Health Education Systems Inc (HESI) A2 Exam Quiz: Order Of Operations

20 questions · exam conditions

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Order Of OperationsQuestion 1 of 20

Evaluate the following expression, which includes a zero exponent: $12 \times 2 - (4 + 8 \div 4)^0$

Health Education Systems Inc (HESI) A2 Exam Quiz

Health Education Systems Inc (HESI) A2 Exam Quiz: Order Of Operations

Practice Order Of Operations in Health Education Systems Inc (HESI) A2 Exam with focused quiz questions that help you check what you know, review explanations, and build confidence with test-style prompts.

What this quiz covers

This quiz focuses on Order Of Operations, giving you a quick way to practice the rules, question types, and explanations that matter most for Health Education Systems Inc (HESI) A2 Exam.

How to use this quiz

Try each quiz question before looking at the correct answer. Use the explanations to review missed ideas, then come back to similar questions until the pattern feels familiar.

All questions

Question 1

Evaluate the following expression, which includes a zero exponent: $12 \times 2 - (4 + 8 \div 4)^0$

18
23 (correct answer)
24
28

Explanation: When you encounter expressions with zero exponents, remember that any non-zero number raised to the power of zero equals 1. This fundamental rule is key to solving this problem correctly. Let's work through this step-by-step using the order of operations (PEMDAS). First, evaluate the expression inside the parentheses:

4 + 8 \div 4 = 4 + 2 = 6

. Next, apply the zero exponent:

(6)^0 = 1

. Now the expression becomes:

12 \times 2 - 1

. Following order of operations, multiply first:

24 - 1 = 23

. Choice A (18) represents a common error where students might have calculated

12 \times 2 - 6 = 18

, forgetting to apply the zero exponent rule entirely. Choice C (24) occurs when students incorrectly treat the zero exponent as making the entire term disappear, calculating just

12 \times 2 = 24

. Choice D (28) results from mistakenly thinking

(6)^0 = 6

instead of 1, leading to

12 \times 2 - 6 + 6 = 28

or similar computational errors. The correct answer is B (23) because we properly applied the zero exponent rule and followed order of operations. For HESI math success, always remember that

a^0 = 1

for any non-zero number

a

. When you see zero exponents, don't let them intimidate you—simply replace them with 1 and continue with standard order of operations. This rule appears frequently on standardized exams and is often used to test whether you'll make careless mistakes under pressure.

Question 2

What is the value of $3^3 - 5 \times 2 + (16 - 4) \div 6$ ?

4
19 (correct answer)
21
25

Explanation: When you encounter mathematical expressions with multiple operations, you must follow the order of operations (PEMDAS): Parentheses, Exponents, Multiplication and Division (left to right), Addition and Subtraction (left to right). Let's work through

3^3 - 5 \times 2 + (16 - 4) \div 6

step by step: First, handle parentheses:

(16 - 4) = 12

Next, calculate the exponent:

3^3 = 27

Now we have:

27 - 5 \times 2 + 12 \div 6

Then perform multiplication and division from left to right:

$5 \times 2 = 10$
$12 \div 6 = 2$

This gives us:

27 - 10 + 2

Finally, perform addition and subtraction from left to right:

27 - 10 = 17

, then

17 + 2 = 19

The answer is 19, which is choice B. Choice A (4) likely results from incorrectly performing operations left to right without following PEMDAS. Choice C (21) might come from calculating

27 - 5 + 2 - 3

by mishandling the multiplication

5 \times 2

. Choice D (25) could result from errors in the parentheses calculation or adding instead of subtracting somewhere in the process. For HESI math questions, always write out each step of PEMDAS clearly. Don't try to do multiple operations mentally at once—this prevents costly errors and ensures you follow the correct sequence every time.

Question 3

Evaluate the following expression: $60 - 3 \times (4 + 1)^2 \div 5$

15
45 (correct answer)
57
285

Explanation: When you encounter complex mathematical expressions on the HESI, success depends on correctly applying the order of operations (PEMDAS/BODMAS). This determines which calculations you perform first, second, and so on. Let's work through

60 - 3 \times (4 + 1)^2 \div 5

step by step: First, solve what's in parentheses:

(4 + 1) = 5

Next, handle the exponent:

5^2 = 25

Now the expression becomes:

60 - 3 \times 25 \div 5

For multiplication and division, work from left to right:

3 \times 25 = 75

, then

75 \div 5 = 15

Finally, subtract:

60 - 15 = 45

The answer is B) 45. Looking at the wrong answers: A) 15 represents just the result of the multiplication and division portion (

3 \times 25 \div 5

), forgetting to complete the subtraction from 60. C) 57 likely comes from incorrectly calculating the exponent as

5^1 = 5

instead of

5^2 = 25

, leading to

60 - 3 \times 5 \div 5 = 60 - 3 = 57

. D) 285 results from ignoring order of operations entirely and working left to right:

60 - 3 = 57

57 \times 5 = 285

. For HESI math success, always write out each step of PEMDAS separately. Don't try to do multiple operations mentally at once—this prevents the order-of-operations errors that create most wrong answer choices on standardized exams.

Question 4

Which of the following expressions evaluates to a value of 20?

$5 \times 3 + 10 \div 2$ (correct answer)
$5 \times (3 + 10) \div 2$
$(5 \times 3 + 10) \div 2$
$5 \times (3 + 10 \div 2)$

Explanation: When you encounter mathematical expressions with multiple operations, success depends on correctly applying the order of operations (PEMDAS/BODMAS): Parentheses, Exponents, Multiplication/Division (left to right), Addition/Subtraction (left to right). Let's evaluate each expression systematically: Option A:

5 \times 3 + 10 \div 2

Following order of operations: multiplication and division first (left to right), then addition.

5 \times 3 = 15

10 \div 2 = 5

, so

15 + 5 = 20

✓ Option B:

5 \times (3 + 10) \div 2

Parentheses first:

3 + 10 = 13

Then left to right:

5 \times 13 = 65

65 \div 2 = 32.5

Option C:

(5 \times 3 + 10) \div 2

Parentheses first:

5 \times 3 = 15

15 + 10 = 25

Then:

25 \div 2 = 12.5

Option D:

5 \times (3 + 10 \div 2)

Parentheses first, but within them, division before addition:

10 \div 2 = 5

3 + 5 = 8

Then:

5 \times 8 = 40

Only option A equals 20. Study tip: On math questions, write out each step of the order of operations rather than trying to calculate mentally. The HESI often includes expressions where skipping steps or misapplying the order leads directly to one of the wrong answer choices. Always double-check by working through the operations systematically.

Question 5

What is the result of the expression $64 \div 4 \times 2 - 12 \div 3$ ?

-32
4
26
28 (correct answer)

Explanation: When you encounter mathematical expressions with multiple operations, success depends on following the correct order of operations, remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division from left to right, Addition and Subtraction from left to right). Let's work through

64 \div 4 \times 2 - 12 \div 3

step by step. Since there are no parentheses or exponents, we handle multiplication and division from left to right first:

64 \div 4 = 16

, then

16 \times 2 = 32

. Next, we calculate

12 \div 3 = 4

. Our expression now becomes

32 - 4 = 28

. Looking at the wrong answers reveals common order of operations mistakes. Choice A (-32) likely results from incorrectly calculating

64 \div 4 \times 2

64 \div (4 \times 2) = 64 \div 8 = 8

, then

8 - 12 \div 3 = 8 - 4 = 4

, followed by some sign error. Choice B (4) represents calculating

12 \div 3

correctly but making errors with the first part of the expression. Choice C (26) might come from miscalculating one of the division operations, such as getting

64 \div 4 \times 2 = 30

instead of 32, then

30 - 4 = 26

. The correct answer is D (28). For HESI math success, always write out each step when working with order of operations. Don't try to do multiple steps mentally—this prevents calculation errors and ensures you follow PEMDAS correctly. Practice problems with mixed operations until the sequence becomes automatic.

Question 6

A child weighing 44 lbs requires a medication that is dosed at 25 mg/kg per day. The total daily dose is to be divided into two equal doses. Use the conversion factor 1 kg = 2.2 lbs.

Which calculation determines the amount of medication (in mg) to be administered in a single dose?

250 mg (correct answer)
500 mg
550 mg
1210 mg

Explanation: Pediatric dosage calculations require careful attention to weight conversion and dose division. When you encounter these problems, work systematically through each step to avoid common calculation errors. First, convert the child's weight from pounds to kilograms:

44 \text{ lbs} \div 2.2 \text{ lbs/kg} = 20 \text{ kg}

. Next, calculate the total daily dose:

20 \text{ kg} \times 25 \text{ mg/kg/day} = 500 \text{ mg/day}

. Since this total is divided into two equal doses, each single dose is:

500 \text{ mg} \div 2 = 250 \text{ mg}

. Choice A (250 mg) is correct—this represents one of the two equal doses given per day. Choice B (500 mg) represents the total daily dose before division. This is a common error where students forget the final step of dividing by two doses per day. Choice C (550 mg) likely results from rounding errors during weight conversion or arithmetic mistakes in the multiplication step. Choice D (1210 mg) appears to come from multiplying 44 pounds directly by 25 mg without converting to kilograms first, then dividing by two. This demonstrates the critical error of skipping unit conversion. Study tip: Always write out each step in dosage calculations: convert weight units, calculate total daily dose, then divide by frequency. Double-check that your final answer makes clinical sense—pediatric doses should be smaller than adult doses, and a single dose should be less than the total daily amount.

Question 7

Calculate: $36 - 6 \div 2 + 4 \times 3$

21
33
45 (correct answer)
57

Explanation: When you encounter mathematical expressions with multiple operations, you must follow the order of operations (PEMDAS/BODMAS): Parentheses, Exponents, Multiplication and Division (left to right), then Addition and Subtraction (left to right). Let's work through

36 - 6 \div 2 + 4 \times 3

step by step. First, handle multiplication and division from left to right:

6 \div 2 = 3

and

4 \times 3 = 12

. This gives us

36 - 3 + 12

. Now perform addition and subtraction from left to right:

36 - 3 = 33

, then

33 + 12 = 45

. Answer A (21) represents a common error where someone might incorrectly group operations, perhaps calculating

(36 - 6) \div 2 + 4 \times 3 = 30 \div 2 + 12 = 15 + 12 = 27

, though this still doesn't yield 21. Answer B (33) occurs when you stop after the subtraction step (

36 - 3 = 33

) and forget to add the final term. Answer D (57) results from incorrectly performing operations left to right without following proper order:

36 - 6 = 30

30 \div 2 = 15

15 + 4 = 19

19 \times 3 = 57

. The correct answer is C (45). Remember: On math sections of standardized tests, order of operations questions are designed to test whether you'll rush and work left to right versus following proper mathematical rules. Always identify all operations first, then systematically apply PEMDAS to avoid careless errors.

Question 8

A nurse works three 12-hour shifts during the week at a rate of $30 per hour. On the weekend, the nurse works one 8-hour shift at a rate of 1.5 times the weekday hourly rate. A flat tax of $200 is deducted from the total weekly earnings.

Which expression represents the nurse's take-home pay for the week?

$3 \times 12 \times 30 + 8 \times 30 \div 1.5 - 200$
$3 \times 12 \times 30 + 8 \times (30 \times 1.5) - 200$ (correct answer)
$(3 \times 12 + 8) \times (30 + 1.5 \times 30) - 200$
$3 \times 12 \times 30 + 8 \times 30 + 1.5 - 200$

Explanation: When you encounter word problems involving multiple pay rates and deductions, break down each component systematically and translate the written information into mathematical expressions. The nurse's total weekly earnings come from two sources: weekday shifts at the regular rate and weekend shifts at an enhanced rate. For weekdays, the nurse works 3 shifts × 12 hours × $30/hour = $

3 \times 12 \times 30

. For the weekend, the hourly rate increases to 1.5 times the regular rate, so the weekend pay is 8 hours × (1.5 × $30/hour) = $

8 \times (30

\times

1.5)$$. The total gross pay is the sum of these amounts, then subtract the $200 flat tax deduction. Option B correctly represents this calculation: $$3 \times 12 \times 30 + 8 \times (30 \times 1.5) - 200$$. The parentheses properly group the weekend rate calculation (30 × 1.5), then multiply by 8 hours. Option A incorrectly divides by 1.5 instead of multiplying, which would decrease rather than increase the weekend rate. Option C adds the total hours worked to the sum of both pay rates, which makes no mathematical sense for calculating earnings. Option D treats the 1.5 multiplier as an additional flat amount rather than a rate multiplier, completely misrepresenting the weekend pay structure. For HESI math problems, always identify each distinct component first, then build your expression step by step. Pay special attention to rate multipliers and ensure your parentheses group operations correctly to follow the order of operations.

Question 9

Evaluate the expression: $4 \times [15 - (6+6) \div 3] + 2$

14
26
46 (correct answer)
58

Explanation: When you encounter complex expressions with multiple operations, success depends on applying the correct order of operations (PEMDAS/BODMAS): Parentheses/Brackets, Exponents/Orders, Multiplication and Division (left to right), Addition and Subtraction (left to right). Let's work through

4 \times [15 - (6+6) \div 3] + 2

step by step. Start with the innermost parentheses:

(6+6) = 12

. The expression becomes

4 \times [15 - 12 \div 3] + 2

. Next, handle the division inside the brackets:

12 \div 3 = 4

. Now you have

4 \times [15 - 4] + 2

. Continue with the subtraction in brackets:

15 - 4 = 11

, giving you

4 \times 11 + 2

. Perform the multiplication:

4 \times 11 = 44

, leaving

44 + 2

. Finally, add:

44 + 2 = 46

. The answer is C) 46. The wrong answers represent common order-of-operations errors. A) 14 likely results from incorrectly performing operations left to right without following PEMDAS. B) 26 might come from mishandling the bracket operations or incorrectly grouping terms. D) 58 could result from adding before multiplying or making calculation errors within the brackets. Remember: Always work from the inside out with nested grouping symbols, and strictly follow PEMDAS. Write out each step clearly to avoid arithmetic mistakes, especially when brackets contain multiple operations. The HESI often tests whether you can maintain accuracy through multi-step calculations.

Question 10

A patient is prescribed a liquid medication. The initial plan is a 5 mL dose taken three times a day for a full 7-day period. However, after the first 3 days, the physician increases the dosage to 7 mL for each subsequent dose for the remainder of the period. The patient also received a single, separate 10 mL loading dose at the very beginning of treatment.

Based on the patient's treatment plan, what is the total volume of medication administered over the entire 7-day period?

115 mL
129 mL
139 mL (correct answer)
157 mL

Explanation: Medication dosage calculations require careful attention to timing and dose changes throughout the treatment period. When you encounter multi-step dosing schedules, break down each phase separately to avoid calculation errors. Let's work through this systematically. First, calculate the loading dose: 10 mL given once at the beginning. Next, determine the regular dosing phases. Days 1-3: 5 mL three times daily =

5 \times 3 \times 3 = 45

mL. Days 4-7: 7 mL three times daily =

7 \times 3 \times 4 = 84

mL. Total medication =

10 + 45 + 84 = 139

mL. Answer A (115 mL) likely results from forgetting the 10 mL loading dose entirely:

5 \times 9 + 7 \times 12 = 129 - 14 = 115

mL, or miscalculating the day distribution. Answer B (129 mL) represents calculating the regular doses correctly but omitting the single loading dose:

45 + 84 = 129

mL. Answer D (157 mL) suggests an error in the time periods, possibly calculating 5 days at the higher dose instead of 4 days, or double-counting doses. The correct answer is C (139 mL). For HESI dosage calculations, always identify each distinct dosing phase, account for all special doses (loading doses, single doses), and double-check your day counts. Create a timeline when multiple dose changes occur to ensure you don't miss any components of the total calculation.

Question 11

A patient's temperature starts at 102°F. Over the next hour, it rises by 3°F, and then it drops by 7°F. A nurse must record the final temperature in Celsius, rounded to the nearest whole number. The conversion formula is $C = \frac{5}{9}(F - 32)$ .

What is the patient's final temperature in degrees Celsius?

22°C
35°C
37°C (correct answer)
39°C

Explanation: Temperature conversion problems on the HESI often combine multi-step calculations with formula application, testing both your arithmetic skills and attention to detail under pressure. Start by tracking the temperature changes step by step. The patient begins at 102°F, rises by 3°F (102 + 3 = 105°F), then drops by 7°F (105 - 7 = 98°F). So the final temperature is 98°F. Now apply the conversion formula:

C = \frac{5}{9}(F - 32)

. Substituting 98°F:

C = \frac{5}{9}(98 - 32) = \frac{5}{9}(66) = \frac{330}{9} = 36.67°C

. Rounded to the nearest whole number, this gives us 37°C, confirming answer C. Let's examine why the other options are incorrect. Answer A (22°C) would result from a major calculation error, possibly confusing the temperature change sequence or misapplying the formula. Answer B (35°C) likely comes from rounding 36.67°C down instead of following proper rounding rules (since 0.67 > 0.5, you round up). Answer D (39°C) might result from using the starting temperature of 102°F instead of calculating the final temperature of 98°F, or from arithmetic errors in the conversion process. Study tip: For temperature conversion problems, always work methodically: first complete all Fahrenheit calculations, then convert to Celsius in one step. Double-check your rounding—since patient care depends on accuracy, the HESI emphasizes precision in medical calculations.

Question 12

A clinic starts the week with 5 boxes of bandages, with 100 bandages per box. On Monday and Tuesday, they use 75 bandages each day. On Wednesday, they receive a shipment of 3 new boxes. For the rest of the week (Thursday and Friday), they use 120 bandages each day.

How many bandages remain in the clinic at the end of the day on Friday?

110
290
410 (correct answer)
605

Explanation: When you encounter word problems involving inventory tracking, break down the changes chronologically and keep a running total. This tests your ability to organize information and perform sequential calculations accurately. Let's track the bandage inventory day by day: Starting inventory: 5 boxes × 100 bandages = 500 bandages Monday: 500 - 75 = 425 bandages remaining Tuesday: 425 - 75 = 350 bandages remaining Wednesday: 350 + (3 boxes × 100) = 350 + 300 = 650 bandages after shipment Thursday: 650 - 120 = 530 bandages remaining Friday: 530 - 120 = 410 bandages remaining The correct answer is C) 410. Looking at the wrong answers: A) 110 likely results from forgetting to add the Wednesday shipment or making calculation errors with the daily usage amounts. B) 290 probably comes from incorrectly calculating the initial inventory or the shipment size. D) 605 suggests someone added the Wednesday shipment correctly but forgot to subtract Thursday's and Friday's usage. Study tip: For multi-step word problems on the HESI, always write out each step rather than trying to do all calculations mentally. Create a simple timeline or chart showing changes to help prevent errors. Double-check that you've accounted for every piece of information given in the problem—here, that means the initial inventory, each day's usage, and the Wednesday shipment.

Question 13

A medication's concentration is reduced over time. The initial concentration is 100 mg/L. The final concentration is given by the formula: $C_{final} = C_{initial} - 2 \times (4+1)^2$ . What is the final concentration?

50 mg/L (correct answer)
80 mg/L
84 mg/L
90 mg/L

Explanation: When you encounter medication concentration problems on the HESI, you're typically dealing with pharmacokinetics calculations that require careful attention to order of operations and formula interpretation. To find the final concentration, you need to work through the given formula step by step:

C_{final} = C_{initial} - 2 \times (4+1)^2

Start with the parentheses:

(4+1) = 5

Next, handle the exponent:

5^2 = 25

Then multiply:

2 \times 25 = 50

Finally, subtract from the initial concentration:

100 - 50 = 50

mg/L This confirms that A) 50 mg/L is correct. Looking at the wrong answers, B) 80 mg/L likely results from incorrectly calculating

(4+1)^2

as 10 instead of 25, giving you

100 - (2 \times 10) = 80

. C) 84 mg/L suggests you might have calculated

2 \times (4+1) = 10

and subtracted twice, or made an error with the exponent. D) 90 mg/L could come from ignoring the exponent entirely and calculating

100 - 2 \times (4+1) = 100 - 10 = 90

. Study tip: On HESI math problems, always follow PEMDAS (Parentheses, Exponents, Multiplication/Division, Addition/Subtraction) religiously. Write out each step to avoid calculation errors, especially with exponents and nested operations. These systematic approaches prevent the common mistakes that create the distractor answers.

Question 14

A nurse needs to set up an IV drip to administer 1200 mL of saline solution over an 8-hour period. The IV tubing has a drop factor of 15 gtt/mL (drops per milliliter). The drip rate must be calculated in drops per minute (gtt/min).

Which of the following expressions correctly calculates the required IV drip rate in gtt/min?

$(1200 \times 8) \div (15 \times 60)$
$(1200 \times 15) \div 8$
$(8 \times 60) \div (1200 \times 15)$
$(1200 \times 15) \div (8 \times 60)$ (correct answer)

Explanation: IV drip rate calculations are fundamental nursing skills that require converting between different time units and applying the correct formula. When you encounter these problems, always identify what you're given and what units you need for your final answer. Here's the step-by-step logic: You need drops per minute, so think about what creates drops (volume × drop factor) and how to get "per minute" (divide by total minutes). The formula is:

\text{Drip rate} = \frac{\text{Total volume} \times \text{Drop factor}}{\text{Total time in minutes}}

Plugging in the values: Total volume = 1200 mL, drop factor = 15 gtt/mL, and time = 8 hours = 480 minutes. This gives you

\frac{1200 \times 15}{8 \times 60}

, which matches answer choice D. Let's examine why the other options are incorrect: Choice A multiplies 1200 by 8 instead of 15, confusing hours with the drop factor. This fundamental mix-up would give you an incorrect rate. Choice B calculates

(1200 \times 15) \div 8

, which gives you drops per hour, not drops per minute. This is a common trap—forgetting to convert hours to minutes. Choice C inverts the entire calculation, putting time in the numerator and volume/drop factor in the denominator. This would give you minutes per drop, which is meaningless for IV administration. Remember this pattern: For IV calculations on the HESI, always ensure your time units match your desired answer units. Most drip rates are expressed per minute, so convert hours to minutes by multiplying by 60. Keep the formula structure: (volume × drop factor) ÷ (time in minutes).

Question 15

Calculate the value of the following expression: $18 \div \frac{2}{3} - 2 \times (3+1)^2$

-20
-5 (correct answer)
5
11

Explanation: When you encounter complex expressions with multiple operations, success depends on following the order of operations (PEMDAS) systematically: Parentheses, Exponents, Multiplication/Division (left to right), Addition/Subtraction (left to right). Let's work through

18 \div \frac{2}{3} - 2 \times (3+1)^2

step by step: First, handle operations inside parentheses:

(3+1) = 4

Next, calculate the exponent:

4^2 = 16

Now evaluate multiplication and division from left to right:

$18 \div \frac{2}{3} = 18 \times \frac{3}{2} = 27$
$2 \times 16 = 32$

Finally, subtract:

27 - 32 = -5

The correct answer is B) -5. Here's why the other answers are wrong: A) -20 likely results from miscalculating the division as

18 \div \frac{2}{3} = 12

instead of 27, then computing

12 - 32 = -20

. C) 5 comes from getting the correct intermediate values but making a sign error in the final subtraction, calculating

27 - 32 = 5

instead of

-5

. D) 11 suggests multiple errors, possibly calculating

18 \div \frac{2}{3} = 27

correctly but then computing

2 \times (3+1)^2 = 16

instead of 32, yielding

27 - 16 = 11

. Study tip: On HESI math questions, write out each step of PEMDAS separately rather than trying to do multiple operations mentally. This prevents order-of-operations errors and sign mistakes that create attractive wrong answers.

Question 16

Calculate the value of the following expression: $48 \div 8 \times 3 - 2 + 9 \div 3$

3
13
19 (correct answer)
20

Explanation: When you encounter mathematical expressions with multiple operations, you must follow the order of operations (PEMDAS/BODMAS) to get the correct answer. This means performing operations in this sequence: Parentheses/Brackets, Exponents/Orders, Multiplication and Division (left to right), then Addition and Subtraction (left to right). Let's work through

48 \div 8 \times 3 - 2 + 9 \div 3

step by step: First, handle all multiplication and division from left to right:

$48 \div 8 = 6$
$6 \times 3 = 18$
$9 \div 3 = 3$

Now the expression becomes:

18 - 2 + 3

Next, perform addition and subtraction from left to right:

$18 - 2 = 16$
$16 + 3 = 19$

The answer is 19, which is choice C. Let's examine why the other answers are incorrect. Choice A (3) likely results from incorrectly calculating only the final division

9 \div 3

and ignoring the rest. Choice B (13) could come from performing operations out of order, perhaps doing

48 \div 8 - 2 + 9 \div 3 = 6 - 2 + 3 + 6 = 13

by mistakenly treating the multiplication separately. Choice D (20) might result from adding instead of subtracting in the final steps, getting

18 + 2 = 20

before adding 3. Remember: HESI math questions often test whether you can correctly apply order of operations under time pressure. Always work systematically from left to right within each operation level, and double-check your arithmetic at each step.

Question 17

A patient's fluid intake is being calculated. The patient consumed $\frac{3}{4}$ of a 12-ounce drink and $\frac{1}{2}$ of an 8-ounce soup. What is the total fluid intake in ounces?

10 ounces
13 ounces (correct answer)
15 ounces
17 ounces

Explanation: Fluid intake calculations are fundamental in healthcare for monitoring patient hydration and medication administration. When you encounter fractional consumption problems, you need to calculate what portion of each item was actually consumed, then sum the results. For this patient's intake, start with the drink:

\frac{3}{4} \times 12 \text{ ounces} = \frac{3 \times 12}{4} = \frac{36}{4} = 9 \text{ ounces}

Next, calculate the soup consumption:

\frac{1}{2} \times 8 \text{ ounces} = \frac{1 \times 8}{2} = \frac{8}{2} = 4 \text{ ounces}

Total fluid intake:

9 + 4 = 13 \text{ ounces}

Therefore, B) 13 ounces is correct. Looking at the incorrect options: A) 10 ounces likely results from miscalculating the fractions, perhaps computing

\frac{3}{4} \times 12

as 6 instead of 9. C) 15 ounces suggests adding the original container sizes (12 + 8 = 20) then subtracting something incorrectly, or making computational errors with the fractions. D) 17 ounces might come from incorrectly adding partial calculations or mishandling the fraction multiplication. Remember to always multiply the fraction by the total amount available, not add fractions to whole numbers. On the HESI, fluid intake questions test your ability to handle real-world nursing scenarios where patients rarely consume complete portions. Practice converting fractions to decimals if that's easier for you:

\frac{3}{4} = 0.75

and

\frac{1}{2} = 0.5

can make multiplication more straightforward.

Question 18

Evaluate the expression: $4.5 + 2.5 \times (6 - 2^2)$

9.5 (correct answer)
14.0
15.5
44.5

Explanation: When you encounter complex mathematical expressions on the HESI, always remember to follow the order of operations (PEMDAS/BODMAS): Parentheses/Brackets, Exponents/Orders, Multiplication and Division (left to right), Addition and Subtraction (left to right). Let's work through

4.5 + 2.5 \times (6 - 2^2)

step by step. First, handle what's inside the parentheses:

6 - 2^2

. The exponent comes before subtraction, so

2^2 = 4

, making this

6 - 4 = 2

. Now our expression becomes

4.5 + 2.5 \times 2

. Next, perform the multiplication:

2.5 \times 2 = 5.0

. Finally, add:

4.5 + 5.0 = 9.5

. Looking at the wrong answers: Choice B (14.0) likely results from incorrectly calculating

6 - 2^2

6 - 2 = 4

, then

4.5 + 2.5 \times 4 = 4.5 + 10 = 14.5

, or making a similar computational error. Choice C (15.5) might come from adding before multiplying, calculating

4.5 + 2.5 = 7

, then

7 \times 2 = 14

, plus various calculation mistakes. Choice D (44.5) appears to result from major order of operations errors, possibly treating the entire expression as

(4.5 + 2.5) \times (6 - 2^2) \times \text{something}

. The correct answer is A (9.5). Study tip: On HESI math problems, write out each step of PEMDAS separately. Don't try to do multiple operations mentally at once—this prevents costly order-of-operations mistakes that create tempting wrong answer choices.

Question 19

Evaluate the expression: $5 + [30 - (2+3)^2] \div 5$

5
6 (correct answer)
10
12

Explanation: When you encounter complex mathematical expressions with multiple operations and grouping symbols, you must follow the order of operations (PEMDAS/BODMAS): Parentheses/Brackets, Exponents/Orders, Multiplication and Division (left to right), Addition and Subtraction (left to right). Let's work through this step-by-step:

5 + [30 - (2+3)^2] \div 5

First, solve the innermost parentheses:

(2+3) = 5

Next, handle the exponent:

5^2 = 25

Now work inside the brackets:

30 - 25 = 5

The expression becomes:

5 + 5 \div 5

Following order of operations, division comes before addition:

5 \div 5 = 1

Finally:

5 + 1 = 6

Looking at the wrong answers: Choice A (5) results from incorrectly adding before dividing, getting

10 \div 5 = 2

, then somehow arriving at 5. Choice C (10) comes from forgetting to divide by 5 at the end, stopping at

5 + 5 = 10

. Choice D (12) likely results from multiple order-of-operations errors, possibly calculating

(2+3)^2

incorrectly or mishandling the bracket operations. The correct answer is B (6). For HESI math success, always write out each step of complex expressions rather than trying to solve them mentally. This prevents order-of-operations mistakes, which are among the most common errors on standardized exams. When you see nested grouping symbols, work from the inside out systematically.

Question 20

Evaluate the expression: $100 - [2 \times (15 - 5) + 3^2]$

62
66
71 (correct answer)
74

Explanation: When you encounter complex mathematical expressions with multiple operations, the order of operations (PEMDAS/BODMAS) is crucial. You must work systematically: Parentheses/Brackets first, then Exponents, then Multiplication and Division (left to right), and finally Addition and Subtraction (left to right). Let's solve

100 - [2 \times (15 - 5) + 3^2]

step by step: First, resolve the innermost parentheses:

(15 - 5) = 10

Next, handle the exponent:

3^2 = 9

Now the expression becomes:

100 - [2 \times 10 + 9]

Perform the multiplication:

2 \times 10 = 20

Add within the brackets:

20 + 9 = 29

Finally, subtract:

100 - 29 = 71

The correct answer is C) 71. Let's examine why the other options are incorrect: A) 62 likely results from incorrectly calculating

3^2

as 6 instead of 9, giving you

100 - [20 + 6] = 100 - 26 = 74

, then making an additional error. B) 66 might occur if you forget to square the 3 entirely, treating it as

100 - [20 + 3] = 77

, then subtracting incorrectly. D) 74 happens when you calculate

3^2

as 6 instead of 9, resulting in

100 - [20 + 6] = 100 - 26 = 74

. Study tip: Always write out each step when working with order of operations. The most common errors involve mishandling exponents or rushing through the sequence. Double-check that you've correctly identified and calculated all exponential terms before proceeding.