -6y = 78 check 12. x 9 6 check 13. x 15 5 check k = -91 check Write an equation for each problem and solve it. Show all steps on both sides of the equation, write your solution and circle it, and show your check step. 15. How many boxes of cereal can you buy with $15 if one box costs $5? 16. DeShawn bought five fancy pens for a total of $20. How much did each pen cost? 17. At a restaurant, Imani and her six friends decided to divide the bill evenly. If each person paid $12 then what was the total bill?

31 18. Cereal cost $2 / box. How many boxes did Joe buy if he spent $6? Review Lesson 1 Verbal Phrases Write an algebraic expression for each statement. 1. the difference of n and 12 is twice a number is Eli has 23 rocks in her collections. She adds one rock a day to her collection. a). Write an algebraic expression that shows how many rocks she will have after any number of days. b) How many rocks will Eli have after 2 weeks? (careful)

32 Lesson 2 Parts of an Expression Identify the terms, like terms, coefficients, and constants of the expression q + 6-6q Terms: Like terms: Coefficient(s): Constant(s): Lesson 3 Simplifying Expressions Simplify the expression. 5. 4x + 5 3y Write a simplified expression for the perimeter of the rectangle (combine like terms of the sides). 6. 2x 2x + 10 Perimeter =

33 Lesson 4 Simplifying Expressions using the Distributive Property 7. 5(a 20) 10 + a 8. -2(7-8y) - 3(-5 + 4y) Write a simplified expression for the area of the rectangle. (Area of a rectangle = length x width) 9. 3 y + 10 Area =

34 One-Step Equations All Operations

35 Show all steps on both sides of the equation, write your solution and circle it, and show your check step. 1. x + 7 = 26 check 2. n 6 13 check 3. x 5 12 check 4. x + 19 = 26 check 5. b 11 = -21 check 6. v 10 = 9 check 7. n 1 = -7 check 8. m check 9. -2x = -12 check n = -126 check k 11. x + 14 = 19 check check

36 13. x + 6 = -12 check 14. a 6 20 check 15. n + 14 = 3 check 16. p 19 = -15 check Write an equation for each problem and solve it. Show all steps on both sides of the equation, write your solution and circle it, and show your check step. 17. Jennifer won 75 lollipops playing the bean bag toss at her school's game night. Later, she gave one to each of her friends. She only has 52 remaining. How many did she give away? 18. How many boxes of cereal can you buy with $9 if one box costs $3? 19. Elisa and her best friend found some money in an envelope. They split the money evenly, each getting $25. How much money did they find?

37 20. Mary wants to buy a sled for $105. She gives the cashier $200. How much change does she receive? 21. Find the price of one candy bar if three candy bars cost $ Four workers are hired to weed a field by hand. Each is given a plot which is 7 7 feet in size. What is the total area of the field? Review Lesson 1 Verbal Phrases Write an algebraic expression for each statement. 1. seven less a number is a number less than seven is 12

38 3. Adam has 52 guitar picks. He buys a new pack of ten every month. a). Write an algebraic expression that shows how many picks he will have after any number of months. b) How many picks will Adam have after 4 months? Lesson 2 Parts of an Expression Identify the terms, like terms, coefficients, and constants of the expression s t + 2t + 7s Terms: Like terms: Coefficient(s): Constant(s): Lesson 3 Simplifying Expressions Simplify the expression s t + 2t + 7s

39 Write a simplified expression for the perimeter of the rectangle (combine like terms of the sides) x + 12 Perimeter = Lesson 4 Simplifying Expressions using the Distributive Property 7. 2(10b + 8) (9m + 9) - 2(-6m + 9) Write a simplified expression for the area of the rectangle. (Area of a rectangle = length x width) x + 4 Area =

40 Lesson 7: Two-Step Equations Day 1

41 Show all steps on both sides of the equation, write your solution and circle it, and show your check step 1. n check 2. 1 r 9 0 check 3. 3 x 2 check b = -14 check 9 x v check check

42 x a = 21 check check p 9. 3k - 2 = 1 check check x check 12. -m - 4 = -4 check n check r = 35 check

43 15. 2 x 1 9 n check check b v = 11 check check x = 5 check k = -15 check 21. 3x - 1 = -10 check x = -8 check

44 23. -2p - 3 = -19 check n 3 6 check m check x = 15 check n = 42 check m 2 3 check r x = -5 check check

45 Review Lesson 1 Verbal Phrases Write an algebraic expression for each statement. 1. the quotient of a number a seven is Emily has 3 pairs of drum sticks. She plans on buying two new pair every month. a). Write an algebraic expression that shows how many pairs of drum sticks he will have after any number of months. b) How many pairs of drumsticks will Emily have after 6 months? Lesson 2 Parts of an Expression Identify the terms, like terms, coefficients, and constants of the expression. 4. w + 8w 6 7w Terms: Like terms: Coefficient(s): Constant(s):

46 Lesson 3 Simplifying Expressions Simplify the expression. 5. w + 8w 6 7w Write a simplified expression for the perimeter of the rectangle (combine like terms of the sides) x + 2 Perimeter = Lesson 4 Simplifying Expressions using the Distributive Property 7. 10(3-3x) + 3(5x - 4) 8. -7(-3-2g) - 6(5g + 9) Write a simplified expression for the area of the rectangle. (Area of a rectangle = length x width) x - 5 Area =

47 Lesson 7: Two-Step Equations Day 2

48 Write an equation for each problem and solve it. Use a let statement where needed. Show all steps on both sides of the equation, write your solution and circle it, and show your check step. 1. A basketball team played 25 games. They won 7 more games than they lost. How many games did they win and lose? Let = Equation: 2. Fred has twice as much money as Jake. Together they have $54. How much money does each have? Let = Equation: 3. There are 15 more girls than boys in camp. There are 135 campers in all. How many boys and how many girls are there? Let = Equation:

49 4. A car dealer sold 37 vehicles. They sold 5 more cars than trucks. How many cards and trucks were sold? Let = Equation: 5. A hog weighs twice as much as sheep. Together they weigh 285 pounds. How much does each weigh? Let = Equation: 6. An apple has twice as many calories as a peach. The two fruit together have 105 calories. How many calories are in each fruit? Let = Equation:

50 7. The Bruins scored a total of 114 points in their first two games. They scored twice as many points in the second game than the first. How many points did they score in each game? Let = Equation: 8. Jackson s golf score is 6 less than Devon s. Their two scores total 156. What is each boys score? Let = Equation: 9. Alexis has three times as much money as Cora. Together they have $40. How much money does each have? Let = Equation:

51 10. A board 140 cm long is cut into two pieces. One piece is 6 cm longer than the other. Find the length of both pieces. Let = Equation: Review Lesson 1 Verbal Phrases Write an algebraic expression for each statement. 1. three more than a number 2. fives times a number added to six is twenty-one 3. Isabel has 5 different colors of paint. To increase her collection, she plans on buying three new jars of paint a week. a). Write an algebraic expression that shows how many jars of paint she will have after any number of weeks. b) How many jars of paint will Isabel have after 3 weeks?

52 Lesson 2 Parts of an Expression Identify the terms, like terms, coefficients, and constants of the expression. 4. 7x - 5t + 5x - q + 3t Terms: Like terms: Coefficient(s): Constant(s): Lesson 3 Simplifying Expressions Simplify the expression. 5. 7x - 5t + 5x - q + 3t Write a simplified expression for the perimeter of the rectangle (combine like terms of the sides). 6. 2x 5x Perimeter =

53 Lesson 4 Simplifying Expressions using the Distributive Property 7. 19s + 3(3s - 12) 8. -7(9-5v) - 3(-3 5v) Write a simplified expression for the area of the rectangle. (Area of a rectangle = length x width) x + 25 Area = Lesson 5 & 6 One Step Equations Show all steps on both sides of the equation, write your solution and circle it, and show your check step x = -8 Check: 11. y + 10 = 32 Check: 12. x 13 = 13 Check: x 2 Check:

54 Write an equation for each problem and solve it. Show all steps on both sides of the equation, write your solution and circle it, and show your check step. 14. Five less than a number equals 20. Write an equation for each problem and solve it. Use a let statement where needed. Show all steps on both sides of the equation, write your solution and circle it, and show your check step. 15. The sale price of a video game is $48. This is $12 less than the regular price. How much is the regular price of the video game? Let = Equation:

55 All Equation Review Day

56 Show all steps on both sides of the equation, write your solution and circle it, and show your check step. 1.) x + 6 = 8 2.) x + 7 = 15 3.) x - 10 = ) x - 2 = 6 5.) 8 + x = 8 6.) - 5 = x ) x - 10 = ) -1 + x = ) -1 = x ) 4x = ) - 5-4x = ) - 7-2x = 13

57 13.) x = ) - 6x - 7 = ) x = ) 9 + 7x = ) 4x + 1 = ) 4x + 2 = ) x = ) 2x + 8 = ) 7x - 9 = ) - 4x - 6 = ) - 6x + 6 = ) 4x + 4 = 44

58 Write an equation for each problem and solve it. Use a let statement where needed. Show all steps on both sides of the equation, write your solution and circle it, and show your check step. 25. Joe has $37 more than Moe. Together they have $175. How much money do each of them have? Let = Equation: 26. You bought a magazine for $5 and four erasers. You spent a total of $25. How much did each eraser cost? Let = Equation: 27. Last Friday VJ had $29. Over the weekend he received some money for cleaning the attic. He now has $41. How much money did he receive? Let = Equation:

59 28. Besides his regular wage of $7 per hour, Jack also received $152 in tips this week. How many hours did he work if his total pay was $292? Let = Equation: 29. Maddy won 40 super bouncy balls playing horseshoes at her school's game night. Later, she gave two to each of her friends. She only has 8 remaining. How many friends does she have? Let = Equation: 30. Lisa is cooking muffins. The recipe calls for 7 cups of sugar. She has already put in 2 cups. How many more cups does she need to put in? Let = Equation: