# Mathematics Practice Test for the HESI® exam

#### Which number is represented by the Roman numeral XXVII?

In Roman numerals, an “X” represents the number 10, a “V” represents 5, and “I” is representative of the number 1. In this problem we have 2 X’s, 1 V, and two II’s, which means we have two 10’s (20), one 5, and two 1’s (2). Written mathematically, 20 + 5 + 2 = 27

#### What is (−5)2(−5)^{2} ?

25 is correct. In this situation you address the parenthesis and then the exponent, and the negatives would cancel each other out for a positive answer.

#### What is x^{2}x^{4} ?

x^{6} is correct because you add the exponents, 2 + 4

#### Lance makes $11.35 an hour and earns time and a half pay for every hour over 40. If Lance worked 47 hours this week, about how much will his paycheck be? Round to the hundredths place.

The correct answer is: $573.18 Explanation: $573.18 is correct because $11.35 an hour x 40 hours a week equals $454. Time and a half pay for Lance would be $17.025, and you figure that out by multiplying $11.35 an hour by 1.5. Then multiply $17.025 times 7 overtime hours to get $119.175. Lastly, add $454 and $119.175 and you will get $573.175. Rounded to the hundredth place would be $573.18.

#### Dawn has a 20% off one shirt coupon at her favorite store. If she buys 3 shirts at $29.99 each and uses her coupon, how much will her total bill be? Round to the nearest hundredth.

$83.97 is correct because $29.99 multiplied by 3 shirts is $89.97. To get 20% off of ONE shirt, $29.99 is multiplied by 0.20, which equals $5.998. You subtract $5.998 from $89.97 to get $83.972. Rounded to the nearest hundredth you would get the correct answer, $83.97.

#### What is 0.85 x 0.65?

Multiply 0.85 by 0.65. If it’s easier for you to conceptualize, you can just multiply 85 x 65 to get 5525, and then add the decimal point in after to get 0.5525.

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#### A number is 5 more than half of another number. How would you write this as a mathematical expression?

First, we let N represent any number.
We then express half of N as ^{1}⁄_{2}(N) or ^{N}⁄_{2} .
The phrase 5 more than indicates the mathematical expression 5+.
Putting terms together, we get the correct answer.

#### |7|+|−2|=? Note: This problem is the number -2 within an absolute value sign, not the number -21.

9 is the correct answer because the brackets around the numbers mean you are adding the absolute value of those numbers. An absolute value looks at the actual number within the brackets and not any sign associated with it, including a negative sign. Therefore, 7 + 2 = 9.

#### Monica bought 7 peaches at the grocery store for $2.94. How many could she buy for $4.62?

11 is the correct answer because $2.94/ 7 peaches means each peach costs $0.42 individually. $4.62 divided by $0.42 equals 11 peaches.

#### If you lost 4% of your original weight of 168, what would you now weigh?

To figure out what 4% is, 168 is multiplied by .04 to get 6.72. Then 6.72 is subtracted from 168 to get 161.28.

#### 12.5 x 24.6 = ?

When doing manual multiplication (without the aid of a calculator), multiply 12.5 by 24.6 as if there were no decimals involved. Thus, 125 x 246 =30750. Count the decimal places in the numbers 12.5 and 24.6 - it’s easy to see that there are 2 decimal places. Going back to the product we initially computed, 30750; move the decimal, which we assume to be at the end of the last digit, 2 places to the left. This gives us the correct answer, 307.5. With the calculator, though, simply press the given numbers and the required math operation sign to arrive at the correct answer.

#### What is 8.4 + 2.3 + 0.05?

When adding numbers with decimals manually, write the numbers (called addends) in a column observing correct alignment as to place value and decimal. Write 8.4, then write 2.3 below it, then write 0.05 still below the two numbers. Add vertically. When the addends are written this way, it’s easy to see that the sum is 10.75. When adding with a calculator, simply key in the given numbers with properly placed decimals and the sign of addition to get the correct sum.

#### Which of the following is correct?

Multiply 2/4 by 3/3 to get 9/12. 3/4 *3/3 =9/12. We have introduced a fraction 3/3 which is actually equal to 1. it's like 3/4 *1=3/4; by introducing 1, we're not changing the equation. We just used 3/3 instead of 1. Therefore, 3/4 * 1= 9/12; 3/4* 3/3+9/12; 9/12=9/12.

#### Which number is in the hundredths place in 0.5983?

The spot immediately to the right of the decimal is the tenths place (in this problem, 5), followed by the hundredths place (9), thousandths place (8), and ten thousandths (3).

#### What is 4 ^{3}⁄_{8} +2 ^{2}⁄_{7}

6^{37}⁄_{56}is the correct answer because the whole numbers (4 and 2) are first added together to get 6, and then a common denominator must be found for the fractions. 8 multiplied by 7 equals 56, which will be the common denominator in this equation.
Whatever is done to the denominator must also be done to the numerator, so: ^{3}⁄_{8}=^{21}⁄_{56} and ^{2}⁄_{7}=^{16}⁄_{56}
Since the denominators are now the same, you can just add the numerators:
^{21}⁄_{56}+^{16}⁄_{56}=^{37}⁄_{56}
Add the whole number 6 from the beginning and you have 6 ^{37}⁄_{56}

#### Which of the following is correct?

Multiply ^{6}⁄_{8} by ^{2}⁄_{2} to get ^{12}⁄_{16} . ^{6}⁄_{8} * ^{2}⁄_{2}= ^{12}⁄_{16} . By doing this, we’re not changing the value of the equation because ^{2}⁄_{2} is also equal to 1 and multiplying a number with 1 does not change the value of a number. Therefore, ^{6}⁄_{8} * 1 = ^{12}⁄_{16}; ^{6}⁄_{8}* ^{2}⁄_{2}=^{12}⁄_{16} ; ^{12}⁄_{16}=^{12}⁄_{16} .

#### Reduce ^{72}⁄_{108}to its lowest terms.

Find the factors of the numerator and denominator. ^{72}⁄_{108} = ^{36*2}⁄_{36*3}. The 36 in the numerator and the 36 in the denominator cancel out. The simplified fraction, or the reduced fraction is ^{2}⁄_{3}, the correct answer.

#### What number would you need to multiply 3/4 by to get an answer of 1?

Any fraction multiplied by its reciprocal is equal to 1. In this question, the reciprocal of is 3/4 is 4/3 . 3/4 * 4/3= 12/12 = 1

#### What is the value of x if 4x + 3 = 23?

Try plugging each of the given choices as x in the expression 4x+3 and see which one will give the value of 23. If we take x=5, we have 5x4 equals 20, and 20+3 equals 23. Clearly, 5 is the correct answer. Another method would be to solve algebraically: 4x+3=23; isolate the term with the x variable: 4x=23−3=20; we then have: 4x=20; divide both sides of the equation by 4 to get the value of x: 4x/4=20/4; this gives us the value of x: x=5.

#### What is 10^{4}?

The expression 10^{4} means the base. 10, is raised to the power of 4 or multiplied by itself 4 times. Thus, 10x10x10x10 = 10,000.

#### 5 is what percentage of 40?

Remember always that percentage is a mathematical expression for “a part of a whole” or per 100. For problems such as this, the following formula is very useful: part/whole=percentage/100part/whole=percentage/100. Since we want to know what percentage of 40 is 5, simply substitute the given numbers to the formula, and so we have: 5/40=percentage/100. 0.125x100=percentage. The correct answer is 12.5.

#### What is the decimal equivalent of 3/8?

To get the decimal equivalent of a fraction, simply divide the numerator by the denominator. For the fraction 3/8, divide 3 by 8 to get 0.375, the correct answer.

#### How many cubic centimeters (cc) are there in one milliliter (ml)?

Cubic centimeters (cc) and milliliters (ml) are equal units of measurement, though many scientific disciplines prefer the use of cc to ml. However, in the medical profession it is becoming increasingly a cause for concern when written out in documents, as “cc” can easily be mistaken for “00.”

#### Convert 86 degrees Fahrenheit to Celsius using the following formula:

(F-32)∗^{5}⁄_{9}=C

Plug 86 degrees F into the given formula, thus, we have: (86 - 32) * 5/9 = 54 * 5/9 ; multiply 54 and 5 equals 270; then 270 divided by 9 equals 30, the correct answer.

#### A salesman spent $34 at the store in the first week of December. He spent $73 during each of weeks two and three. The last week, he spent another $123. What was his average weekly expense during the month of December?

To get the average of several amounts, add all amounts then divide by the number of amounts added.

n the question, we add all the weekly expenses, then divide by how many amounts were added: ($34+$73+$73+$123)÷4=$303÷4=$75.75In the question, we add all the weekly expenses, then divide by how many amounts were added:

#### What is

18∗34?

When multiplying manually, multiply the first number by the first digit (ones value) of the second number, in this case: ; then multiply the first number by the second digit (tens value) of the second number, in this case: ; then add the two results: .

When multiplying with a calculator, simply key in the correct numbers (18 and 34) using the correct mathematical operational sign (x) in between the numbers.

#### What is (9 + 4) + (13 + 2)?

This question can be solved easily by adding the numbers inside the parenthesis first, then adding the resulting sums together. But since the mathematical operation involved is only addition, you may actually simply add all numbers without regard for order or parentheses. It’s actually the same as 9+4+13+2=28.

#### Convert .125 into fraction form

To convert 0.125 to its fraction form, think of a number to multiply it with so that it becomes a whole number. That would be 1000, because 0.125 * 1000 = 125, a whole number. Then divide 125 with the same number that you multiplied it with, thus: ^{125}⁄_{1000}. Now we have a fraction. The next step is to reduce this huge fraction to its lowest form. Factor out the numerator and denominator: ^{125}⁄_{1000}=^{125*1}⁄_{125*8}. The 125 in the numerator and denominator cancel out, leaving us the reduced form of the fraction,^{1}⁄_{8} .

#### Which number is a factor of 42?

Factors are numbers you can multiply together to get another number. The factors of 42 are 7, 6, 2, 21, 1, 42, 14 and 3 . From the choices given, 21 is the correct answer.

#### What is 80% of 500?

Always remember that percentage is a mathematical expression for “a part of a whole” or per 100. For this question, we know the percentage and the whole, but not the part. Simply substitute the given numbers to the formula, = ; we don’t know the part, so we call it a, and so we have: = . Then, a = 500 * 0.80 = 400. The correct answer is 400.

If you become familiar with questions like this, you know that to get the part represented by the percentage, you simply multiply the given number (500) by the decimal form of the percentage (0.80); and quickly get 0.80 * 500 = 400.

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