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LearningExpress Editors Updated on Oct 3, 2011
To review these concepts, go to SingleVariable Expressions Study Guide.
SingleVariable Expressions Practice Questions
Problems
Practice 1
 5 – 6 ÷ 2
 –2(10 + 3)
 3^{2}(7) + 1
 (–5 + 12)(21 – 13)
 (10 – (8 – 2^{2}))3
Practice 2
 What is –9z when z = 9?
 What is 4u – 3 when u = 7?
 What is –8 + 2g when g = –5?
 What is + 30 when k = 20?
 What is 12(4 – x) when x = 1?
 What is q^{2} + 15 when q = –6?
 What is –8m^{2} when m = 4?
 What is 4d ÷ 3 – 20 when d = 12?
 What is (2b + 1)^{2} when b = –2?
 What is –5(3a^{2} – 24) when a = 3?
Practice 3
 What is y + 11y when y = 6?
 What is 12n – 8n + 7 when n = 9?
 What is 2r^{2} + 3r^{2} when r = –3?
 What is 4h – 8h + 6(h + 2) when h = 4?
 What is 5s + s^{2} – 9 when s = –2?
Solutions
Practice 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.

Parentheses are first in the order of operations.
10 + 3 = 13, and the expression becomes –2(13).
Multiply: –2(13) = –26.

This expression contains an exponent, multiplication, and addition. Exponents come before multiplication and addition, so begin with 3^{2}: 3^{2} = 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.

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.

The left side of the expression contains parentheses within parentheses, so start with the innermost parentheses: (8 – 2^{2}). Because exponents come before subtraction, start with the exponent:
2^{2} = 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

Replace z with 9 and multiply:
–9(9) = –81

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.

Replace g with –5:
–8 + 2(–5)
Multiply before adding: 2(–5) = –10
The expression becomes –8 + –10.
Add: –8 + –10 = –18.

Replace k with 20:
Multiply before adding:
The expression becomes 5 + 30.
Add: 5 + 30 = 35.

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.

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.

Replace m with 4:
–8(4)^{2}
Exponents come before multiplication, so handle the exponent first:
4^{2}= 16
The expression becomes –8(16).
Multiply: –8(16) = –128.

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.

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.

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

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

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.

Add 2r^{2} and 3r^{2} by adding the coefficients and keeping the base and exponent: 2r^{2} + 3r^{2} = 5r^{2}
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.

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.

None of the terms in the expression 5s + s^{2} – 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.
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