Chapter 1 of 814% of exam
Arithmetic Reasoning
Arithmetic Reasoning tests your ability to solve real-world word problems using basic arithmetic. Rather than testing raw calculation, it measures whether you can translate a situation into the right operation and carry it out accurately. This subtest counts toward the AFQT score that determines eligibility, so it is one of the most important sections. Success comes from reading carefully, identifying what is asked, and choosing the correct sequence of steps.
Reading and Setting Up Word Problems
The first skill is translating words into math. Look for the question actually being asked and the numbers that matter, then decide which operation connects them. Underlining key quantities and units helps you avoid setup errors that lead to wrong answers even when your arithmetic is correct.
Identify the unknown
Restate what the question asks in your own words before touching the numbers so you solve for the right quantity.
Match keywords to operations
Words like total and combined signal addition, difference signals subtraction, of often signals multiplication, and per signals division.
Track your units
Carry units such as miles, dollars, or hours through the work; the units of your answer should match what the question asks for.
Watch for extra information
Some problems include numbers you do not need, so select only the values relevant to the question.
Fractions, Decimals, and Percents
Many problems require moving fluidly between fractions, decimals, and percents. Being able to convert quickly lets you pick the easiest form for a given calculation and check that your answer is reasonable.
Convert percent to decimal
Divide a percent by 100 to get a decimal, so 8% becomes 0.08 before you multiply.
Find a percent of a number
Multiply the whole by the decimal form of the percent; 25% of 240 is 0.25 times 240, or 60.
Convert fractions to decimals
Divide the numerator by the denominator, so 3/4 equals 0.75.
Increase or decrease by a percent
For a 15% discount multiply by 0.85; for an 8% tax multiply by 1.08.
Ratios, Proportions, and Rates
Ratios and rates compare two quantities, and proportions let you scale them up or down. These appear constantly in mixing, pricing, and map-scale problems.
Write a ratio in lowest terms
Reduce a ratio the same way you reduce a fraction to compare quantities clearly.
Set up a proportion
Place matching quantities in the same position across an equals sign, then cross-multiply to solve for the unknown.
Use unit rates
Divide to find the cost or amount per single unit, which makes comparison and scaling straightforward.
Apply scale factors
Multiply every part of a ratio by the same factor so the relationship stays the same.
Averages, Interest, and Multi-Step Problems
Higher-value questions combine several steps, such as finding an average, computing simple interest, or working with rates of work. Organizing the steps prevents mistakes.
Compute an average
Add all the values and divide by how many there are; to find a missing value, multiply the average by the count to get the total first.
Use simple interest
Interest equals principal times rate times time, calculated only on the original amount.
Solve work and rate problems
Multiply rate by number of workers and by time to find total output, keeping units consistent.
Estimate to check
Round the numbers and estimate the answer to confirm your exact result is in a sensible range.
Test your knowledge
Practice questions on Arithmetic Reasoning