Order of Operations (PEMDAS) – ASVAB Math Review

1. Parentheses (P)

Grouping symbols: (), [], {}

Solve inside first

Start with the innermost grouping symbols.

Example

Evaluate $$2 \times (3 + 5)$$

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Step 1: Solve inside parentheses: $$(3 + 5) = 8$$.

Step 2: Multiply by 2: $$2 \times 8 = 16$$.

Result: 16.

Practice problems

Problem 1
Evaluate $$5 \times (2 + 4)$$
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Answer: 30

Step-by-step evaluation:
- Correct Answer Value: 30
=> Correct Option: A (30).
Problem 2
Evaluate $$4 \times [3 + (8 - 5)]$$
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Answer: 24

Step-by-step evaluation:
- Correct Answer Value: 24
=> Correct Option: B (24).
Problem 3
Evaluate 2 × {$$15 - [2 \times (4 + 1)]$$}.
Show solution
Answer: 10

Step-by-step evaluation:
- Correct Answer Value: 10
=> Correct Option: B (10).

2. Exponents (E)

Powers and Roots

$$x^n$$ or $$\sqrt{x}$$

Calculate all powers and roots after parentheses are cleared.

Example

Evaluate $$3 \times 2^3 + \sqrt{16}$$.

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Step 1: Exponent & Root: $$2^3 = 8$$ and $$\sqrt{16} = 4$$.

Step 2: Multiply: $$3 \times 8 = 24$$.

Step 3: Add: $$24 + 4 = 28$$.

Result: 28.

Practice problems

Problem 4
Evaluate $$3^2 + 5$$
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Answer: 14

Step-by-step evaluation:
- Correct Answer Value: 14
=> Correct Option: B (14).
Problem 5
Evaluate $$5^2 - 2 \times \sqrt{36}$$.
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Answer: 13

Step-by-step evaluation:
- Correct Answer Value: 13
=> Correct Option: A (13).
Problem 6
Evaluate $$(2 + 3)^2 - \sqrt{81} / 3$$.
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Answer: 22

Step-by-step evaluation:
- Correct Answer Value: 22
=> Correct Option: A (22).

3. Mult & Div (MD)

Multiplication and Division

* and /

Left to Right Rule: Solve whichever comes first as you read from left to right.

Example

Evaluate $$\frac{12}{3} \times 2$$

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Step 1: Read left to right. Division comes first: $$\frac{12}{3} = 4$$.

Step 2: Multiply: $$4 \times 2 = 8$$.

Result: 8 (NOT $$\frac{12}{6} = 2$$).

Practice problems

Problem 7
Evaluate $$\frac{16}{4} \times 2$$
Show solution
Answer: 8

Step-by-step evaluation:
- Correct Answer Value: 8
=> Correct Option: B (8).
Problem 8
Evaluate $$\frac{24}{6} \times \frac{2}{4}$$
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Answer: 2

Step-by-step evaluation:
- Correct Answer Value: 2
=> Correct Option: A (2).
Problem 9
Evaluate $$\frac{36}{3} \times \frac{(2 + 1)}{6}$$
Show solution
Answer: 6

Step-by-step evaluation:
- Correct Answer Value: 6
=> Correct Option: A (6).

4. Add & Sub (AS)

Addition and Subtraction

+ and -

Left to Right Rule: Solve whichever comes first as you read from left to right.

Example

Evaluate $$10 - 4 + 2$$

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Step 1: Read left to right. Subtraction comes first: $$10 - 4 = 6$$.

Step 2: Add: $$6 + 2 = 8$$.

Result: 8 (NOT $$10 - 6 = 4$$).

Practice problems

Problem 10
Evaluate $$15 - 5 + 3$$
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Answer: 13

Step-by-step evaluation:
- Correct Answer Value: 13
=> Correct Option: B (13).
Problem 11
Evaluate $$20 - 8 + 6 - 4$$
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Answer: 14

Step-by-step evaluation:
- Correct Answer Value: 14
=> Correct Option: A (14).
Problem 12
Evaluate $$50 - 5 \times 6 + \frac{12}{3} - 2$$
Show solution
Answer: 22

Step-by-step evaluation:
- Correct Answer Value: 22
=> Correct Option: B (22).