21. 25% = 1/4, so divide by 4: 84 / 4 = 21. Alternatively, 25% of 84 = 0.25 x 84 = 21.

17/12. Find LCD (12): 3/4 = 9/12 and 2/3 = 8/12. Add: 9/12 + 8/12 = 17/12 or 1 5/12.

Using mental math, what is 47 x 9?

423. Multiply by 9 trick: 47 x 10 = 470, then subtract 47: 470 - 47 = 423.

Evaluate: 5 + 3 x 2^2 - 4

13. PEMDAS: First exponent: 2^2 = 4. Then multiply: 3 x 4 = 12. Finally add/subtract: 5 + 12 - 4 = 13.

Number Operations

Critical: NO calculator is allowed on the ASVAB! All calculations must be done by hand using scratch paper or mental math.

The Mathematics Knowledge (MK) and Arithmetic Reasoning (AR) subtests together account for half of your AFQT score. Mastering basic number operations is essential for success.

The Four Basic Operations

Addition & Subtraction

Mental Addition Strategies:

Left to Right: Add hundreds, then tens, then ones
Make Tens: Group numbers that sum to 10
Compensation: Round up, then adjust

Example (Left to Right): $347 + 256 = 300 + 200 + 40 + 50 + 7 + 6 = 500 + 90 + 13 = 603$

Example (Compensation): $98 + 47 = 100 + 47 - 2 = 145$

Multiplication & Division

Multiplication Shortcuts:

To Multiply By	Do This
5	Divide by 2, multiply by 10
9	Multiply by 10, subtract the original
11	Multiply by 10, add the original
25	Divide by 4, multiply by 100
50	Divide by 2, multiply by 100

Example (Multiply by 25): $36 \times 25 = (36 \div 4) \times 100 = 9 \times 100 = 900$

Example (Multiply by 9): $47 \times 9 = 47 \times 10 - 47 = 470 - 47 = 423$

Fractions

Key Fraction Concepts

Operation	Method
Adding/Subtracting	Find common denominator first
Multiplying	Multiply numerators, multiply denominators
Dividing	Flip the second fraction and multiply
Simplifying	Divide both by Greatest Common Factor (GCF)

Common Fractions to Memorize

Fraction	Decimal	Percent
$\frac{1}{2}$	0.5	50%
$\frac{1}{3}$	0.333...	33.33%
$\frac{1}{4}$	0.25	25%
$\frac{1}{5}$	0.2	20%
$\frac{1}{8}$	0.125	12.5%
$\frac{2}{3}$	0.666...	66.67%
$\frac{3}{4}$	0.75	75%

Worked Example: Adding Fractions

Problem: $\frac{2}{3} + \frac{3}{4}$

Step 1: Find common denominator: LCD of 3 and 4 is 12

Step 2: Convert each fraction: $\frac{2}{3} = \frac{8}{12}$ and $\frac{3}{4} = \frac{9}{12}$

Step 3: Add: $\frac{8}{12} + \frac{9}{12} = \frac{17}{12} = 1\frac{5}{12}$

Decimals

Decimal Operations

Addition/Subtraction: Line up decimal points vertically

Multiplication: Multiply as whole numbers, then count total decimal places

Division: Move decimal points to make divisor a whole number

Worked Example: Decimal Multiplication

Problem: $2.5 \times 0.4$

Step 1: Multiply as whole numbers: $25 \times 4 = 100$

Step 2: Count decimal places: 1 + 1 = 2 places

Step 3: Place decimal: $1.00 = 1$

Percentages

Percentage Formulas

To Find	Formula
Percent of a number	$\text{Number} \times \frac{\text{Percent}}{100}$
What percent?	$\frac{\text{Part}}{\text{Whole}} \times 100$
Original amount	$\frac{\text{Part}}{\text{Percent}} \times 100$

Quick Percentage Tricks

Percent	Mental Math Method
10%	Move decimal one place left
5%	Find 10%, divide by 2
15%	Find 10% + half of 10%
20%	Find 10%, double it
25%	Divide by 4
50%	Divide by 2

Worked Example: Finding a Percentage

Problem: What is 15% of 80?

Method 1 (Direct): $80 \times 0.15 = 12$

Method 2 (Mental Math):

10% of 80 = 8
5% of 80 = 4
15% of 80 = 8 + 4 = 12

Order of Operations (PEMDAS)

Always follow this order:

Parentheses
Exponents
Multiplication and Division (left to right)
Addition and Subtraction (left to right)

Worked Example: Order of Operations

Problem: $3 + 4 \times 2^2 - (6 \div 2)$

Step 1: Parentheses: $6 \div 2 = 3$ Step 2: Exponents: $2^2 = 4$ Step 3: Multiplication: $4 \times 4 = 16$ Step 4: Add/Subtract left to right: $3 + 16 - 3 = 16$

ASVAB

1Introduction

2Verbal Domain (WK + PC)

3Mathematics Domain (AR + MK)

4Science & Technical Domain (GS + EI + MC)

5Technical Skills Domain (AI + SI + AO)

Key Takeaways