Turn a word problem into a calculation, keep the units straight and check whether the answer makes sense.
A crew completes three fifths of a 240-foot fence on Monday. On Tuesday it completes one quarter of what remained. How many feet still need to be completed?
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This original example is free to use without an account and is separate from the scored practice bank.
A crew completes three fifths of a 240-foot fence on Monday. On Tuesday it completes one quarter of what remained. How many feet still need to be completed?
Answer: C — 72 feet
Monday leaves two fifths of 240: 240 ÷ 5 × 2 = 96 feet. Tuesday completes one quarter of those 96 feet, or 24 feet. The unfinished length is 96 − 24 = 72 feet. The second fraction applies to the remainder, not the original length.
Open a topic to review the method, then practice applying it to a new question.
Identify the unknown, list the quantities you have, then write the relationship before inserting numbers. A diagram or short table often makes a long paragraph easier to follow.
Words such as “remaining,” “per,” “combined” and “of the original” change the calculation. Estimate the likely size of the answer so an arithmetic slip is easier to catch.
Use equivalent forms: 1/2 = 0.5 = 50%, 1/4 = 0.25 = 25%, and 1/5 = 0.2 = 20%. Reduce fractions before multiplying when possible. To add unlike fractions, first use a common denominator.
Multiplying by a fraction finds that fraction of a quantity. Dividing by a fraction asks how many portions of that size fit. Keep that distinction clear in recipe, length and capacity problems.
A container is 3/5 full. After 8 liters are added, it is 4/5 full. What is its total capacity?
Answer: 40 liters.
The increase is 1/5 of the container. If 1/5 is 8 liters, all 5 fifths hold 5 × 8 = 40 liters.
In a 2:3 mixture, the total is 5 parts, not 3. If you know the total amount, divide by the sum of the parts before multiplying by the required share.
Each percentage change acts on a particular starting amount. A discount followed by tax uses the discounted price as the tax base when the question says so. A 20% rise followed by a 20% fall does not return to the original amount.
An $80 item is discounted by 15%. An 8% sales tax then applies to the discounted price. What is the total?
Answer: $73.44.
The discount is $12, leaving $68. Tax is 0.08 × $68 = $5.44. The total is $68 + $5.44 = $73.44.
For constant motion, distance = rate × time. Convert time and distance into compatible units before calculating. Average speed over a whole trip is total distance divided by total time.
For work problems, express each worker or machine as a fraction of the job completed per unit of time. Combined rates add when the problem says they work independently at constant rates.
One machine completes a job in 6 hours and another in 3 hours. How long do they take together at constant independent rates?
Answer: 2 hours.
Their rates are 1/6 and 1/3 of a job per hour. Together they complete 1/2 of a job per hour, so one job takes 2 hours.
Write units alongside your working. If one quantity is in feet and another in inches, convert before comparing or combining them. Area and volume conversions require squared and cubed scale factors.
The mean is total ÷ count. When a person or item is added to a group, update both the total and the count. Do not average two group averages unless the groups have equal sizes or you account for their weights.
Arithmetic Reasoning asks you to choose and apply mathematics in a written situation. Mathematics Knowledge focuses more directly on mathematical rules and relationships. Fractions, algebra and geometry can support both.
Calculators are not allowed on the official ASVAB. Practice by hand with scratch paper, showing enough working to check units, signs and intermediate steps.
Original independent practice. Scores show performance on our questions, not an official ASVAB result.
Turn a word problem into a calculation, keep the units straight and check whether the answer makes sense.
4,700+ candidates · 68,000+ practice sessions across Game Assessment Prep.
A crew completes three fifths of a 240-foot fence on Monday. On Tuesday it completes one quarter of what remained. How many feet still need to be completed?
This original example is free to use without an account and is separate from the scored practice bank.
A crew completes three fifths of a 240-foot fence on Monday. On Tuesday it completes one quarter of what remained. How many feet still need to be completed?
Answer: C — 72 feet
Monday leaves two fifths of 240: 240 ÷ 5 × 2 = 96 feet. Tuesday completes one quarter of those 96 feet, or 24 feet. The unfinished length is 96 − 24 = 72 feet. The second fraction applies to the remainder, not the original length.
Open a topic to review the method, then practice applying it to a new question.
Identify the unknown, list the quantities you have, then write the relationship before inserting numbers. A diagram or short table often makes a long paragraph easier to follow.
Words such as “remaining,” “per,” “combined” and “of the original” change the calculation. Estimate the likely size of the answer so an arithmetic slip is easier to catch.
Use equivalent forms: 1/2 = 0.5 = 50%, 1/4 = 0.25 = 25%, and 1/5 = 0.2 = 20%. Reduce fractions before multiplying when possible. To add unlike fractions, first use a common denominator.
Multiplying by a fraction finds that fraction of a quantity. Dividing by a fraction asks how many portions of that size fit. Keep that distinction clear in recipe, length and capacity problems.
A container is 3/5 full. After 8 liters are added, it is 4/5 full. What is its total capacity?
Answer: 40 liters.
The increase is 1/5 of the container. If 1/5 is 8 liters, all 5 fifths hold 5 × 8 = 40 liters.
In a 2:3 mixture, the total is 5 parts, not 3. If you know the total amount, divide by the sum of the parts before multiplying by the required share.
Each percentage change acts on a particular starting amount. A discount followed by tax uses the discounted price as the tax base when the question says so. A 20% rise followed by a 20% fall does not return to the original amount.
An $80 item is discounted by 15%. An 8% sales tax then applies to the discounted price. What is the total?
Answer: $73.44.
The discount is $12, leaving $68. Tax is 0.08 × $68 = $5.44. The total is $68 + $5.44 = $73.44.
For constant motion, distance = rate × time. Convert time and distance into compatible units before calculating. Average speed over a whole trip is total distance divided by total time.
For work problems, express each worker or machine as a fraction of the job completed per unit of time. Combined rates add when the problem says they work independently at constant rates.
One machine completes a job in 6 hours and another in 3 hours. How long do they take together at constant independent rates?
Answer: 2 hours.
Their rates are 1/6 and 1/3 of a job per hour. Together they complete 1/2 of a job per hour, so one job takes 2 hours.
Write units alongside your working. If one quantity is in feet and another in inches, convert before comparing or combining them. Area and volume conversions require squared and cubed scale factors.
The mean is total ÷ count. When a person or item is added to a group, update both the total and the count. Do not average two group averages unless the groups have equal sizes or you account for their weights.
Arithmetic Reasoning asks you to choose and apply mathematics in a written situation. Mathematics Knowledge focuses more directly on mathematical rules and relationships. Fractions, algebra and geometry can support both.
Calculators are not allowed on the official ASVAB. Practice by hand with scratch paper, showing enough working to check units, signs and intermediate steps.
Original independent practice. Scores show performance on our questions, not an official ASVAB result.