Number Operations

ASVAB Armed Services Vocational Aptitude Battery

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1 Introduction

About the ASVAB AFQT Score and Military Eligibility Line Scores and Military Jobs (MOS) How to Use This Guide

2 Verbal Domain (WK + PC)

Word Knowledge Basics Word Knowledge Practice Paragraph Comprehension Basics Paragraph Comprehension Practice

3 Mathematics Domain (AR + MK)

Number Operations Word Problems Algebra Geometry Test Strategies

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

Life Science Physical Science Electronics Fundamentals Mechanical Principles Applied Science Questions

5 Technical Skills Domain (AI + SI + AO)

Automotive Basics Automotive Systems Shop Tools and Practices Shop Safety and Materials Assembling Objects

Key Takeaways Explain This Topic AI

Master mental math techniques since NO calculator is allowed on the ASVAB.

Fractions, decimals, and percentages are interconvertible—learn the common conversions by heart.

Use estimation to quickly eliminate wrong answers and check your work.

Break complex calculations into simpler steps for easier mental computation.

Memorize multiplication tables through 12 and common squares/cubes for speed.

Last updated: January 2026

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 = 603 347 + 256 = 300 + 200 + 40 + 50 + 7 + 6 = 500 + 90 + 13 = 603 347 + 256 = 300 + 200 + 40 + 50 + 7 + 6 = 500 + 90 + 13 = 603

Example (Compensation): 98 + 47 = 100 + 47 − 2 = 145 98 + 47 = 100 + 47 - 2 = 145 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 × 25 = ( 36 ÷ 4 ) × 100 = 9 × 100 = 900 36 \times 25 = (36 \div 4) \times 100 = 9 \times 100 = 900 36 × 25 = ( 36 ÷ 4 ) × 100 = 9 × 100 = 900

Example (Multiply by 9): 47 × 9 = 47 × 10 − 47 = 470 − 47 = 423 47 \times 9 = 47 \times 10 - 47 = 470 - 47 = 423 47 × 9 = 47 × 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
1 2 \frac{1}{2} 2 1 0.5 50%
1 3 \frac{1}{3} 3 1 0.333... 33.33%
1 4 \frac{1}{4} 4 1 0.25 25%
1 5 \frac{1}{5} 5 1 0.2 20%
1 8 \frac{1}{8} 8 1 0.125 12.5%
2 3 \frac{2}{3} 3 2 0.666... 66.67%
3 4 \frac{3}{4} 4 3 0.75 75%
Worked Example: Adding Fractions
Problem: 2 3 + 3 4 \frac{2}{3} + \frac{3}{4} 3 2 + 4 3
Step 1: Find common denominator: LCD of 3 and 4 is 12

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

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

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 × 0.4 2.5 \times 0.4 2.5 × 0.4
Step 1: Multiply as whole numbers: 25 × 4 = 100 25 \times 4 = 100 25 × 4 = 100
Step 2: Count decimal places: 1 + 1 = 2 places
Step 3: Place decimal: 1.00 = 1 1.00 = 1 1.00 = 1
Percentages
Percentage Formulas

To Find Formula

Percent of a number Number × Percent 100 \text{Number} \times \frac{\text{Percent}}{100} Number × 100 Percent

What percent? Part Whole × 100 \frac{\text{Part}}{\text{Whole}} \times 100 Whole Part × 100
Original amount Part Percent × 100 \frac{\text{Part}}{\text{Percent}} \times 100 Percent Part × 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 × 0.15 = 12 80 \times 0.15 = 12 80 × 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:

P arentheses
E xponents
M ultiplication and D ivision (left to right)
A ddition and S ubtraction (left to right)
Worked Example: Order of Operations
Problem: 3 + 4 × 2 2 − ( 6 ÷ 2 ) 3 + 4 \times 2^2 - (6 \div 2) 3 + 4 × 2 2 − ( 6 ÷ 2 )

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