ESL Arithmetic Flashcards
49 cards from real Accuplacer College Placement practice questions. Tap to flip, then mark Knew It or Still Learning — missed cards come back until you master them.
Read the first 20 ESL Arithmetic flashcards as text
23.4 x 2.53 =
Answer: 59.202
To multiply decimals, first multiply the numbers as if they were whole numbers: 234 x 253 = 59202. Next, count the total number of decimal places in the original numbers. 23.4 has one decimal place, and 2.53 has two decimal places, for a total of three. Therefore, place the decimal point three places from the right in the product, resulting in 59.202.
Which of the following is the greatest?
Answer: 0.67
To compare decimals, align them by their decimal points and compare the digits from left to right. For 0.62, 0.65, 0.67, and 0.668, all start with '0.6'. Comparing the next digit, we have 2, 5, 7, and 6. Since 7 is the largest of these digits, 0.67 is the greatest number among the choices.
What percentage of 128 is 96?
Answer: 75%
To find what percentage of 128 is 96, divide the part (96) by the whole (128) and then multiply by 100%. The fraction 96/128 simplifies to 3/4 by dividing both numerator and denominator by their greatest common divisor, 32. Converting 3/4 to a decimal gives 0.75, and multiplying by 100% yields 75%. Thus, 96 is 75% of 128.
1.4 + 0.06 + 0.522 =
Answer: 1.982
To add decimals, align the numbers vertically by their decimal points. It's helpful to add trailing zeros so all numbers have the same number of decimal places: 1.400 + 0.060 + 0.522. Then, add each column from right to left, carrying over when necessary. The sum of these numbers is 1.982.
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?
Answer: 50 degrees
The sum of angles in any triangle is 180 degrees. Given one angle is 30 degrees, the sum of the remaining two angles is 180 - 30 = 150 degrees. Let the smaller of the two remaining angles be 'x'. The larger angle is twice as large, so it is '2x'. Setting up the equation x + 2x = 150, we get 3x = 150, which means x = 50 degrees. Therefore, the smaller angle measures 50 degrees.
7 2⁄3 + 4 1⁄4
Answer: 1111⁄12
To add mixed numbers, first add the whole number parts: 7 + 4 = 11. Next, add the fractional parts: 2/3 + 1/4. Find a common denominator for the fractions, which is 12. Convert 2/3 to 8/12 and 1/4 to 3/12. Adding these gives 8/12 + 3/12 = 11/12. Combine the whole number and fraction to get the final answer: 11 11/12.
6⁄7 ÷ 1⁄8 =
Answer: 6 6⁄7
To divide fractions, you multiply the first fraction by the reciprocal of the second fraction. The reciprocal of 1/8 is 8/1. So, the problem becomes 6/7 * 8/1. Multiply the numerators (6 * 8 = 48) and the denominators (7 * 1 = 7) to get 48/7. Converting this improper fraction to a mixed number, 48 divided by 7 is 6 with a remainder of 6, resulting in 6 6/7.
16⁄64 is equivalent to which of the following fractions?
Answer: 1⁄4
To find an equivalent fraction, simplify the given fraction by dividing both the numerator and the denominator by their greatest common divisor (GCD). For 16/64, the GCD of 16 and 64 is 16. Dividing 16 by 16 gives 1, and dividing 64 by 16 gives 4. Therefore, 16/64 is equivalent to 1/4.
25.6 x 10.42 is closest to which of the following?
Answer: 260
To estimate the product of 25.6 x 10.42, round each number to a convenient whole number. 25.6 can be rounded to 26, and 10.42 can be rounded to 10. Multiplying these rounded numbers gives 26 x 10 = 260. This estimate is closest to the actual product, making 260 the correct answer.
6 3⁄4 - 3 1⁄3 =
Answer: 3 5⁄12
To subtract mixed numbers, first subtract the whole number parts: 6 - 3 = 3. Next, subtract the fractional parts: 3/4 - 1/3. Find a common denominator for the fractions, which is 12. Convert 3/4 to 9/12 and 1/3 to 4/12. Subtracting these gives 9/12 - 4/12 = 5/12. Combine the whole number and fraction to get the final answer: 3 5/12.
5⁄8 =
Answer: 0.625
To convert a fraction to a decimal, divide the numerator by the denominator. For 5/8, divide 5 by 8. Performing the division (5 ÷ 8) yields 0.625. This is the decimal equivalent of the fraction 5/8.
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?
Answer: 1⁄6
First, calculate the total number of rough marbles: 2/3 of the 30 marbles are smooth, meaning 1/3 are rough. So, (1/3) * 30 = 10 rough marbles. If half of these rough marbles are green, then there are (1/2) * 10 = 5 rough green marbles. To find the fraction of the total bag that is rough green marbles, divide the number of rough green marbles by the total number of marbles: 5/30, which simplifies to 1/6.
1⁄3 of 250 is approximately ____.
Answer: 85
To find 1/3 of 250, divide 250 by 3. The calculation 250 ÷ 3 results in approximately 83.33. Among the given options, 85 is the closest approximation to this value. Therefore, 1/3 of 250 is approximately 85.
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?
Answer: 3⁄8
A pizza has 8 slices. Pepperoni (P) is 1/2 of 8 = 4 slices. Mushrooms (M) is 3/8 of 8 = 3 slices. Both (P and M) is 1/4 of 8 = 2 slices. To find slices with any topping, use the formula: P + M - (P and M) = 4 + 3 - 2 = 5 slices. The number of slices with no extra topping is the total slices minus slices with any topping: 8 - 5 = 3 slices. As a fraction of the pie, this is 3/8.
6⁄7 + 5⁄4 =
Answer: 59⁄28
To add fractions with different denominators, first find a common denominator. For 6/7 and 5/4, the least common multiple of 7 and 4 is 28. Convert the fractions: 6/7 becomes 24/28 (multiply numerator and denominator by 4), and 5/4 becomes 35/28 (multiply numerator and denominator by 7). Now, add the new fractions: 24/28 + 35/28 = 59/28. This is an improper fraction and can be left as such or converted to a mixed number (2 3/28).
3⁄5 ÷ 2⁄4 =
Answer: 1 1⁄5
To divide fractions, multiply the first fraction by the reciprocal of the second fraction. The reciprocal of 2/4 is 4/2. So, the problem becomes 3/5 * 4/2. Multiply the numerators (3 * 4 = 12) and the denominators (5 * 2 = 10) to get 12/10. This improper fraction simplifies to 6/5, which can be expressed as the mixed number 1 1/5.
3⁄4 is equivalent to which of the following?
Answer: 18⁄24
To find an equivalent fraction, you can multiply or divide both the numerator and denominator by the same non-zero number. For 3/4, let's check option A) 18/24. If you divide both 18 and 24 by their greatest common divisor, 6, you get 18 ÷ 6 = 3 and 24 ÷ 6 = 4. Thus, 18/24 simplifies to 3/4, making it equivalent.
9⁄5 - 2⁄3 =
Answer: 17⁄15
To subtract fractions with different denominators, first find a common denominator. For 9/5 and 2/3, the least common multiple of 5 and 3 is 15. Convert the fractions: 9/5 becomes 27/15 (multiply numerator and denominator by 3), and 2/3 becomes 10/15 (multiply numerator and denominator by 5). Now, subtract the new fractions: 27/15 - 10/15 = 17/15. This is an improper fraction and can be left as such or converted to a mixed number (1 2/15).
If 2 1⁄4 + x = 5 1⁄8, then which of the following is true of x?
Answer: It is greater than 2 and less than 3.
To solve for x, first convert the mixed numbers to improper fractions: 2 1/4 = 9/4 and 5 1/8 = 41/8. The equation becomes 9/4 + x = 41/8. To isolate x, subtract 9/4 from both sides: x = 41/8 - 9/4. Find a common denominator for the subtraction, which is 8, so 9/4 becomes 18/8. Then, x = 41/8 - 18/8 = 23/8. Converting 23/8 back to a mixed number gives 2 7/8, which is greater than 2 and less than 3.
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?
Answer: 50 feet
Sally buys 400 feet of fencing and uses 7/8 of it. This means 1 - 7/8 = 1/8 of the fencing is left over. To find the amount left over, calculate 1/8 of 400 feet. (1/8) * 400 = 400 / 8 = 50 feet. Therefore, Sally will have 50 feet of fencing left over.