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Algebra Unit Review Name: _______ANSWER KEY___________ Date: _______________________ Directions: In your own words, explain what each term means. 1) Order of Operations The order in which operations are done in calculations. (PEMDAS) 2) Variable A symbol, usually a letter, used to represent a number. 3) Inverse Operations Operations that undo each other. (Opposites) It states that multiplying a sum (or difference) is the same as multiplying each number in the sum (or 4) Distributive difference) by the number and adding (or subtracting) Property the products. Ex: 5(3+2)=25 and 5x3+5x2=25 Ex: 5(3-2)=5 and 5x3-5x2=5 The order of addends (or factors) can be changed and 5) Commutative the sum (or product) remains the same. Property Ex: 7+3=10 and 3+7=10 Ex: 8x2=16 and 2x8=16 Addends (or factors) can be regrouped and the sum (or product) remains the same. 6) Associative Ex: 1+(3+5)=9 and (1+3)+5=9 Property Ex: 2x(4x3)=24 and (2x4)x3=24 Directions: Evaluate each expression. Make sure to use your order of operations. Don’t forget to show your work! 7. 53 – 8 x 4 + 9 53 – 32 + 9 21 + 9 30 9. 3 x 6 + (18 - 5) 3 x 6 + 13 18 + 13 31 8. 5 x 8 + 63 ÷ 9 40 + 63 ÷ 9 40 + 7 47 10. 17 + (44-8) ÷ 6 17 + 36 ÷ 6 17 + 6 23 11. 54 ÷ y + 13 x 2; y = 6 12. 39 + 18 – n x 7; n=4 54 ÷ 6 + 13 x 2 39 + 18 – 4 x 7 9 + 13 x 2 39 + 18 – 28 9 + 26 57 – 28 35 29 Directions: Evaluate each equation. Don’t forget to show your work! 13. 8y = 40 14. ÷8 x7 ÷8 y = 5 x7 n = 105 15. y + 13 = 92 -13 = 15 16. n ÷ 9 = 14 -13 Y = 79 x9 x9 n = 126 Directions: Translate the following mathematical equations into words. 17. n x 7 = 70 a number times 7 equals 70 18. k - 17 = 15 a number minus 17 equals 15 19. 2n +9 = 17 2 times a number plus 9 equals 17 20. 35-8y = 3 35 minus eight times a number equals 3 Directions: Write a mathematical equation for each word problem, then solve. 21. Two of the same candy bars and a $1 soda cost $5. How much was each candy bar? 2x + 1 = 5 -1 -1 2x = 4 ÷2 ÷2 x = 4 Each candy bar cost $4 22. Three sets of cards, each containing the same number of cards, were spread out and added to 5 loose cards, giving a total of 26 cards. How many cards were in each set? 3x + 5 = 26 -5 -5 3x = 21 ÷3 ÷3 x = 7 Each set contained 7 cards 23. Five packets of balloons and 4 loose balloons totaled 59 balloons. How many balloons are in each packet? 5x + 4 = 59 -4 -4 5x = 55 ÷5 = ÷5 X = 11 Each packet contains 11 balloons. 24. Roberta’s age, increased by 5, and then doubled is 46. How old is she? (X + 5) x 2 = 46 ÷2 ÷2 X + 5 = 23 -5 -5 X = 18 Roberta is 18 years old.