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Single-Variable Expressions Practice Questions

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Updated on Oct 3, 2011

To review these concepts, go to Single-Variable Expressions Study Guide.

Single-Variable Expressions Practice Questions

Problems

Practice 1

  1. 5 – 6 ÷ 2
  2. –2(10 + 3)
  3. 32(7) + 1
  4. (–5 + 12)(21 – 13)
  5. (10 – (8 – 22))3

Practice 2

  1. What is –9z when z = 9?
  2. What is 4u – 3 when u = 7?
  3. What is –8 + 2g when g = –5?
  4. What is + 30 when k = 20?
  5. What is 12(4 – x) when x = 1?
  6. What is q2 + 15 when q = –6?
  7. What is –8m2 when m = 4?
  8. What is 4d ÷ 3 – 20 when d = 12?
  9. What is (2b + 1)2 when b = –2?
  10. What is –5(3a2 – 24) when a = 3?

Practice 3

  1. What is y + 11y when y = 6?
  2. What is 12n – 8n + 7 when n = 9?
  3. What is 2r2 + 3r2 when r = –3?
  4. What is 4h – 8h + 6(h + 2) when h = 4?
  5. What is 5s + s2 – 9 when s = –2?

Solutions

Practice 1

  1. This expression contains subtraction and division. Since division comes before subtraction in the order of operations, divide first: 6 ÷ 2 = 3.  

    The expression becomes 5 – 3.  

    Subtract: 5 – 3 = 2.

  2. Parentheses are first in the order of operations.  

    10 + 3 = 13, and the expression becomes –2(13).  

    Multiply: –2(13) = –26.

  3. This expression contains an exponent, multiplication, and addition. Exponents come before multiplication and addition, so begin with 32: 32 = 9.  

    The expression is now 9(7) + 1.  

    Multiplication comes before addition, so multiply next:  

    9(7) = 63, and the expression becomes 63 + 1.  

    Finally, add: 63 + 1 = 64.

  4. There are two sets of parentheses in this expression, so work on each of them separately.  

    The first set of parentheses contains addition: –5 + 12 = 7.  

    The second set of parentheses contains subtraction: 21 – 13 = 8.  

    The expression is now (7)(8).  

    Multiply: (7)(8) = 56.

  5. The left side of the expression contains parentheses within parentheses, so start with the innermost parentheses: (8 – 22).   Because exponents come before subtraction, start with the exponent:  

    22 = 4, and the parentheses become (8 – 4).  

    Subtract: 8 – 4 = 4.  

    The expression is now (10 – 4)3.  

    The subtraction is in parentheses, so handle it before multiplying:  

    10 – 4 = 6. The expression becomes (6)3.  

    Finally, multiply: (6)3 = 18.

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