HESI Math Practice Test

Change the decimal to a percent: 0.000026 = a. 0.0026% b. 0.026% c. 2.6% d. 26%

A: The answer is 0.0026%. This problem requires you to understand the conversion of decimals into percentages. Remember that percent is equivalent to quantity out of a hundred; 75%, for instance, is 75 out of 100. To convert a decimal into a percentage, then, multiply the given decimal by 100. A simple way to perform this calculation is to shift the decimal point two places to the right. So for this problem, 0.000026 is equivalent to 0.0026%.

Change the fraction to a decimal and round to the hundredths place: 78 = a. 0.88 b. 0.92 c. 0.84 d. 0.78

A: The answer is 0.88. This problem requires you to understand the conversion of fractions to decimals. The process is fairly simple: Divide the numerator by the denominator. In order to make this possible, you will have to write 7 as 7.000. The resulting quotient will be 0.875. Remember that the instructions require you to round to the nearest hundredths place. The digit in the thousandths place will be 5, meaning that you need to round up. The final answer is 0.88.

Round to the nearest whole number: What is 18% of 600? a. 108 b. 76 c. 254 d. 176

A: The answer is 108. This problem requires you to understand how to find equivalencies involving percentages. One way to solve this problem is to set up the equation 18100=𝑥600 . In words, this equation states that 18 out of 100 is equal to some unknown amount out of 600. The first step in solving such an equation is to cross-multiply; in other words, 18 × 600 = 100x. This produces 10,800 = 100x, a problem that can be solved for x by dividing both sides by 100. This calculation shows that x = 108, meaning that 108 is 18% of 600. A simpler way is to remember that the word "of" in mathematics means to multiply. To multiply 18% by 600, convert the percentage to a decimal by moving the decimal point two places to the left: 0.18. Then multiply 0.18 and 600 to derive 108.

Express the answer in simplest form: A recipe calls for 112cups sugar, 323cups flour, and 23cup milk. If you want to double the recipe, what will be the total amount of cups of ingredients required? a. 1123 b. 8 c. 1216 d. 623

A: The answer is 1123 . This problem requires you to understand word problems involving the addition and multiplication of mixed numbers and improper fractions. To begin with, convert the three mixed numbers to improper fractions by multiplying the whole number by the denominator and adding the product to the numerator. The resulting fractions will be 32 (sugar), 113 (flour), and 23 (milk). Then find the least common multiple of 2 and 3, which is 6, and convert the three fractions so that they have this denominator: 96 (sugar), 226 (flour), and 46 (milk). Add these fractions together and multiply the sum by two to double the recipe: 96+226+46=356 . 356×2=706=353 . Finally, convert this improper fraction to a simple mixed number by dividing numerator by denominator and simplifying the leftover fraction: 353=1123 .

Report all decimal places: 3.7 + 7.289 + 4 = a. 14.989 b. 5.226 c. 15.0 d. 15.07

A: The answer is 14.989. To solve this problem, you must know how to add a series of numbers when some of the numbers include decimals. As with addition problems 1 and 2, the most important first step is to set up the proper vertical alignment. This step is even more important when working with decimals. Be sure that all of the decimal points are in alignment; in other words, the 7 in 3.7 should be above the 2 in 7.289. Since the final term, 4, is a whole number, we assume a 0 in the tenths place. Similarly, you may assume zeros in the hundredths and thousandths places, if you prefer to have a digit in every relevant place. Then beginning at the rightmost place value (in this case, the thousandths), add the terms together as you would with whole numbers. The decimal point of the sum should be aligned with the decimal points of the terms.

Solve for x: 3:2 :: 24:x a.16 b. 12 c. 2 d. 22

A: The answer is 16. To solve this problem, you must understand proportions. A proportion is a comparison between two or more equivalent ratios. A simple proportion is 1:2 :: 2:4, which can be expressed in words as "1 is to 2 as 2 is to 4." Just as 2 is twice 1, 4 is twice 2. Problem 37 asks you to identify a missing term in a proportion. One way to do this is to set up the problem as a set of equivalent fractions and solve for the variable: 32=24𝑥 . To solve this equation, cross-multiply. You will end up with 3x = 48. Divide both sides by 3 to find that x = 16.

4790 - 2974 = a. 1816 b. 1917 c. 2109 d. 1779

A: The answer is 1816. This problem requires you to understand subtraction with multiple-digit numbers. As in problem 3, the most important step is to align the problem vertically such that the 0 in 4790 is above the 4 in 2974. Again, as in problem 3, you will have to borrow from the place value to the left when the number on the bottom is bigger than the number on top. Be sure to practice this kind of problem with special attention to borrowing from adjacent place values. The HESI exam will often include a few wrong answers that you could mistakenly derive by simply forgetting to borrow.

Express the answer in simplest form: 23+27 = a. 2021 b. 410 c. 421 d. 25

A: The answer is 2021 . This problem requires you to understand addition of fractions with unlike denominators. The denominator is the bottom term in a fraction; the top term is called the numerator. In order to perform addition with fractions, all of the terms must have the same denominator. In order to derive the lowest common denominator in this problem, you must list the multiples for 3 and 7 until you find one that both have in common. In increasing order, multiples of 3 are 3, 6, 9, 12, 15, 18, and 21; multiples of 7 are 7, 14, and 21. The least common multiple is 21. This is also the lowest common denominator for the two fractions. To convert each term into a fraction with this common denominator, you must multiply both numerator and denominator by the same number. To make the denominator of 23 into 21, you must multiply by 7; therefore, you must also multiply the numerator, 2, by 7. The new fraction is 1421 . For the second term, you must multiply numerator and denominator by 3: 27×33=621 . The new addition problem is 1421+621=2021 . Remember that when adding fractions, only the numerators are combined.

4.934 + 7.1 + 9.08 = a. 21.114 b. 21.042 c. 20.214 d. 59.13

A: The answer is 21.114. This problem requires you to understand addition involving a series of numbers, some of which include decimals. This problem is solved in the same manner as problem 9. Be sure to align the terms correctly, such that the 9 in 4.934 is above the 1 in 7.1 and the 0 in 9.08. Assume zeros for the hundredths and thousandths place of 7.1 and for the thousandths place of 9.08. The usual rules for carrying in addition still apply when working with decimals.

474 + 2038 = a. 2512 b. 2412 c. 2521 d. 2502

A: The answer is 2512. To solve this problem, you must know how to add numbers with multiple digits. It may be easier for you to complete this problem if you align the numbers vertically. The crucial thing when setting up the vertical problem is to make sure that the place values are lined up correctly. In this problem, the larger number (2038) should be placed on top, such that the 8 is over the 4, the 3 is over the 7, and so on. Then add the place value farthest to the right. In this case, the 4 and the 8 that we find in the ones place have a sum of 12; the 2 is placed in the final sum, and the 1 is carried over to the next place value to the left, the tens. The tens place is the next to be added: 3 plus 7 equal 10, with the addition of the carried 1 making 11. Again, the first 1 is carried over to the next place value. The problem proceeds on in this vein.

Round your answer to the hundredths place: 28 ÷ 0.6 = a. 46.67 b. 0.021 c. 17.50 d. 16.8

A: The answer is 46.67. To solve this problem, you must know how to divide a whole number by a decimal. To begin with, set the problem up in the form . You cannot perform division when the divisor is less than one, however, so shift the decimal point one place to the right. For every action in the divisor, an identical action must be taken in the dividend: Shift the decimal point (which can be assumed after the 8 in 28) in the dividend as well. The problem is now 6 . This 28 6 .0280 problem can now be solved just like problems 7 and 8. Remember to round your answer to the hundredths place for this problem (this means you will need to solve to the thousandths place). With a knowledge of place value, you can immediately eliminate answer choices B and D, since they are solved to the nearest thousandth and tenth place, respectively.

Karen goes to the grocery store with $40. She buys a carton of milk for $1.85, a loaf of bread for $3.20, and a bunch of bananas for $3.05. How much money does she have left? a. $30.95 b. $31.90 c. $32.10 d. $34.95

B: The answer is $31.90. To solve this problem, you must know how to solve word problems involving decimal subtraction. In this scenario, Karen starts out with a certain amount of money and spends some of it on groceries. To calculate how much money she has left, simply subtract the money spent from the original figure: 40 - 1.85 - 3.20 - 3.05. There is no reason to include the dollar sign in your calculations, so long as you remember that it exists. You cannot subtract the costs of these items at the same time, so you must either subtract them one by one or add them up and subtract the sum from 40. Either way will generate the right answer.

Express the answer in simplest form: 2324−1124 = a. 1123 b. 12 c. 23 d. 1224

B: The answer is 12 . To solve this problem, you must understand subtraction involving fractions with like denominators. As with addition involving fractions with like denominators, you should only subtract the numerators. So, this problem is solved 2324−1124=1224. This answer can be simplified by dividing by the greatest common factor (a factor is any number that can be divided into the given number equally). The factors of 12 are 1, 2, 3, 4, 6, and 12. The factors of 24 are 1, 2, 3, 4, 6, 8, 12, and 24. The greatest common factor of 12 and 24 is 12, so divide both numerator and denominator by 12 to derive the answer in simplest form: 12÷1224÷12=12.

What is the numerical value of the Roman number XVII? a. 22 b. 17 c. 48 d. 57

B: The answer is 17. This problem requires you to know about Roman numerals. This system of numeration is still used in a number of professional contexts. The Roman numerals are as follows: I (1), V (5), X (10), L (50), C (100), D (500), and M (1000). You may also see the lowercase versions of these letters used. The order of the numerals is typically largest to smallest. However, when a smaller number is placed in front of a larger one, the smaller number is to be subtracted from the larger one that follows. For instance, the Roman numeral XIV is 14, as the 1 (I) is to be subtracted from the 5 (V). If the number had been written XVI, it would represent 16, as the 1 (I) is to be added to the 5 (V).

3703 - 1849 = a. 1954 b. 1854 c. 1974 d. 1794

B: The answer is 1854. To solve this problem, you must know how to subtract one multiple-digit number from another. As with the above addition problems, the most important step in this kind of problem is to set up the proper vertical alignment. In subtraction problems, the larger number must always be on top, and there can be only two terms in all (an addition problem can have an infinite number of terms). In this problem, the ones places should be aligned such that the 3 in 3703 is above the 9 in 1849. This problem also requires you to understand what to do when you have a larger value on the bottom of a subtraction problem. In this case, the 3 on the top of the ones place is smaller than the 9 beneath it, so it must borrow 1 from the number to its left. Unfortunately, there is a 0 to the left of the three, so we must extract a 1 from the next place over again. The 7 in 3703 becomes a 6, the 0 becomes a 10 only to have 1 taken away, leaving it as a 9. The 3 in the ones place becomes 13, from which we can now subtract the 9.

27 - 3.54 = a. 24.56 b. 23.46 c. 33.3 d. 24.54

B: The answer is 23.46. To solve this problem, you must know how to subtract a number with a decimal from a whole number. At first glance, this problem seems complex, but it is actually quite simple once you set it up in vertical form. Remember that the decimal point must remain aligned and that a decimal point can be assumed after the 7 in 27. In order to solve this problem, you should assume zeros for the tenths and hundredths places of 27. The problem is solved as 27.00 - 3.54. Obviously, in order to solve this problem you will have to borrow from the 7 in 27.00. The normal rules for borrowing in subtraction still apply when working with decimals. Be sure to keep the decimal point of the difference aligned with the decimal points of the terms.

Round to the nearest whole number: What is 17 out of 68, as a percent? a. 17% b. 25% c. 32% d. 68%

B: The answer is 25%. This problem requires you to understand how to convert fractions into percentages. One way to make this conversion is to divide 17 by 68, which will create a decimal quotient, and then convert this decimal into a percentage. The procedure for division is the same as was used in problem 45; simply divide the numerator (17) by the denominator (68). In order to do so, you will have to express 17 as 17.0. Take the resulting quotient, 0.25, and convert it into a percentage by multiplying it by a hundred or simply shifting the decimal point two places to the right. Of course, you may skip this last step if your quotient makes the right answer apparent. In this problem, for instance, a quotient of 0.25 suggests that only answer choice B can be correct.

Change the fraction to a decimal and round to the hundredths place: 437 = a. 4.37 b. 4.43 c. 4.56 d. 4.78

B: The answer is 4.43. To solve this problem, you must know how to convert mixed numbers into decimals. Perhaps the easiest way to perform this operation is to convert the mixed number into an improper fraction and then divide the numerator by the denominator. Convert the mixed number into an improper fraction by multiplying the whole number by the denominator and adding the product to the numerator: 4 × 7 + 3 = 31, so the improper fraction is 317 . Next divide 31 by 7, according to the same procedure used in problems 7 and 8. Remember that when you have to add 0 to 31 in order to continue your calculations, you must put a decimal point directly above in the quotient. Also, since the problem asks you to round to the hundredths place, you must solve the problem to the nearest thousandth.

Change the fraction to the simplest possible ratio: 814 = a. 2:3 b. 4:7 c. 4:6 d. 3:5

B: The answer is 4:7. To solve this problem, you must know how to convert fractions into ratios. A ratio expresses the relationship between two numbers. For instance, the ratio 2:3 suggests that for every 2 of one thing, there will be 3 of the other. If we applied this ratio to the length and width of a rectangle, for instance, we would be saying that for every 2 units of length, the rectangle must have 3 units of width. A fraction is just one way to express a ratio: The fraction 814 is equivalent to the ratio 8:14. To simplify the ratio, divide both sides by the greatest common factor, 2. The simplest form of this ratio is 4:7.

Round to the nearest whole number: 435 ÷ 7 = a. 16 b. 62 c. 74 d. 86

B: The answer is 62. To solve this problem, you must know how to divide a multiple-digit number by a single-digit number. To begin with, set up the problem as . Then determine the number of times that 7 will go into 43 (one way to do this is to multiply 7 by various numbers until you find a product that is either 43 exactly or no more than 6 fewer than 43). In this case, you will find that 7 goes into 43 six times. Place the 6 above the 3 in 435 and multiply the 6 by 7. The product, 42, should be subtracted from 43, leaving a difference of 1. Since 7 cannot go into 1, bring down the 5 to create 15. The 7 will go into 15 twice, so place a 2 to the right of the 6 on top of the problem. At this point, you should recognize that only answer choice B can be correct. If you proceed further, however, you will find that 435 must become 435.0 so that the 0 can be brought down to make a large enough number to be divided by 7. Once a decimal point is introduced to the dividend, a decimal point must be placed directly above it in the quotient. If you continue working this problem, you will end up with an answer of 62.14.... Note that the instructions tell you only to round to the nearest whole number. Once you have solved to the tenths place, there is no need to continue. 435 7

Change the decimal to a percent: 0.64 = a. 0.64% b. 64% c. 6.4% d. 0.064%

B: The answer is 64%. To solve this problem, you must know how to convert a decimal into a percent. A percentage is a number expressed in terms of hundredths. When we say, for instance, that a candidate received 55% of the vote, we mean that she received 55 out of every 100 votes cast. When we say that the sales tax is 6%, we mean that for every 100 cents in the price another 6 cents are added to the final cost. To convert a decimal into a percentage, multiply it by 100 or just shift the decimal point two places to the right. In this case, by moving the decimal point two places to the right you can derive the correct answer, 64%.

Change the fraction to a percent and round to the nearest whole number: 913 = a. 33% b. 69% c. 72% d. 78%

B: The answer is 69%. To solve this problem, you must know how to convert fractions into percentages. This is done by dividing the numerator by the denominator. In this case, the problem is set up as , because a decimal point and 0 are required to make the calculation possible. Although the decimal point is there, you should still treat 9.0 as if it were 90 when performing your division. Since 13 will go into 90 six times, you can place a 6 above the 0 in 9.0. Remember that your quotient will have a decimal point in the identical place; that is, directly to the left of the 6. If you 0.913 continue your calculations, you will derive an answer of 0.692... However, once you derive that first 6, you should be able to select the correct answer choice. Remember that percentage is the same as hundredths; in other words, 69% is the same as sixty-nine hundredths.

Round to the nearest whole number: Bill got 79 of the answers right on his chemistry test. On a scale of 1 to 100, what numerical grade would he receive? a. 77 b. 78 c. 79 d. 80

B: The answer is 78. To solve this problem, you must know how to convert a fraction into a ratio. In this problem, you are being asked to convert the fraction into a value on a scale from 1 to 100, which is basically like being asked to convert it into a percentage. To do so, divide the numerator by the denominator. The answer will be a repeating seven: 0.777.... Calculate to the thousandths place in order to determine the value. Because the digit in the thousandths place is a 7, you will round up the digit to the left to establish the final answer, 78.

Two-thirds of the students in Mr. Garcia's class are boys. If there are 27 students in the class, how many of them are girls? a. 1 b. 9 c. 12 d. 20

B: The answer is 9. This problem requires you to understand how to approach word problems involving fractions and ratios. You are given the total number of students in the class and the fraction of students who are boys. With this information, you can determine the number of boys by multiplying 23 by 27. You will find that there are 18 boys in the class. You can then find the number of girls by subtracting the number of boys from the total number of students: 27 - 18 = 9. There are nine girls in the class.

Change the percent to a decimal: 17.6% = a. 17.6 b. 1.76 c. 0.176 d. 0.0176

C: The answer is 0.176. This problem requires you to understand the conversion of percentages into decimals. A percentage is an amount out of 100; 17.6%, then, is equivalent to 17.6 out of 100, or 17.6100. A percentage can be converted into decimal form by dividing it by 100, or, more simply, by shifting the decimal point two places to the left. Therefore, 17.6% is equivalent to 0.176.

Express the answer in simplest form: Dean has brown, white, and black socks. One-third of his socks are white; one-sixth of his socks are black. What fraction of his socks are brown? a. 13 b. 26 c. 12 d. 34

C: The answer is 12 . To solve this problem, you must know how to solve word problems requiring fraction addition and subtraction. You are given the proportions of Dean's socks that are white and black. The best approach to this problem is adding together the two known quantities and subtracting the sum from 1. First you need to find a common denominator for 13 and 16 . The lowest common multiple of these two numbers is 6, so convert 13 by multiplying the numerator and denominator by 2. The new equation will be 26+16=36 . This sum is equivalent to 12 , meaning that half of Dean's socks are either white or black. The other half, then, are brown. If you need to perform the calculation, however, it will look like this: 22−12=12 .

Express the answer in simplest form: 347−2314 = a. 2314 b. 1114 c. 1514 d. 237

C: The answer is 1514. This problem requires you to understand subtraction with mixed numbers. In order to perform this problem, you must look at the fractions separately from the whole numbers. To subtract 47−314, the two fractions must have the same denominator. Since 14 is a multiple of 7, you only have to alter the first term. Multiply both numerator and denominator by 2: 47𝑥22=814. Then subtract: 814−314=514. Now subtract the whole numbers: 3 - 2 = 1. Putting the whole number and fraction together yields 1514.

229 × 738 = a. 161,622 b. 167,670 c. 169,002 d. 171,451

C: The answer is 169,002. To solve this problem, you must know how to multiply numbers with several digits. These problems often intimidate students because they produce such large numbers, but they are actually quite simple. As with the above addition and subtraction problems, the crucial first step is to align the terms vertically such that the 8 in 738 is above the 9 in 229. In multiplication, it is a good idea to put the larger number on top, although it is only essential to do so when one of the terms has more place values than the other. In a multiple-digit multiplication problem, every digit gets multiplied by every other digit: First the 9 in 229 is multiplied by the three digits in 738, moving from right to left. Only the digit in the ones place is brought down; the digit in the tens place is placed above the digit to the immediate left and added to the product of the next multiplication. In this problem, then, the 9 and 8 produce 72: The 2 is placed below, and the 7 is placed above the 3 in 738. Then the 9 and the 3 are multiplied and produce 27, to which the 7 is added, making 34. The 4 comes down, the 3 goes above the first 2 in 229, and the process continues. The product of 9 multiplied by 738 is placed below and is added to the products of 2 and 738 and 2 and 738, respectively. For each successive product, the first digit goes one place value to the left. So, in other words, 0 is placed under the 2. These three products are added together to calculate the final product of 738 and 229.

Change the fraction to a percent and round to the nearest whole number: 29 = a. 20% b. 21% c. 22% d. 23%

C: The answer is 22%. This problem requires you to understand how to convert fractions into percentages. To do so, divide the numerator by the denominator. This requires placing a decimal point and 0 after the 2. Remember that the instructions ask you to round your quotient to the nearest whole number. The quotient will be an endlessly repeating 0.2, which means that you will round down to 22%. You only need to solve this equation to the thousandths place in order to obtain sufficient information to answer the question.

Solve for x: 7:42 :: 4:x a.12 b. 48 c. 24 d. 16

C: The answer is 24. This problem requires you to understand proportions. You can use the same procedure to solve this problem as you used to solve problem 37. Set up the proportion in the same way as a pair of equivalent fractions: 742=4𝑥 . Then solve for x. To do this, you must cross-multiply (producing 7x = 168), and then divide both sides by 7. Your calculations should determine that x = 24.

Round your answer to the tenths place: 0.088 × 277.9 = a. 21.90 b. 2.5 c. 24.5 d. 24.46

C: The answer is 24.5. This problem requires you to understand multiplication including numbers with decimals. In some ways, multiplying decimals is easier than adding or subtracting them. This is because the decimal points can be ignored until the very end of the process. Simply set this problem up such that the longer term, 277.9, is on top (this term is considered longer because the initial 0 in 0.088 performs no function). Then multiply according to the usual system: Multiply the rightmost 8 by 9, 7, 7, and 2, and then do the same for the next 8. Add the two products together. Finally, count up the number of decimal places to the right of the decimal point in both terms. In this problem, there are four: 0.088 and 277.9. This means that there should be four places to the right of the decimal point in the product. Once the product is found, you must round it to the tenths place. This is done by assessing the digit in the place to the right of the tenths place (that is, the hundredths place). If that digit is lower than 5, round down; if it is 5 or greater, round up. In this case, there is a 5 in the hundredths place, so the 4 in the tenths place becomes a 5.

Change the decimal to the simplest equivalent proper fraction: 3.78 = a. 334 b. 378 c. 33950 d. 378100

C: The answer is 33950 . This problem requires you to understand the conversion of decimals into mixed numbers. 3.78 has value into the hundredths place, so your fraction will have a denominator of 100. There are three whole units and seventy-eight hundredths, a mixed number that can be written as 378100 . Next, you must simplify this fraction. The only common factor of 78 and 100 is 2, so divide both numerator and denominator by 2: 78÷2100÷2=3950 . This fraction cannot be simplified any further, so the answer is 33950 .

32,788 + 1693 = a. 33,481 b. 32,383 c. 34,481 d. 36,481

C: The answer is 34,481. This problem requires that you understand addition of multiple-digit numbers. As in the first problem, the most important step is properly aligning the two addends in vertical formation, such that the final 8 in 32,788 is above the final 3 in 1693. Again, as in the first problem, you will be required to carry numbers over. It is a good idea to practice these addition problems and pay special attention to carrying over, since errors in this area can produce answers that look correct. The makers of the HESI exam will sometimes try to take advantage of these common errors by making a couple of the wrong answers the results one would get by failing to carry over a digit.

Round to the nearest whole number: 4748 ÷ 12 = a. 372 b. 384 c. 396 d. 412

C: The answer is 396. To solve this problem, you must understand division involving multiple-digit numbers. To begin with, set up the problem as . Then solve the problem according to the procedure you followed in problem 7. Since you are asked to round to the nearest whole number, you must solve this problem to the tenths place. If your calculations are correct, you will have a 6 in the tenths place, meaning that the answer should be rounded up from 395 to 396. 748 ,412

Express the answer in simplest form: 38+28 = a. 18 b. 12 c. 58 d. 516

C: The answer is 58 . To solve this problem, you must know how to add fractions with like denominators. This kind of operation is actually quite simple. The denominator of the sum remains the same; the calculation is performed by adding the numerators. On problems like this, the makers of the HESI will probably try to fool you by including one possible answer in which the denominators have been added; in this problem, for instance, you would end up with answer choice D if you added both numerator and denominator. Do not assume that you have answered the question correctly because your calculations match one of the answer choices. Always check your work.

Round to the nearest percentage point: Gerald made 13 out of the 22 shots he took in the basketball game. What was his shooting percentage? a. 13% b. 22% c. 59% d. 67%

C: The answer is 59%. To solve this problem, you must know how to convert a fraction into a percentage. Gerald made 13 out of 22 shots, a performance that can also be expressed by the fraction 13/22. To convert this fraction into a percentage, divide the numerator by the denominator: . Once you derive the initial 5 in the quotient, you can be fairly certain that answer choice C is correct. Whenever possible, try to take these kinds of shortcuts to save yourself some time. Although the HESI exam gives you plenty of time to complete all of the questions, by saving a little time here and there you can give yourself more opportunities to work through the harder problems.

Change the decimal to the simplest equivalent proper fraction: 0.07 = a. 710 b. 0.0710 c. 7100 d. 70100

C: The answer is 7100 . To solve this problem, you must know how to convert decimals into fractions. Remember that all of the numbers to the right of a decimal point represent values less than one. So, a decimal number such as this will not include any whole numbers when it is converted into a fraction. The 7 is in the hundredths place, so the number is properly expressed as 7100 . The fraction cannot be simplified because 7 and 100 do not share any factors besides one.

Change the percent to a decimal: 38% = a. 3.8 b. 0.038 c. 38.0 d. 0.38

D: The answer is 0.38. To solve this problem, you must know how to convert percentages into decimals. This is done by shifting the decimal point two places to the right. This operation is the same as dividing the percentage by 100. In this problem, assume that the decimal is after the eight in 38%. The equivalent decimal, then, is 0.38.

Change the percent to a decimal: 126% = a. 126.0 b. 0.0126 c. 0.126 d. 1.26

D: The answer is 1.26. To solve this problem, you must know how to convert percentages into decimals. Remember that a percentage is really just an expression of a value in terms of hundredths. That is, 25% is the same as 25 out of 100. To convert a percentage into a decimal, shift the decimal point two places to the left. In this case, the decimal point is assumed to be after the six in 126%. By shifting the decimal point two places to the left, you find that the equivalent decimal is 1.26.

Aaron worked 212 hours on Monday, 334 hours on Tuesday, and 723 hours on Thursday. How many hours did he work in all? a. 1056 b. 1212 c. 1314 d. 131112

D: The answer is 131112 . This problem requires you to understand addition involving mixed numbers. The calculation required by this problem is straightforward: In order to derive the number of hours Aaron worked, add up the three mixed numbers. To make this possible, you will need to find the least common multiple of 2, 4, and 3 so that you can establish a common denominator. The lowest common denominator for this problem is 12. You can either add up the whole numbers separately from the fractions or convert the mixed numbers into improper fractions and add them in that form. Either way will yield the correct answer.

Express your answer as a mixed number in simplest form: 413×27 = a. 613 b. 3710 c. 821 d. 1521

D: The answer is 1521 . To solve this problem, you must know how to multiply mixed numbers and fractions. Unlike fraction addition and subtraction, fraction multiplication does not require a common denominator. However, it is necessary to convert mixed numbers into improper fractions. This is done by multiplying the whole number by the denominator and adding the product to the numerator: in this case, 4 × 3 + 1 = 13. So the problem is now 133×27 . Fraction multiplication is performed by multiplying numerator by numerator and denominator by denominator: 13×23×7=2621 . This improper fraction can be converted into a mixed number by dividing numerator by denominator, which gives 1521 .

Express the answer as a mixed number or fraction in simplest form: 27÷16 = a. 121 b. 2112 c. 134 d. 157

D: The answer is 157 . This problem requires you to understand how to divide fractions. The procedure is the same as for the previous problem: Take the reciprocal of the second term and change the problem to one of multiplication: 27×61=127 . Convert this improper fraction into a mixed number according to the usual procedure. The fraction cannot be simplified because 12 and 7 do not share any factors other than 1.

28.19 - 9 = a. 28.1 b. 18.19 c. 27.29 d. 19.19

D: The answer is 19.19. This problem requires you to understand subtraction of a whole number from a number with a decimal. This problem is somewhat similar to problem 11, although here the decimal is on the top in your vertical alignment. Assume zeros for the tenths and hundredths place of the bottom term, creating the problem 28.19 - 9.00. Be sure to keep your decimal point in the same position in the difference as in the terms. The makers of the HESI often try to fool test-takers by including some possible answers that have the correct digits, but in which the decimal point is misplaced.

Round to the tenths place: What is 6.4% of 32? a. 1.8 b. 2.1 c. 2.6 d. 2.0

D: The answer is 2.0. To solve this problem, you must know how to find equivalencies involving percentages. This problem can be solved with the same strategy used in problem 48. To begin with, set up the following equation: 6.4100=𝑥32 . Next cross-multiply: 6.4 × 32 = 100x. This produces 204.8 = 100x, which is solved for x by dividing both sides of the equation by 100. The value of x is 2.048, which is rounded to 2.0. Or change the percent to a decimal, 0.064, and multiply by 32 to obtain 2.048 and round to 2.0.

Change the decimal to the simplest equivalent proper fraction: 2.80 = a. 2.810 b. 2810 c. 0.281 d. 245

D: The answer is 245 . This problem requires you to understand how to convert a decimal into a fraction or, in this case, a mixed number. Because there are values to the left of the decimal point, you can tell that this number will be equivalent to a mixed number. Indeed, the number 2.80 is equivalent to 280100 . Next, list the factors of 80 (1, 2, 4, 5, 8, 10, 16, 20, 40, 80) and 100 (1, 2, 4, 5, 10, 20, 25, 50, 100). The greatest common factor is 20, so divide both numerator and denominator by 20 to derive the simplest form of the fraction, 245 .

Present the sum as a mixed number in simplest form: 112+129 = a. 235 b. 134 c. 313 d. 256

D: The answer is 256. To solve this problem, you must know how to add mixed numbers and improper fractions. To begin with, convert the mixed number (a mixed number includes a whole number and a fraction) into an improper fraction (a fraction in which the numerator is larger than the denominator). This is done by multiplying the whole number by the denominator and adding the product to the numerator: 1 × 2 + 1 = 3. The problem is now 32+129. Then find the lowest common denominator by listing some multiples of 2 and 9. The lowest common multiple is 18, so you must convert both terms: 32×99=2718, and 129×22=2418. The problem is now 2718+2418=5118. This fraction can be reduced by dividing both the numerator and the denominator by 3: 51÷318÷3=176. This improper fraction can be converted to the mixed number 256.

356 × 808 = a. 274,892 b. 278,210 c. 283,788 d. 287,648

D: The answer is 287,648. This problem requires you to understand multiplication of numbers with several digits. The difficulties you may face with this problem are identical to those of problem 5. Be sure set up your vertical alignment properly, such that the 8 in 808 is above the 6 in 356. Multiply the 6 in 356 by 8, 0, and 8, proceeding from right to left. Then multiply the 5 in 356 by 8, 0, and 8; finally, multiply the 3 in 356 by 8, 0, and 8. For each successive product, add one zero at the extreme right of the product. Add the three products together to find your final answer.

Express the answer as a mixed number or fraction in simplest form: 58÷15 = a. 18 b. 234 c. 313 d. 318

D: The answer is 318 . To solve this problem, you must know how to divide fractions. The process of dividing fractions is similar to that of multiplying fractions, except that the second term must first be inverted, or replaced with its reciprocal. Once this is done, the numerator is multiplied by the numerator, and the denominator is multiplied by the denominator. This problem can be solved by multiplying 58 by the reciprocal of 15, which is 51 or 5: 5×58×1=258 . Finally, convert this improper fraction into a mixed number according to the usual procedure.

Roger's car gets an average of 25 miles per gallon. If his gas tank holds 16 gallons, about how far can he drive on a full tank? a. 41 miles b. 100 miles c. 320 miles d. 400 miles

D: The answer is 400 miles. This problem requires you to understand word problems involving mileage rates and multiplication. The problem states that the car gets an average 25 miles per gallon; in other words, every gallon of fuel powers the car for approximately 25 miles. If the car holds 16 gallons of gas, then, and each of these gallons provides 25 miles of travel, you can set up the following equation: 25 miles/gallon × 16 gallons = 400 miles. Since the first term has gallons in the denominator and the second term has gallons in what would be the numerator (if it were expressed as 16 gallons/1), these units cancel each other out and leave only miles.

Express the answer as a mixed number or fraction in simplest form: 239×13 = a. 78 b. 237 c. 1227 d. 79

D: The answer is 79. This problem requires you to understand multiplication of mixed numbers and fractions. The process is the same as for the previous problem: First, reduce the fractional part of the mixed number to 13 . Then convert 213 into the mixed number 73 . Next, multiply numerator by numerator and denominator by denominator to get the answer: 73×13=79 .