Arithmetic Reasoning (AR)
Ability to solve arithmetic word problems. It is one of the four subtests that decide AFQT eligibility.
- 15 questions
- 55 minutes
- ~3.7 min per question
- Counts toward the AFQT
- No calculator
- 12 lessons · 7 h
Lessons
12 lessons · 180 practice questions · 96 flashcards- 01Turning Words into MathTranslate ASVAB word problems into correct arithmetic expressions and equations, including multi-step, rate, ratio, percentage, unit and geometry relationships.28 min15 questions8 cards
- 02Whole-Number Operations and Order of OperationsExecute whole-number arithmetic accurately without a calculator, apply order of operations, interpret remainders, and use efficient estimation/checking methods.26 min15 questions8 cards
- 03Fractions and Mixed NumbersMaster fraction interpretation, simplification, comparison, mixed numbers, four operations, and fraction-based ASVAB word problems without a calculator.30 min15 questions8 cards
- 04Decimals and Place ValueMaster decimal place value, comparison, rounding, four operations, fraction conversions, and decimal-based money, measurement, rate and multi-step problems.30 min15 questions8 cards
- 05PercentagesMaster percentage conversions, percent-of/percent/whole relationships, percent change, reverse percentages, and real-world discount/tax/commission applications.32 min15 questions8 cards
- 06Ratios and ProportionsMaster ratios, proportions, scale factors, unit rates, direct proportion, ratio totals and scale-drawing/mixture applications.34 min15 questions8 cards
- 07Averages and Weighted ThinkingMaster simple and weighted averages, missing-value and combined-group problems, average speed, and basic mixture concentration.32 min15 questions8 cards
- 08Rates and Unit RatesMaster unit rates, distance-rate-time relationships, price/production comparisons, combined work and opposing-rate problems.34 min15 questions8 cards
- 09Distance, Rate and TimeSolve one- and two-object motion problems using D=RT, relative speed, head starts, round trips and average speed.34 min15 questions8 cards
- 10Work and Combined-Rate ProblemsSolve work-rate problems involving solo workers, combined teams, partial work, changing teams, fill/drain systems and production rates.35 min15 questions8 cards
- 11Money, Interest and Everyday QuantitiesSolve everyday money problems involving unit prices, discounts, tax, tips, wages, overtime, commission, markup, budgets and simple interest.36 min15 questions8 cards
- 12Mixed Multi-Step Word ProblemsIntegrate fractions, decimals, percentages, ratios, rates, motion, work and money into multi-step Arithmetic Reasoning solutions.40 min15 questions8 cards
Arithmetic Reasoning practice tests
6 tests · each 15 questions · 55 min · no question repeats between tests
About this section
Arithmetic Reasoning is the word-problem subtest of the ASVAB, and it is one of the four subtests that make up the AFQT. Every question gives you a short real-world situation and asks you to set up and solve the math, with no calculator allowed.
This category has 12 lessons that build those skills step by step. You begin with turning words into math and with whole-number operations and order of operations, then work through fractions and mixed numbers, decimals and place value, percentages, ratios and proportions, and averages and weighted thinking. Later lessons handle rates and unit rates, distance, rate and time, work and combined-rate problems, and money, interest and everyday quantities, before a final lesson on mixed multi-step word problems.
Because AR counts toward the AFQT, steady practice here pays off in your enlistment-qualifying score. Each lesson ends with a short lesson test.
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