# ESL Arithmetic Practice Test for the ACCUPLACER® test

#### 23.4 x 2.53 =

Multiplying 23.4 and 2.53, you get 59.202. Ensure the decimal is in the correct position.

#### Which of the following is the greatest?

To compare decimals, check the tenths place first. If two numbers have the same value in the tenths place, then check the hundredths place, and then the thousandths place if necessary

#### What percentage of 128 is 96?

Divide 96 by 128 to get 0.75, which is equivalent to 75%

#### 1.4 + 0.06 + 0.522 =

Write the three terms vertically and be sure to line them up so that the decimal points are all directly above each other. For the first two terms, you can fill in additional zeroes so that there are three digits to the right of the decimal.

#### One angle of a triangle measures 30 degrees. Of the remaining two angles, the larger one is twice as large as the smaller one. What is the measure of the smaller angle?

The interior angles of a triangle sum to 180 degrees. We know one angle is 30 degrees, so subtracting that from 180, we know the sum of the remaining two angles is 150. The problem then says that the larger remaining angle is twice the measure of the smaller one. From here, we can set up an equation to solve for a smaller angle x:
2x+x=150
Then combine the terms with x: 2x+x=3x
3x=150
Divide both sides by 3 isolate x: ^{3x}⁄_{2} = ^{150}⁄_{3}
x = 150
Therefore, the measure of the smaller angle is 50.

#### 7 ^{2}⁄_{3} + 4 ^{1}⁄_{4}

The least common denominator of ^{2}⁄_{3} and ^{1}⁄_{4} is 12, so convert fractions to have a denominator of 12 and you will get ^{8}⁄_{12} and ^{3}⁄_{12}.
Then, and the fractions and add the whole numbers to get 11^{11}⁄_{12}.

^{6}⁄_{7} ÷ ^{1}⁄_{8} =

To divide by a fraction, multiply by the reciprocal. The problem ^{6}⁄_{7} ÷ ^{1}⁄_{8} then becomes ^{6}⁄_{7} * ^{8}⁄_{1} = ^{48}⁄_{7}.
To simplify the answer, divide 48 by 7.
48 ÷ 7 = 6 because 7 * 6 = 42
48 - 42 = 6 so there are 6 left over, which equals ^{6}⁄_{7}
We arrive at the answer, 6 ^{6}⁄_{7}.

^{16}⁄_{64} is equivalent to which of the following fractions?

The greatest common factor of 16 and 64 is 16, so divide the numerator and denominator by 16 to get ^{1}⁄_{4}.

#### 25.6 x 10.42 is closest to which of the following?

25 x 10 = 250, so the product of the two given numbers will be a bit above 250 with the decimals included. The only other number that is close is 200, but it should be clear that 200 is too low.

#### 6 ^{3}⁄_{4} - 3 ^{1}⁄_{3} =

6 ^{3}⁄_{4} - 3 ^{1}⁄_{3} =
The least common multiple of 3 and 4 is 12, so convert both fractions to 12ths:
6 ^{9}⁄_{12} - 3 ^{4}⁄_{12}.
Then, subtract the whoe numbers and the numerators of the fractions to get 3 ^{5}⁄_{12}.

^{5}⁄_{8} =

Divide 8 into 5 by putting a decimal and extra zeroes at the end of the 5 (such as 5.000). When you get the first two decimal places, you don’t need to go any further since none of the other answers are possible choices any longer.

#### A bag contains 30 colored marbles that have either a rough or smooth texture. Exactly ^{1}⁄_{2} of the marbles are blue, ^{1}⁄_{3} are green, and the rest are yellow. Exactly ^{2}⁄_{3} of the marbles are smooth. If half of the rough marbles are green, then what fraction of the total bag is rough green marbles?

This one is a bit tricky but it can be helpful to translate the fractions into actual numbers. Starting with the colors, half are blue, ^{1}⁄_{} are green, and the rest are yellow. There are 30 marbles total, so this means 15 are blue, 10 are green, and 5 are yellow. Regarding textures, ^{2}⁄_{3} are smooth and the rest are rough, so there are 20 smooth marbles and 10 rough marbles. Half of the rough marbles are green, so there are 5 rough green marbles, and ^{5}⁄_{30} reduces to ^{1}⁄_{6} .

^{1}⁄_{3} of 250 is approximately ____.

We know ^{1}⁄_{3} of 240 is 80, so ^{1}⁄_{3} of 250 is slightly more. The next closest answer is 70, but if it is not clear 70 is too small, divide 250 by 3 to see that 85 is closer to the actual number.

#### A pizza pie has eight slices. Some of the slices have extra toppings of either pepperoni, mushroom, or both, while some slices have no extra toppings. The customer specified that ^{1}⁄_{2} of the pie must contain pepperoni, ^{3}⁄_{8} of the pie must contain mushrooms, and ^{1}⁄_{4} of the pie must contain both pepperoni and mushrooms. What fraction of the pie does not contain any extra topping?

First, convert the fractions into slices of the pie:
^{1}⁄_{2} * 8 = 4 slices (pepperoni)
^{3}⁄_{8} * 8 = 3 slices (mushroom)
^{1}⁄_{4} * 8 = 2 slices (pepperoni and mushroom)
Right away, it looks like there have to be 9 slices total, since the fractional parts in the question add up to ^{9}⁄_{8} . But this is inconsistent with the total of 8 slices given in the question, and the customer’s specification that 1/2 (or 4 slices) of the pie must contain pepperoni and 3/8 (or 3 slices) must contain mushroom.
Going back to the 4 slices containing pepperoni, it does not say “pepperoni only.” So, some of the 4 slices must contain both pepperoni and mushroom. This is the same for the 3 slices containing mushroom, it does not say “mushroom only.”

^{6}⁄_{7} + ^{5}⁄_{4} =

The less common multiple of 7 and 4 is 28, convert both fractions so that they have 28 in the denominator. Multiplying the first fraction by ^{4}⁄_{4} and the second by ^{7}⁄_{7}, we get ^{24}⁄_{28} and ^{35}⁄_{28}. Adding the numerators gives ^{59}⁄_{28}.
Note: Often, you will be required to change an improper fraction, like this answer, to a mixed number. However, ^{59}⁄_{28} is correct and it is the only correct choice given for this question. Some modern tests consider improper fractions to be correct, especially those with “fill-in” responses.

^{3}⁄_{5} ÷ ^{2}⁄_{4} =

To divide by a fraction, multiply by its reciprocal. The question then becomes ^{3}⁄_{5} * ^{4}⁄_{2}, which equals ^{12}⁄_{10}. We can reduce this to ^{6}⁄_{5}, and then to the mixed numbers 1 ^{1}⁄_{5}.

^{3}⁄_{4} is equivalent to which of the following?

^{3}⁄_{4} x ^{6}⁄_{6} = ^{18}⁄_{24}, so the two fractions are equivalent.

^{9}⁄_{5} - ^{2}⁄_{3} =

The least common multiple of 5 and 3 is 15, so multiply the first fraction by ^{3}⁄_{3} and the second by ^{5}⁄_{5} so that both have 15 in the denominator. Then, subtract the numerators to get ^{17}⁄_{15}.
OR, try this method:
The least common multiple of 5 and 3 is 15.
Sinnce you multiplied the 5 in the fraction ^{9}⁄_{5} by 3 to get 15 in the denominator, you have to multiply 9 by 3, as well. So, the first fraction becomes ^{27}⁄_{15}.
Similarly, multiply the 2 in the fraction ^{2}⁄_{3} by 5 since you multiplied the 3 in that fraction by 5 to get the denominator of 15. This second fraction becomes ^{10}⁄_{15}.
The resulting problem is ^{27}⁄_{15} - ^{10}⁄_{15} and the answer is ^{17}⁄_{15}.

#### If 2 ^{1}⁄_{4} + x = 5 ^{1}⁄_{8}, then which of the following is true of x?

First, let’s solve for x:
2 ^{1}⁄_{4} + x = 5 ^{1}⁄_{8}
x = 5 ^{1}⁄_{8} - 2 ^{1}⁄_{4}
x = (4+^{8}⁄_{8} + ^{1}⁄_{8}) - 2 ^{2}⁄_{8}
x = 4 ^{9}⁄_{8} - 2 ^{2}⁄_{8}
x = 2 ^{7}⁄_{8}
xx is clearly “greater than 2 and less than 3”, the correct answer.

#### Sally buys 400 feet of fencing to put up a fence around her backyard. If she ends up using ^{7}⁄_{8} of it, how much fencing will she have left over?

^{7}⁄_{8} of 400 is 350, so Sally will use 350 feet of fencing and have 50 feet left over.

^{6}⁄_{15} * 2 ^{2}⁄_{3} =

Convert the second number from a mixed number to an improper fraction. Then, multiply the numerators and denominators to get ^{48}⁄_{45}. This fraction can be reduced by dividing the numerator and denominator by 3 to get ^{16}⁄_{15}, which is the correct answer.

#### 22.46 + 2.005 + 0.7 =

Write the numbers on top of each other and line up the decimal points. If it is helpful, you can put zeroes after the decimals so that all of the numbers have the same amount of digits to the right of the decimal.

#### 0.3060 + 2.954 + 0.2 =

Write the numbers on top of each other and line up the decimal points. If it is helpful, you can put zeroes after the decimals so that all of the numbers have the same amount of digits to the right of the decimal.

#### 5.3 – 2.96 =

Write the numbers on top of each other and line up the decimal points. Put a zero after the first number so both numbers have two digits to the right of the decimal. Then, subtract as usual and ensure the decimal point stays in the correct spot.

#### 7.9 x 0.35 =

Write the numbers on top of one another. Multiply the numbers and make sure to put the decimal point three places in from the right, because there are a total of 3 decimal places in the 2 numbers being multiplied.

#### Which of the following is closest to 75% of 190?

To get 75% of 190, multiply 0.75 x 190. The correct answer is 142.5, and 140 is the closest choice.

#### Which percentage is equivalent to the fraction ^{5}⁄_{8}?

This problem can be approached in a few ways. First, we know ^{1}⁄_{4} = 25, and ^{1}⁄_{8} is half of ^{1}⁄_{4}, so ^{1}⁄_{8} = 12.5. Then, multiply 12.5 to get ^{5}⁄_{8} = 62.5.
Alternatively, you can just divide 5 by 8 to get the decimal 0.625, which is equivalent to 62.5%.

#### 36÷1.5=

When dividing by decimals, you want to start by making the divisor a whole number. To do this, shift the decimal one place to the right. Ensure you also move the decimal in the dividend (one place to the right). Your problem is now 360÷15, which will give you an answer of 24.

#### 0.65 x 0.33 =

Write the numbers on top of each other, lining up the decimal points. Then, multiply them and ensure the decimal point goes over four places from the right in your final answer.

#### 10 – 2.267 =

Write the numbers on top of each other, lining up the decimal points (put a decimal point to the right of the 10). Then, put three zeroes to the right of the decimal point, so 10 becomes 10.000. Finally, subtract the numbers, borrowing all the way from the left.

#### The answer to 45.4 x 7.7 is closest to which of the following?

Start by estimating, multiplying 45 x 8 to get 360. This narrows it down to the two choices 365 and 385. Based on the estimation, 365 seems like the better choice. To be certain, we can estimate again by rounding both of our original numbers up and multiplying 46 by 8 to get 368. Since our higher estimation is only just above 365 and our first estimation was 360, we know the best choice is 3

#### What is 35% of 26.2?

Convert 35% to a decimal (0.35). Then, multiply 0.35 by 26.2 to get 9.17.

#### Which of the following lists the given numbers in order from least to greatest?

When comparing decimals, start with the tenths place. Only 0.058 has a zero in the tenths place, so it must be the smallest. Then, compare the hundredths place of the remaining three decimals to arrive at the correct answer.

#### Which of the following correctly lists the numbers in order from greatest to least?

First, it is clear that 0.5 is the smallest. Next, converting 65% to a decimal, we see that 0.65 > 0.605. All that remains is 7/8, so either divide 7 by 8 to get 0.875, or we know that 6/8 = 3/4 = 0.75, and 7/8 must be greater than that, so 7/8 must be the greatest number given.

#### Joan bought a new rectangular carpet for her living room. The carpet is 8.5 feet long and 10 feet wide, the area of the room is 20% larger than that of the carpet. What is the area of the room?

First, find the area of the carpet by multiplying 8.5 by 10 to get 85. Then, because the room is 20% larger than the carpet, find 20% of 85 by converting 20% to the equivalent decimal number, .20 and multiplying it by 85. The answer is 17. Add this number to the area of the carpet to get the total area of the room, which is 102 square feet.

#### John orders a box of assorted pens for his office. The pens are either red, blue, black, or green. In the box, ^{1}⁄_{8} of the pens are red and ^{1}⁄_{4} are green. Of the remaining pens (those that are not red or green), ^{1}⁄_{5} are black and the rest are blue. What fraction of the box has blue pens?

Think of the total number of pens contained in the box as a whole number, or a value equal to 1. Represent 1 as a fraction with a denominator common to the given fractions. The fraction ^{40}⁄_{40} is a good choice because each of the denominators evenly divides into 40.
Convert ^{1}⁄_{4} for the green pens to fortieths, and we have ^{10}⁄_{40}.
Convert ^{1}⁄_{8} for the red pens to fortieths, and we have ^{5}⁄_{40}.
Subtract the amount of green and red pens from the total:
^{40}⁄_{40} - ^{5}⁄_{40} - ^{10}⁄_{40} = ^{25}⁄_{40} black and blue pens.
Since ^{1}⁄_{5} of the remaining pens (^{25}⁄_{40}, which reduces to ^{5}⁄_{8}) are black, we compute the fraction of black pens by multiplying ^{1}⁄_{5} with ^{5}⁄_{8}:
^{1}⁄_{5} * ^{5}⁄_{8} = ^{1}⁄_{8} = ^{5}⁄_{40} represents the fraction of black pens in the box.
Solving for the fraction representing the blue pens, we subtract the amount of black pens from the total of blue and black pens:
^{25}⁄_{40} - ^{5}⁄_{40} = ^{20}⁄_{40} = ^{1}⁄_{2} of the box are blue pens.

#### A swimming pool is being filled at a rate of 530 gallons per hour. How many gallons of water will be in the pool after 2 hours and 30 minutes?

Multiply 530 gallons/hour by 2.5 hours to get 1,325 gallons.

#### Jamie’s library has 240 books, some of which are in English and some of which are in Spanish. If 45 percent of the books are written in Spanish, then how many books are written in English?

Multiply .45 (the decimal for 45%) by 240 to find that 108 is 45% of 240. Subtract 108 from 240 to get the number of books in English, which is 132.

#### The largest angle in a triangle is 90 degrees. If one of the other angles is greater than or equal to 60 degrees, what is the largest possible measure of the third angle?

A triangle has 180 degrees. If one angle is 90 degrees and one is 60 degrees, the remaining angle would be 30 degrees. Since the second angle is at least 60, the largest the third angle could be is 30 degrees.

#### A large fish tank is 6 feet wide, 2 feet long, and 5 feet tall. If the tank is currently filled with 20 cubic feet of water, then what fraction of the tank is empty?

The tank is 6 feet x 2 feet x 5 feet, so its total volume is 60 cubic feet. If 20 cubic feet are filled, 40 cubic feet are not, and ^{40}⁄_{60} = ^{2}⁄_{3}.

#### John hit 50 golf balls at the driving range. If 40% of them went farther than 150 yards, then how many balls went over 150 yards?

We are trying to calculate 40% of 50, which is how many golf balls went past the 150-yard mark. To do that, change 40% into a decimal (.40) so we can multiply it by the number of balls, 50. The resulting problem is .40 x 50 = 20 (Remember to move the decimal point in the answer to the left the number of decimal places in the numbers being multiplied.)

#### An animal rescue facility currently has 45 animals available for adoption. If ^{1}⁄_{3} of them are cats and ^{1}⁄_{9} of them are dogs, how many animals are neither cats nor dogs?

^{1}⁄_{3} of the animals are cats and^{1}⁄_{9} are dogs,
^{1}⁄_{3} x 45 = 15 cats
^{1}⁄_{9} x 45 = 5 dogs
Subtracting these 20 animals, there are 25 remaining.

#### Elizabeth wants to buy material for new curtains in her living room. She needs six curtains, each of which is is 4 feet long and 2 feet wide. If the material she wants costs $14.00 per square foot, how much will she have to spend on curtains?

Each curtain is 4 x 2 = 8 square feet. She needs 6 of them, so that makes 6 x 8 = 48 square feet of material total. Each square foot costs $14.00, so the total she spends will be $14.00 x 48 = $672.

#### John is repainting the outside of his shed. The front and back of the shed are rectangles, 10 feet long and 8 feet high. The sides of the shed are also rectangular, but they are 12 feet long and 8 feet high. If one bucket of paint can cover exactly 50 square feet of the shed, how many buckets of paint should he have to buy to ensure the entire shed is painted and to have the smallest amount left over?

The front and back of the shed measure 10 feet x 8 feet = 80 square feet each, times 2 of them = 160 square feet. The sides measure 12 feet x 8 feet = 96 square feet each, times 2 sides = 192 square feet. The total surface area of the shed is then 160 + 192 = 352 square feet. Each bucket of paint covers 50 square feet, so dividing, we see John needs 352÷50=7.04352÷50=7.04 buckets of paint. Since he can only buy whole buckets, and he needs more than 7, he will need to buy 8 buckets of paint.

#### 75 is 60% of what number?

This plain-language question actually translates directly to a mathematical statement or equation. It says: 75 is 60% of what number. In math, that is: 75=0.60⋅x Take note: “is” translates to “equals”; “of” translates to “times or multiply”; the unknown number can be assigned any letter (here we used x). Continuing with the equation, we divide both sides by 0.60 and get: 125=x Of course, it looks nicer with the sides swapped: x=125

#### Linda has a bag that is filled ^{2}⁄_{3} of the way with candy. If she takes out ^{1}⁄_{4} of the candy and gives it to her brother, what fraction of the bag will be filled with candy?

Linda initially has a ^{2}⁄_{3} -full bag of candies. She gives away ^{1}⁄_{4} of ^{2}⁄_{3}:
^{2}⁄_{3} - (^{1}⁄_{4} * ^{2}⁄_{3}) = ^{2}⁄_{3} - ^{1}⁄_{6}
Coverting ^{2}⁄_{3} to its equivalent fraction of ^{4}⁄_{6}, and continuing to solve:
^{4}⁄_{6} - ^{1}⁄_{6} = ^{3}⁄_{6} = ^{1}⁄_{2}

#### At a movie theater, each ticket regularly costs $8.50. If student tickets are sold at a 30% discount, how much does a student ticket cost?

tudent tickets are sold at 30% discount from the regular price of $8.50: 8.50−(8.50⋅0.30)=8.50−2.55=5.95 8.50−(8.50⋅0.30)=8.50−2.55=5.95 A discounted student ticket will cost $5.95.

#### A pair of pants is on sale for $48.00. If the pants are 25% off, what was the original price?

Let’s call the original price P, and write a problem to solve.
We want to restate the information we have in order to solve for P, the answer to the question.
The easiest way to do this is to set up ratios, then a proportion to solve.
If the discount was 25%, we know that the sale price is 75% of the original price, P, which is 100%:
^{75}⁄_{100}
We know that this ratio equals the sale price (we know), compared to P, which we don’t know:
^{48}⁄_{P}
To form the proportion to solve, set these 2 ratios equal to each other:
^{75}⁄_{100} = ^{48}⁄_{P}
(You would read this, “75 is to 100 as 48 is to P”)
To solve a proportion, cross-multiply and you have:
75P=4800
75P=4800
To isolate the P and get the answer, divide both sides by 75:
P=64

#### On Saturday, Amanda worked for 4 hours and earned $34.00. On Sunday, she worked for 6 hours and earned $54.00. What was her average hourly wage over the weekend?

Amanda earned a total of $34.00 + $54.00 = $88.00 over 6 + 4 = 10 hours. Therefore, her average hourly wage was $88.00/10 = $8.80 per hour.

#### Sam has five science tests throughout a semester. He receives the following grades on his first four science tests: 84, 78, 72, 96. If his final average is an 86, what was his score on the final test?

His final average was 86 over 5 tests, so letting x be the score on his final test, we know that:
(^{84+78+72+96+x}⁄_{5}) = 86.
Multiplying both sides of the equation by 5, we get:
330+x=430
x=100

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