Here is our free ACCUPLACER Arithmetic practice test. The arithmetic test has 17 problems that you must solve. These problems are pretty basic, but make sure you review them carefully to be sure you are ready. You will get questions on three basic math skills: (1) Operations with whole numbers and fractions. (2) Operations with decimals and percentages. (3) Applications and problem solving. Start your test prep now with our free ACCUPLACER Math practice test.

**Directions:** *For each question, choose the best answer from the four choices. You may use paper and a pencil for computations, but you may not use a calculator.*

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Question 1 |

### Which of these decimals is the greatest?

$0.028$ | |

$0.0082$ | |

$0.82$ | |

$0.28$ |

Question 1 Explanation:

The correct answer is (C). To determine which of these four numbers is greatest, look for the largest digit in the tenths place (the first place to the right of the decimal). Choice (C) has an “8” in that position, whereas (A) and (B) have a “0” and (D) has a “2.” (C) is the greatest number.

Question 2 |

### What is 14% of 75?

$10.5$ | |

$12.5$ | |

$14.0$ | |

$15.5$ |

Question 2 Explanation:

The correct answer is (A). The word “of” in math means multiplication, so “14% of 75” is equal to 0.14 x 75. The correct answer is 10.5. To estimate, we know that 10% of 75 = 7.5. 4% of 75 would be a little less than half of 7.5 (let’s estimate 3.5), so we can approximate 14% of 75 as something close to 7.5 + 3.5 = 11.

Question 3 |

### $\dfrac{7}{8} ÷ \dfrac{9}{5} = ~?$

$\dfrac{7}{40}$ | |

$\dfrac{35}{72}$ | |

$\dfrac{40}{72}$ | |

$\dfrac{63}{40}$ |

Question 3 Explanation:

The correct answer is (B). When dividing fractions, we flip the denominator and change the division sign to a multiplication sign as follows:

$\dfrac{7}{8} ÷ \dfrac{9}{5}$

$= \dfrac{7}{8} \ast \dfrac{5}{9} = \dfrac{7 \ast 5}{8 \ast 9} = \dfrac{35}{72}$

$\dfrac{7}{8} ÷ \dfrac{9}{5}$

$= \dfrac{7}{8} \ast \dfrac{5}{9} = \dfrac{7 \ast 5}{8 \ast 9} = \dfrac{35}{72}$

Question 4 |

### Add: 1.728 + 0.9975 + 2.42 =

$4.1355$ | |

$5.1455$ | |

$5.1555$ | |

$6.1245$ |

Question 4 Explanation:

The correct answer is (B). To add decimals, vertically align the numbers so that the decimals are lined up. You can pad the shorter decimals by adding zeros to the end, and then add up the numbers:

$\begin{align} 1.7280& \\ 0.9975& \\ \underline{+\quad 2.4200}& \\ 5.1455& \end{align}$

$\begin{align} 1.7280& \\ 0.9975& \\ \underline{+\quad 2.4200}& \\ 5.1455& \end{align}$

Question 5 |

### Rose correctly answered 70% of the spelling bee questions. If there were 220 questions total, how many did she answer incorrectly?

$66$ | |

$82$ | |

$129$ | |

$154$ |

Question 5 Explanation:

The correct answer is (A). 70% of 220 translates to:

$\dfrac{70}{100} \ast 220 = 154$

(We can estimate this value: 70% of 100 = 70 and 70% of 10 = 7, so 70% of 220 must equal 70 + 70 + 7 + 7 = 154.)

The question asks how many she answered incorrectly, so from the total number of questions, we must subtract the number of questions she answered correctly:

$220 − 154 = 66$

$\dfrac{70}{100} \ast 220 = 154$

(We can estimate this value: 70% of 100 = 70 and 70% of 10 = 7, so 70% of 220 must equal 70 + 70 + 7 + 7 = 154.)

The question asks how many she answered incorrectly, so from the total number of questions, we must subtract the number of questions she answered correctly:

$220 − 154 = 66$

Question 6 |

### 44 is 80% of what number?

$51$ | |

$53$ | |

$55$ | |

$57$ |

Question 6 Explanation:

The correct answer is (C). Let’s make up a variable for the correct answer. We can translate the question to read: 44 is 80% of $x$. In math, “is” means equals, and “of” means multiplication. Therefore, we can further translate this question into a simple equation:

$44 = 0.8x$

To solve, divide both sides by the decimal:

$\dfrac{44}{0.8} = x$

$x = 55$

$44 = 0.8x$

To solve, divide both sides by the decimal:

$\dfrac{44}{0.8} = x$

$x = 55$

Question 7 |

### $3\dfrac{2}{5} + 1\dfrac{4}{7} =~?$

$\dfrac{145}{34}$ | |

$\dfrac{174}{35}$ | |

$\dfrac{168}{35}$ | |

$\dfrac{159}{34}$ |

Question 7 Explanation:

The correct answer is (B). To add mixed number fractions, first convert them to improper fractions, then find a common denominator and add or subtract the numerators, placing them over the common denominator. Reduce the final fraction if necessary.

To convert a mixed fraction to an improper fraction, multiply the whole number with the denominator, add this to the numerator, and place the resulting value above the original denominator.

$3\dfrac{2}{5} = \dfrac{17}{5}$

$1\dfrac{4}{7} = \dfrac{11}{7}$

Now find the lowest common denominator between 5 and 7. Since they are both prime numbers, their lowest common denominator is their product, 35. We can rewrite both fractions:

$\dfrac{17}{5} = \dfrac{119}{35}$

$\dfrac{11}{7} = \dfrac{55}{35}$

Now that the denominators are the same, we can add the numerators.:

$119 + 55 = 174$

To convert a mixed fraction to an improper fraction, multiply the whole number with the denominator, add this to the numerator, and place the resulting value above the original denominator.

$3\dfrac{2}{5} = \dfrac{17}{5}$

$1\dfrac{4}{7} = \dfrac{11}{7}$

Now find the lowest common denominator between 5 and 7. Since they are both prime numbers, their lowest common denominator is their product, 35. We can rewrite both fractions:

$\dfrac{17}{5} = \dfrac{119}{35}$

$\dfrac{11}{7} = \dfrac{55}{35}$

Now that the denominators are the same, we can add the numerators.:

$119 + 55 = 174$

Question 8 |

### Enrique is driving to Texas. He travels at 70 kilometers per hour for 2 hours, and 63 kilometers per hour for 5 hours. Over the 7 hour time period what was Enrique's average speed?

$64 \text{ km/h}$ | |

$65 \text{ km/h}$ | |

$66 \text{ km/h}$ | |

$67 \text{ km/h}$ |

Question 8 Explanation:

The correct answer is (B). Use this formula to find his average speed:

$\text{Avg Speed} = \dfrac{\text{Total Distance}}{\text{Total Time}}$

$\text{Total Distance:}$

$= 2(70) + 5(63)$

$= 140 + 315$

$= 455 \text{ km}$

$\text{Total Time:}$

$= 7 \text{ hours}$

$\text{Average Speed:}$

$= 455 ÷ 7$

$= 65 \text{ km/h}$

$\text{Avg Speed} = \dfrac{\text{Total Distance}}{\text{Total Time}}$

$\text{Total Distance:}$

$= 2(70) + 5(63)$

$= 140 + 315$

$= 455 \text{ km}$

$\text{Total Time:}$

$= 7 \text{ hours}$

$\text{Average Speed:}$

$= 455 ÷ 7$

$= 65 \text{ km/h}$

Question 9 |

### What is the value of $x$ in the triangle below?

$35$ | |

$48$ | |

$55$ | |

$68$ |

Question 9 Explanation:

The correct answer is (D). The sum of all 3 interior angles in a triangle is 180°:

$x + 77 + 35 = 180$

$x + 112 = 180$

$x = 180 − 112$

$x = 68$

$x + 77 + 35 = 180$

$x + 112 = 180$

$x = 180 − 112$

$x = 68$

Question 10 |

### Sam wants to cover his garden patio with brick tiles. His patio measures 15 feet by 20 feet. Each tile is 1 foot × 1 foot and costs \$2. How much money will Sam spend if he buys exactly enough tiles to cover his patio?

$\$250$ | |

$\$300$ | |

$\$450$ | |

$\$600$ |

Question 10 Explanation:

The correct answer is (D). First calculate the area of the patio:

$\text{Area} = 15 × 20 = 300 \text{ ft}^2$

Since each tile is 1 square foot (1 × 1), it will take 300 tiles to cover the patio. Each tile costs \$2:

$300 × \$2 = \$600$

$\text{Area} = 15 × 20 = 300 \text{ ft}^2$

Since each tile is 1 square foot (1 × 1), it will take 300 tiles to cover the patio. Each tile costs \$2:

$300 × \$2 = \$600$

Question 11 |

### The fraction below is approximately equal to what value?

$\dfrac{1795}{95}$15 | |

18 | |

20 | |

25 |

Question 11 Explanation:

The correct answer is (B). Begin by rounding the numerator and denominator to numbers that are easier to work with: 1795 is about 1800 and 95 is about 100, so the expression becomes 1800 ÷ 100, which simplifies to 18.

Question 12 |

### $6.6 × 10^{-4} = ~?$

$.00066$ | |

$.0066$ | |

$.066$ | |

$.66$ |

Question 12 Explanation:

The correct answer is (A). Multiplying a decimal value by 10 raised to a power is equivalent to moving the decimal point to the left or right the number of times indicated by the power.

The negative exponent here, −4, indicates that the decimal point is to be moved to the left 4 places:

$6.6 × 10^{-4}$

$= 0.66 × 10^{-3}$

$= 0.066 × 10^{-2}$

$= 0.0066 × 10^{-1}$

$= 0.00066 × 10^0$

$= 0.00066$

*In the case of a negative exponent, the decimal is moved to the left*(this is the same as dividing by 10 a number of times).The negative exponent here, −4, indicates that the decimal point is to be moved to the left 4 places:

$6.6 × 10^{-4}$

$= 0.66 × 10^{-3}$

$= 0.066 × 10^{-2}$

$= 0.0066 × 10^{-1}$

$= 0.00066 × 10^0$

$= 0.00066$

Question 13 |

### $0.0000000579 × 10^{6} = ~?$

$.000579$ | |

$.00579$ | |

$.0579$ | |

$.579$ |

Question 13 Explanation:

The correct answer is (C). Multiplying a decimal value by 10 raised to a power is equivalent to moving the decimal point to the left or right the number of times indicated by the power.

The positive exponent here, 6, indicates that the decimal point is to be moved to the right 6 places:

$0.0000000579 × 10^{6}$

$= 0.000000579 × 10^{5}$

$= 0.00000579 × 10^{4}$

$= 0.0000579 × 10^{3}$

$= 0.000579 × 10^{2}$

$= 0.00579 × 10^{1}$

$= 0.0579 × 10^0$

$= 0.0579$

*In the case of a positive exponent, the decimal is moved to the right*(this is the same as multiplying by 10 a number of times).The positive exponent here, 6, indicates that the decimal point is to be moved to the right 6 places:

$0.0000000579 × 10^{6}$

$= 0.000000579 × 10^{5}$

$= 0.00000579 × 10^{4}$

$= 0.0000579 × 10^{3}$

$= 0.000579 × 10^{2}$

$= 0.00579 × 10^{1}$

$= 0.0579 × 10^0$

$= 0.0579$

Question 14 |

### $\dfrac{3}{7} × \dfrac{15}{12} =~?$

$\dfrac{3}{21}$ | |

$\dfrac{15}{84}$ | |

$\dfrac{36}{77}$ | |

$\dfrac{15}{28}$ |

Question 14 Explanation:

The correct answer is (D). To multiply fractions, simply multiply the numerators to get the new numerator, and multiply the denominators get the new denominator.

$\dfrac{3}{7} × \dfrac{15}{12} = \dfrac{3 × 15}{7 × 12}$

Cancelling out a 3 in the top and bottom, we get:

$\dfrac{1 × 15}{7 × 4} = \dfrac{15}{28}$

$\dfrac{3}{7} × \dfrac{15}{12} = \dfrac{3 × 15}{7 × 12}$

Cancelling out a 3 in the top and bottom, we get:

$\dfrac{1 × 15}{7 × 4} = \dfrac{15}{28}$

Question 15 |

### Divide: 12 ÷ 50 = ?

$0.24$ | |

$4.2$ | |

$2.4$ | |

$0.024$ |

Question 15 Explanation:

The correct answer is (A). We can double check our answer by multiplying:

$0.24 × 50 = 12$

$0.24 × 50 = 12$

Question 16 |

### Multiply: 2.86 × 5.3 =

$15.158$ | |

$16.246$ | |

$151.58$ | |

$162.46$ |

Question 16 Explanation:

The correct answer is (A). When multiplying these two terms, the placement of the decimal in the correct answer must be three places to the left; this is because there are 3 total digits to the right of the decimal point in the numbers multiplied. Only (A) and (B) correctly put the decimal in its place. (To multiply decimal numbers, first count the total number of digits to the right of the decimal point, next multiply the numbers as usual, lastly, place the decimal point in the final answer so that there is the same number of digits to the right of the decimal point as there were in the original question.)

Question 17 |

### Karen, James, Frank, and Dan were left an inheritance by their late grandfather. If Karen receives one-eighth of the inheritance, James receives one quarter of the inheritance, Frank receives three-eighths of the inheritance, and Dan receives the remainder, what fraction of the inheritance does Dan receive?

$\dfrac{1}{4}$ | |

$\dfrac{5}{16}$ | |

$\dfrac{3}{8}$ | |

$\dfrac{3}{4}$ |

Question 17 Explanation:

The correct answer is (A). We can add up the fractions received by Karen, James, and Frank as follows:

$\dfrac{1}{8} + \dfrac{1}{4} + \dfrac{3}{8}$

$= \dfrac{1}{8} + \dfrac{2}{8} + \dfrac{3}{8}$

$= \dfrac{6}{8} = \dfrac{3}{4}$

We can find the fraction Dan receives by subtracting the sum of the other three fractions from one, since all the fractions must add up to one. Dan will receive:

$1 - \dfrac{3}{4} = \dfrac{1}{4}$

$\dfrac{1}{8} + \dfrac{1}{4} + \dfrac{3}{8}$

$= \dfrac{1}{8} + \dfrac{2}{8} + \dfrac{3}{8}$

$= \dfrac{6}{8} = \dfrac{3}{4}$

We can find the fraction Dan receives by subtracting the sum of the other three fractions from one, since all the fractions must add up to one. Dan will receive:

$1 - \dfrac{3}{4} = \dfrac{1}{4}$

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