1. Unit 4 Study GuideMath 6 Overhead Version

2. 1) Define inverse operations. • Inverse operations are operations that “undo” each other: addition/subtraction; multiplication/division

3. 2) Explain the difference between an expression and an equation. • An equation has a set value or a mathematical sentence that contains an = sign; • Example 4 + 2 = 6 • An expression will change as the value of the variable changes OR • An expression is a variable or combination of variables, numbers, and symbols that represents a mathematical relationship • An expression is a math sentence that contains numbers, symbols (not equals) and letters AND the value of the variable can change. • Example 3a + 4

4. 3) Give the definition of variable and constant. • A variable is a letter or symbol that represents a quantity that can change. • Example: a b c • A constant is a quantity that does not change. • Example: 5 13 116

5. 4) Solve the expression 24 ÷ 2³ - 2 + 19 24 ÷ 2³ - 2 + 19 24 ÷ 8 – 2 + 19 3 – 2 + 19 1 + 19 20

6. 5) Solve the expression 52 + 33 – (22 ÷ 2) 52 + 33 – (22 ÷ 2) 52 + 33 - (11) 52 + 27 – (11) 79 – (11) 68

7. Solve the equations.6) 8 8 1x = 12 x = 12

8. Solve the equations.7) x – 47 = 83 x – 47 = 83 +47 +47 x – 0 = 130 x = 130

9. Solve the equations.8) x + 34 = 55 x + 34 = 55 -34 -34 x – 0 = 21 x = 21

10. Solve the equations.9) 6 6 1x = 72 x = 72

11. 10) What is the product of 9 and 3 decreased by x if x = 15? 9 3 – x 9 3 – 15 27 – 15 12

12. 11) Evaluate the expression ab – c + d if a = 9, b = 7, c = 6, and d = 5. ab – c + d 9 7 – 6 + 5 63 - 6 + 5 57 + 5 62

13. 12) Given the equations below, find the product of x and y. 6x = 72 = 10 5 6 6 1x = 12 1y = 50 x = 12 y = 50 12 50 600

14. 13) Simplify: The quotient of x and 3if x = 45. x 3 45 3 15

15. 14) Write this out as a mathematical sentence: The difference of a number and four is eleven. n – 4 = 11

16. 15) If 3 pairs of shoes cost $69, how much would 1 pair cost? Write an equation and solve. 69 = 3n OR 69 ÷ 3 = n 69 ÷ 3 = n 23 = n

17. 16) What is the length of a rectangle that has an area of 35 cm2 and a width of 5 cm? Write an equation and solve. area = length x width 35 = L x 5 5 5 7 = L

18. 17) From your house, you travel 5 miles to your friend John’s house. From John’s house you go to visit Emma. When you get to Emma’s house you realize that you have traveled a total of 17 miles. Write an equation to show how far you have traveled. Solve the equation to find how far it is from John’s house to Emma’s house. (Draw a picture)

19. 18) Rashad spent $117 on batteries. If n represents the number of batteries purchased and each battery was $9, write an equation to represent how many batteries he bought. (Use 117, n, and 9 in the equation.) 117 = 9n 9 9 1 3 = n

20. 19) Jaime drives from Marietta to Atlanta and back again five times a week. The approximate distance from Marietta to Atlanta is 32 miles. How many total numbers of miles driving is round trip for 5 days? • (Think: How many times does Jamie drive to Atlanta from Marietta in one day? Think about it.) 2 32 5 62 5 320

21. 20) If a rectangle has an area of 48in.² and a width of 8in., what is the length of the base? (The in2 means that the unit is being squared, not the number.) area = length x width 48 = L x 8 8 8 6 = L