Name Class Date. Tell whether each expression is a numerical expression or a variable expression. For a variable expression, name the variable.

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1 Practice 1-1 Variables and Expressions Write an expression for each quantity. 1. the value in cents of 5 quarters 2. the value in cents of q quarters 3. the number of months in 7 years the number of months in y years 5. the number of gallons in 21 quarts the number of gallons in q quarts Write a variable expression for each word phrase less than k m divided by 6 9. twice x 4 more than twice x 11. the sum of eighteen and b three times the quantity 2 plus a Tell whether each expression is a numerical expression or a variable expression. For a variable expression, name the variable d k (12) The room temperature is c degrees centigrade. Write a word phrase for each expression (9) 6 c p x 22. c 2 7 Pre-Algebra Chapter 1 Lesson 1-1 Practice 1

2 Practice 2-1 Properties of Numbers Simplify each expression using mental math. 1. 4? 13? ? 3? 4? (286) 125? 9? ? 7? ? 12? (29) Write the letter of the property shown (mn) 5 (14m)n k? 1 5 k (x 1 y) 1 z 5 x 1 (y 1 z) 65t 5 t(65) p p n 5 1? n (x 1 p) 1 (r 1 t) 5 (r 1 t) 1 (x 1 p) (h 1 0) h 1 4 x 1 yz 5 x 1 zy Evaluate each expression using mental math. 23. x(yz), for x 5 8, y 529, z ? 1? 30 a. commutative property of addition b. associative property of addition c. commutative property of multiplication d. associative property of multiplication e. additive identity f. multiplicative identity 2 q 1 r 1 s, for q 5 46, r 5 19, s a(b)(2c), for a 5 7, b 522, c 5 15 Pre-Algebra Chapter 2 Lesson 2-1 Practice 1

3 Practice 2-2 The Distributive Property Write an expression using parentheses for each model. Then multiply Multiply each expression. 3. 6(h 2 4) 5. 23(x 1 8) 7. 2(7n 2 11) Use the distributive property to simplify ? 7 9? ? 8 7(2,009) ? 5 30? ? ? 5 7? (23) (3) 1 (24)(6) 6(8) 1 6(22) Solve using mental math. (p 1 3)5 (4 2 y)(29) 210(2a 1 5) 19. A shipping container holds 144 boxes. How many boxes can be shipped in 4 containers? 2 Lesson 2-2 Practice Pre-Algebra Chapter 2

4 Practice 2-3 Simplifying Variable Expressions Simplify each expression y m m 3. 5(3t) 2 7(2t) 2x 2 9y 1 7x 1 20y 5. 3(9k 2 4) 2 4(5n 2 3) 6(g 2 h) 2 6(g 2 h) (a 1 2b) 1 14a 2 9b 27a 1 3(a 2 c) 1 5c 9. 22(25)q 1 (272)(2q) Name the coefficients, any like terms, and any constants. Coefficients Like Terms Constants x 1 7 4m 1 (23n) 1 n 6kp 1 9k 1 kp y 1 6ab ba c 1 2c 1 c 2 5c 1 1 Write an expression for each model. Simplify the expression. 15. Justify each step (n 1 4) 1 9n 5 (5n 1 20) 1 9n 5 5n 1 (20 1 9n) 5 5n 1 (9n 1 20) 5 (5n 1 9n) (5 1 9)n n 1 20 Pre-Algebra Chapter 2 Lesson 2-3 Practice 3

5 Practice 2-4 Variables and Equations Is the given number a solution of the equation? 1. 9k k; g 4 (26) g; e 5 2e 2 16; (x 2 2) 2 5x 5 5(2 2 x); 7 27r r; 23 23p 5 4p 1 35; s s; 3 6a (3a 2 2); 4 Is each equation true, false, or an open sentence? x (5 2 9) (23) Write an equation for each sentence. Is each equation true, false, or an open sentence? 15. One fifth of a number n is equal to 7. The product of 13 and 7 is Fifty-four divided by six equals negative nine. Seven less than the product of a number z and 3 is equal to Write an equation. Is the given value a solution? x (5 2 8) 5 2(10 2 1) 19. A truck driver drove 468 miles on Tuesday. That was 132 miles farther than she drove on Monday. Let d represent the distance she drove on Monday. Did she drive 600 miles on Monday? 4 Lesson 2-4 Practice Pre-Algebra Chapter 2

6 Practice 2-5 Solving Equations by Adding or Subtracting Use mental math to solve each equation k x ,000 1 y 5 9, f p n 81 5 x 2 19 w Solve each equation. 9. m n x x k n k z t 1 (22) The combined enrollment in the three grades at Jefferson Middle School is 977. There are 356 students in the seventh grade and 365 in the eighth grade. Write and solve an equation to find how many students are in the ninth grade. Equation Solution k p c 2 (212) 31 5 p y h 1 (2219) 1,523 1 c 5 2, (27) m x Pre-Algebra Chapter 2 Lesson 2-5 Practice 5

7 Practice 2-6 Solving Equations by Multiplying or Dividing Solve each equation. k x y n m 22 s z x p h m x v h 5 3, , x 2 m A bamboo tree grew 3 in. per day. Write and solve an equation to find how many days d it took the tree to grow 144 in. Equation: Solution: 2 Carl drove 561 miles. His car averages 33 miles per gallon of gas. Write and solve an equation to find how much gas g Carl s car used. Equation: For what values of y is each equation true? Solution: 2 m y 24s g 22x w t 20 5 e 225 y ,000 5 x 240 y y y Lesson 2-6 Practice Pre-Algebra Chapter 2