ACCUPLACER Math

ACCUPLACER Arithmetic Practice Test: 15 Questions Solved

Fifteen original ACCUPLACER Arithmetic questions, three from each official area, solved step by step without a calculator.

Professor Chacha October 9, 2026 6 min read 10 views
Young person in a hooded sweatshirt writing on a worksheet at a table, with a calculator nearby

The ACCUPLACER Arithmetic test checks the math you learned before algebra: whole numbers, fractions, decimals, percents, and comparing numbers written in different ways. Below are 15 original practice questions, three from each of those five areas, each solved step by step.

Do them on paper, without a calculator. On the real test, many arithmetic questions don't give you one.

What the Arithmetic test covers

According to the College Board's test specifications, an Arithmetic test has 20 questions, with about 3 to 5 from each area. The test adapts to your answers, so the exact mix changes from student to student.

Area Typical questions In this practice set
Whole number operations Multi-digit arithmetic, order of operations, word problems Questions 1 to 3
Fraction operations Adding, multiplying, and dividing fractions and mixed numbers Questions 4 to 6
Decimal operations Adding, multiplying, and rounding decimals Questions 7 to 9
Percent Percent of a number, percent of change, successive percents Questions 10 to 12
Number comparisons and equivalents Ordering fractions, decimals, and percents; equivalent forms Questions 13 to 15

For how the whole ACCUPLACER math placement works, including scores and the other two math tests, see our ACCUPLACER math practice test.

Whole number operations

1.Subtract: \(3{,}204 - 1{,}867\)

  1. A2,663
  2. B1,337
  3. C1,437
  4. D1,347
Show solution

Line up the digits and borrow where the top digit is smaller.

\[\begin{array}{r} 3{,}204 \\ -\;1{,}867 \\ \hline 1{,}337 \end{array}\]

Check by adding: \(1{,}337 + 1{,}867 = 3{,}204\).

Common trap: Subtracting the smaller digit from the larger one in every column instead of borrowing. That gives 2,663. Adding your answer back is the fastest check.

Answer: B (1,337)

2.Evaluate: \(24 - 6 \times 3 + 8 \div 2\)

  1. A58
  2. B2
  3. C10
  4. D7
Show solution

Multiply and divide first, from left to right, then add and subtract from left to right.

\[\begin{gathered}24 - 18 + 4 \\ = 6 + 4 = 10\end{gathered}\]

Common trap: Working left to right without the order of operations: \((24 - 6) \times 3 = 54\), and so on. Another slip is subtracting \(18 + 4\) from 24, which gives 2. Addition and subtraction are done left to right.

Answer: C (10)

3.A school orders 26 boxes of markers with 24 markers in each box. The markers are shared equally among 13 classrooms. How many markers does each classroom get?

  1. A48
  2. B624
  3. C52
  4. D37
Show solution \[\begin{gathered}26 \times 24 = 624 \\ 624 \div 13 = 48\end{gathered}\]

Shortcut: \(26 \div 13 = 2\), so each classroom gets 2 boxes, or \(2 \times 24 = 48\) markers.

Common trap: Stopping at 624, the total number of markers. The question asks for one classroom's share.

Answer: A (48)

Fraction operations

4.Add: \(\tfrac{2}{3} + \tfrac{3}{5}\)

  1. A\(\tfrac{5}{8}\)
  2. B\(1\tfrac{1}{15}\)
  3. C\(\tfrac{6}{15}\)
  4. D\(1\tfrac{4}{15}\)
Show solution

Use the common denominator 15.

\[\tfrac{2}{3} + \tfrac{3}{5} = \tfrac{10}{15} + \tfrac{9}{15} = \tfrac{19}{15} = 1\tfrac{4}{15}\]

Common trap: Adding the tops and the bottoms: \(\tfrac{2 + 3}{3 + 5} = \tfrac{5}{8}\). A quick sense check: both fractions are more than \(\tfrac{1}{2}\), so the sum must be more than 1.

Answer: D (\(1\tfrac{4}{15}\))

5.Multiply: \(1\tfrac{1}{2} \times 2\tfrac{2}{3}\)

  1. A4
  2. B\(2\tfrac{1}{3}\)
  3. C\(3\tfrac{1}{3}\)
  4. D\(4\tfrac{1}{2}\)
Show solution

Change mixed numbers to improper fractions before multiplying.

\[\tfrac{3}{2} \times \tfrac{8}{3} = \tfrac{24}{6} = 4\]

Common trap: Multiplying the whole numbers and the fractions separately: \(1 \times 2 = 2\) and \(\tfrac{1}{2} \times \tfrac{2}{3} = \tfrac{1}{3}\), for \(2\tfrac{1}{3}\). That skips two of the four products.

Answer: A (4)

6.A recipe calls for \(2\tfrac{1}{4}\) cups of sugar. How much sugar do you need to make half of the recipe?

  1. A\(1\tfrac{1}{4}\)
  2. B\(4\tfrac{1}{2}\)
  3. C\(1\tfrac{1}{8}\)
  4. D\(1\tfrac{1}{2}\)
Show solution \[2\tfrac{1}{4} \div 2 = \tfrac{9}{4} \times \tfrac{1}{2} = \tfrac{9}{8} = 1\tfrac{1}{8}\]

Common trap: Halving only the whole number and keeping the \(\tfrac{1}{4}\), which gives \(1\tfrac{1}{4}\). Both parts of a mixed number get halved.

Answer: C (\(1\tfrac{1}{8}\))

Decimal operations

7.Add: \(4.7 + 0.38 + 12\)

  1. A6.28
  2. B17.08
  3. C17.8
  4. D16.98
Show solution

Line up the decimal points. A whole number like 12 has its decimal point at the end: 12.00.

\[\begin{array}{r} 4.70 \\ 0.38 \\ +\;12.00 \\ \hline 17.08 \end{array}\]

Common trap: Lining up the last digits instead of the decimal points, so 12 is treated like 1.2. That gives 6.28.

Answer: B (17.08)

8.Multiply: \(2.4 \times 0.15\)

  1. A3.6
  2. B0.036
  3. C36
  4. D0.36
Show solution

Multiply as whole numbers, then count decimal places: one in 2.4 and two in 0.15, so three in the answer.

\[\begin{gathered}24 \times 15 = 360 \\ \Rightarrow\; 0.360 = 0.36\end{gathered}\]

Common trap: Placing the decimal point by guessing. Estimate first: \(2.4 \times 0.15\) is a little more than \(2 \times 0.15 = 0.3\), so 0.36 fits and 3.6 does not.

Answer: D (0.36)

9.Round 7.0496 to the nearest hundredth.

  1. A7.05
  2. B7.04
  3. C7.1
  4. D7.0
Show solution

The hundredths digit is 4. Look at the next digit, 9: it is 5 or more, so round the 4 up to 5.

\[7.0496 \approx 7.05\]

Common trap: Cutting off the extra digits without rounding, which gives 7.04. Always look one place to the right of where you are rounding.

Answer: A (7.05)

Percent

10.What is 35% of 240?

  1. A156
  2. B8.4
  3. C84
  4. D68.6
Show solution \[0.35 \times 240 = 84\]

Without a calculator: 10% of 240 is 24, so 30% is 72 and 5% is 12. Then \(72 + 12 = 84\).

Common trap: Answering 156, which is what is left after taking 35% away. The question asks for 35% of the number, not the rest.

Answer: C (84)

11.18 is what percent of 72?

  1. A4%
  2. B25%
  3. C400%
  4. D54%
Show solution \[\tfrac{18}{72} = \tfrac{1}{4} = 25\%\]

Common trap: Dividing the wrong way: \(72 \div 18 = 4\). The number after "of" (72) goes on the bottom.

Answer: B (25%)

12.A store raises the price of a $60 jacket by 20%. Later, it puts the jacket on sale at 20% off the new price. What is the sale price?

  1. A$60.00
  2. B$48.00
  3. C$62.40
  4. D$57.60
Show solution

Each percent applies to the price at that moment.

\[\begin{gathered}60 \times 1.20 = 72 \\ 72 \times 0.80 = 57.60\end{gathered}\]

Common trap: Assuming 20% up and 20% down cancel out, which gives $60. The 20% discount is taken from $72, a bigger number, so it removes more than the increase added.

Answer: D ($57.60)

Number comparisons and equivalents

13.Which of these is equal to 0.45?

  1. A\(\tfrac{9}{20}\)
  2. B\(\tfrac{4}{5}\)
  3. C\(\tfrac{45}{10}\)
  4. D4.5%
Show solution \[0.45 = \tfrac{45}{100} = \tfrac{9}{20}\]

Common trap: Choosing 4.5%. As a percent, 0.45 is 45%: move the decimal point two places to the right.

Answer: A (\(\tfrac{9}{20}\))

14.Which statement is true?

  1. A\(-\tfrac{3}{4} \lt -\tfrac{2}{3}\)
  2. B\(0.3 \gt \tfrac{1}{3}\)
  3. C\(\tfrac{5}{8} \lt 0.6\)
  4. D\(-1.5 \gt -1.2\)
Show solution

Convert to decimals: \(-\tfrac{3}{4} = -0.75\) and \(-\tfrac{2}{3} \approx -0.667\). On the number line, \(-0.75\) is farther left, so it is smaller.

The others are false: \(\tfrac{1}{3} \approx 0.333 \gt 0.3\), \(\tfrac{5}{8} = 0.625 \gt 0.6\), and \(-1.5\) is to the left of \(-1.2\).

Common trap: Comparing negative numbers as if they were positive. With negatives, the number that looks bigger (like 1.5 in \(-1.5\)) is actually smaller.

Answer: A (\(-\tfrac{3}{4} \lt -\tfrac{2}{3}\))

15.Which number is between \(\tfrac{1}{4}\) and \(\tfrac{1}{3}\)?

  1. A0.35
  2. B0.24
  3. C0.3
  4. D0.34
Show solution

\(\tfrac{1}{4} = 0.25\) and \(\tfrac{1}{3} \approx 0.333\). Only 0.3 is between them.

Common trap: Picking 0.34 because it "looks close" to one third. 0.34 is slightly more than \(0.333\ldots\), so it is outside the range.

Answer: C (0.3)

Answer key

  1. 1 B
  2. 2 C
  3. 3 A
  4. 4 D
  5. 5 A
  6. 6 C
  7. 7 B
  8. 8 D
  9. 9 A
  10. 10 C
  11. 11 B
  12. 12 D
  13. 13 A
  14. 14 A
  15. 15 C

How did you do?

This set is practice, not a real ACCUPLACER score, but it shows you where to spend your time:

  • 13 to 15 correct: Arithmetic is solid. Move on to the Quantitative Reasoning, Algebra, and Statistics questions, since your college may place you there.
  • 9 to 12 correct: Look at which area your misses came from. Two misses in the same area is your study plan for the week.
  • 8 or fewer: Start with fractions and percents. They appear in almost every other part of placement math, so the work pays off twice.

Teacher's note: With fractions, I give students one rule to follow without exception: the moment you see a mixed number in a multiplication or division, rewrite it as an improper fraction before doing anything else. It feels like an extra step, but it removes the guesswork about what to multiply by what. Questions 5 and 6 above are exactly where that rule saves the point.

Tags: ACCUPLACER Arithmetic Decimals Fractions Percents
Professor Chacha
Professor Chacha Math teacher and educational psychologist

Math teacher and educational psychologist with more than 20 years of classroom experience. He writes every practice question on this site from scratch and solves it step by step, the way he explains it to his own students.

Keep practicing

Comments (0)

Be the first to comment.

Leave a comment