Single-Variable Expressions Practice Questions (page 3)

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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.

Practice 2

1. Replace z with 9 and multiply:  

   –9(9) = –81

2. Replace u with 7:  

   4(7) – 3  

   Multiplication comes before subtraction in the order of operations, so multiply next:   4(7) = 28   The expression becomes 28 – 3.  

   Subtract: 28 – 3 = 25.

3. Replace g with –5:  

   –8 + 2(–5)  

   Multiply before adding:   2(–5) = –10  

   The expression becomes –8 + –10.  

   Add: –8 + –10 = –18.

4. Replace k with 20:    

   Multiply before adding:    

   The expression becomes 5 + 30.  

   Add: 5 + 30 = 35.

5. Replace x with 1:  

   12(4 – 1)  

   Subtraction is in parentheses, so subtract before multiplying:  

   (4 – 1) = 3  

   The expression becomes 12(3).  

   Multiply: 12(3) = 36.

6. Replace q with –6:   (–6)² + 15  

   Exponents come before addition in the order of operations, so handle the exponent first:  

   (–6)² = 36  

   The expression becomes 36 + 15.  

   Add: 36 + 15 = 51.

7. Replace m with 4:  

   –8(4)²  

   Exponents come before multiplication, so handle the exponent first:  

   4²= 16  

   The expression becomes –8(16).  

   Multiply: –8(16) = –128.

8. Replace d with 12:  

   4(12) ÷ 3 – 20  

   Multiply first:   4(12) = 48  

   The expression becomes 48 ÷ 3 – 20.  

   Division comes before subtraction:  

   48 ÷ 3 = 16   We are left with 16 – 20.  

   Subtract: 16 – 20 = –4.

9. Replace b with –2:  

   (2(–2) + 1)²  

   There is multiplication and addition inside the parentheses. Multiply first:  

   2(–2) = –4  

   The expression becomes (–4 + 1)².  

   Because the addition is in parentheses, it must be done before the exponent is handled:  

   –4 + 1 = –3  

   We are left with (–3)².  

   Finally, square –3: (–3)² = 9.

10. Replace a with 3:  

    –5(3(3)² – 24)  

    There is multiplication, an exponent, and subtraction inside the parentheses. Because exponents come before multiplication and subtraction, handle the exponent first:  

    (3)² = 9  

    The expression becomes –5(3(9) – 24).  

    Multiplication inside the parentheses comes next:  

    3(9) = 27  

    The expression becomes –5(27 – 24).  

    The subtraction is in parentheses, so it must be done before the multiplication:  

    27 – 24 = 3   We are left with –5(3).  

    Multiply: –5(3) = –15.