Single-Variable Expressions Practice Questions

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.

Practice 3

1. Add y and 11y by adding the coefficients and keeping the base and exponent: 1 + 11 = 12, so y + 11y = 12y.   Replace y with 6 and multiply:  

   12(6) = 72

2. Subtract 8n from 12n. Remember, subtract the coefficient of 8n from the coefficient of 12n and keep the base and exponent:  

   12n – 8n = 4n  

   The expression is now 4n + 7.  

   Replace n with 9:  

   4(9) + 7  

   Multiplication comes before addition in the order of operations:  

   4(9) = 36  

   The expression is now 36 + 7.  

   Add: 36 + 7 = 43.

3. Add 2r² and 3r² by adding the coefficients and keeping the base and exponent:   2r² + 3r² = 5r²  

   Replace r with –3:   5(–3)²  

   Exponents come before multiplication in the order of operations:   (–3)2 = 9   The expression is now 5(9).  

   Multiply: 5(9) = 45.

4. Replace every h with 4:  

   4(4) – 8(4) + 6((4) + 2)  

   Begin with addition inside the parentheses:  

   4 + 2 = 6  

   The expression is now:  

   4(4) – 8(4) + 6(6)  

   Multiplication comes before subtraction or addition, so multiply next:  

   4(4) = 16  

   8(4) = 32  

   6(6) = 36  

   The expression is now:  

   16 – 32 + 36  

   Add –32 and 36:  

   –32 + 36 = 4  

   The expression is now:  

   16 + 4  

   Add: 16 + 4 = 20.

5. None of the terms in the expression 5s + s² – 9 can be combined because they are unlike terms. Replace every s with –2:   5(–2) + (–2)² – 9  

   Work with the exponent first:  

   (–2)² = 4  

   The expression is now:  

   5(–2) + 4 – 9  

   Multiplication comes before addition or subtraction, so multiply next:  

   5(–2) = –10  

   The expression is now:  

   –10 + 4 – 9  

   You can add before subtracting (or you can subtract before adding):  

   –10 + 4 = –6  

   The expression is now:  

   –6 – 9  

   Finally, subtract: –6 – 9 = –15.