HESI A2 Math Practice

Question 1

What is the result of adding: 6 3/4 + 8 1/6 = ?

Your Answer: Option(s)

Correct Answer: Option(s) A

Rationale

14 & 11/12 is the result of adding 6 3/4 and 8 1/6.

To solve the addition of mixed numbers, we first convert them to improper fractions, then find a common denominator, and finally perform the addition. The correct sum of 6 3/4 and 8 1/6 simplifies to 14 & 11/12.

A) 14 & 11/12
This choice represents the correct sum of the two mixed numbers. Converting 6 3/4 to an improper fraction gives 27/4, and converting 8 1/6 yields 49/6. Finding a common denominator of 12, we convert 27/4 to 81/12 and 49/6 to 98/12, leading to a total of 179/12, which simplifies to 14 & 11/12.

B) 12 & 3/24
This choice incorrectly suggests a sum that is much lower than the actual result. The fraction 3/24 also simplifies to 1/8, which does not relate to the addition of the two original mixed numbers. The calculation does not align with the proper addition of 6 3/4 and 8 1/6.

C) 35/6
This choice represents an improper fraction that does not equate to the sum of the two mixed numbers. While 35/6 is a valid fraction, it does not correctly represent the addition of 6 3/4 and 8 1/6, which produces a sum significantly greater than 35/6.

D) 14 & 2/5
This option also fails to capture the correct total from the addition. The fraction 2/5 does not reflect any calculations derived from the original numbers. The addition of the two mixed numbers results in a larger value than what is presented here.

Conclusion
The addition of 6 3/4 and 8 1/6 correctly results in 14 & 11/12 after properly converting and summing the values. The other options either provide incorrect sums or misrepresent the values derived from the addition process. Understanding how to add mixed numbers accurately is crucial for arriving at the correct answer.

Select an answer to continue →

Question 2

How many cakes are needed to provide 24 servings for a class of 70 students and 3 staff members?

Your Answer: Option(s)

Correct Answer: Option(s) A

Rationale

Four cakes are needed to provide 24 servings for a class of 70 students and 3 staff members.

To determine the number of cakes required, we first calculate the total number of servings needed for 73 individuals (70 students + 3 staff). Since each cake provides 24 servings, dividing the total servings by the servings per cake gives us the required number of cakes.

A) 4
This choice is correct because to serve 73 people, we need a total of 4 cakes. Each cake serves 24, so 4 cakes provide 96 servings (4 x 24), which is sufficient for the 73 individuals.

B) 2
Choosing 2 cakes would only yield 48 servings (2 x 24), which is insufficient for 73 people. This option fails to meet the requirement, as 48 servings are far fewer than the 73 needed.

C) 3
Three cakes would provide 72 servings (3 x 24), which is still inadequate since it falls short by 1 serving for the total of 73 individuals. Thus, this choice does not fulfill the serving requirement.

D) 5
While 5 cakes would provide 120 servings (5 x 24), which exceeds what is needed, it does not represent the most efficient solution. The question specifically asks for the minimum number of cakes required, making this choice unnecessary and excessive.

Conclusion
To serve a class of 70 students and 3 staff members, a total of 73 servings is required. By calculating the servings per cake, we find that 4 cakes provide sufficient servings without surplus, making this the optimal answer. Other options either fall short of the requirement or unnecessarily exceed it, confirming that four is the correct and most efficient choice.

Select an answer to continue →

Question 3

If 5 is to 30 as X is to 1, find the value of X. (Round to the nearest tenth.)

Your Answer: Option(s)

Correct Answer: Option(s) A

Rationale

X equals 6.

To find the value of X, we need to recognize the relationship in the proportion given. The ratio of 5 to 30 is the same as the ratio of X to 1, and solving the equation shows that X must be 6 to maintain this relationship.

A) 6
This choice correctly represents the solution to the proportion. The relationship can be expressed as \( \frac{5}{30} = \frac{X}{1} \). Simplifying \( \frac{5}{30} \) gives \( \frac{1}{6} \), leading to \( X = 6 \) when cross-multiplying.

B) 5.5
This option does not satisfy the proportional relationship established by the problem. If we substitute 5.5 into the equation \( \frac{5}{30} = \frac{5.5}{1} \), we find that \( \frac{5.5}{1} \) simplifies to 5.5, which does not equal \( \frac{1}{6} \). Thus, it is incorrect.

C) 5
Choosing 5 fails to maintain the ratio between the numbers. If we set \( \frac{5}{30} = \frac{5}{1} \), we see that it simplifies to \( \frac{1}{6} \) on the left side and 5 on the right side, which are clearly not equal. Therefore, this choice is not valid.

D) 4.5
This choice also does not fulfill the original proportion. Substituting 4.5 results in \( \frac{5}{30} = \frac{4.5}{1} \), which simplifies to \( \frac{1}{6} \) on the left and 4.5 on the right. Since these values differ, this option is incorrect.

Conclusion
The proportional relationship in the question requires that the value of X matches the established ratio of 5 to 30. Through solving the proportion, we find that X must equal 6 to maintain this equality, while all other choices lead to incorrect interpretations of the ratio. Understanding these relationships is essential in solving similar proportional problems effectively.

Select an answer to continue →

Question 4

What is the temperature in Celsius when 98.6 degrees Fahrenheit is converted?

Your Answer: Option(s)

Correct Answer: Option(s) B

Rationale

98.6 degrees Fahrenheit is equivalent to 37 degrees Celsius.

To convert Fahrenheit to Celsius, the formula used is C = (F - 32) × 5/9. Applying this formula to 98.6 degrees Fahrenheit yields a temperature of 37 degrees Celsius, which is recognized as the normal human body temperature.

A) 30 Celsius
This temperature is lower than the actual conversion result. If we applied the conversion formula, we would find that 30 degrees Celsius corresponds to approximately 86 degrees Fahrenheit, which is not the same as 98.6 degrees Fahrenheit.

B) 37 Celsius
This is the correct conversion from 98.6 degrees Fahrenheit. Using the formula C = (F - 32) × 5/9, substituting F with 98.6 gives: C = (98.6 - 32) × 5/9 = 37 degrees Celsius, confirming that this is indeed the accurate temperature in Celsius.

C) 47 Celsius
This temperature is significantly higher than the actual conversion. In fact, 47 degrees Celsius equals approximately 116.6 degrees Fahrenheit, which is far above 98.6 degrees Fahrenheit, indicating that this option is incorrect.

D) 21 Celsius
This option is also incorrect, as 21 degrees Celsius is equivalent to about 69.8 degrees Fahrenheit. This temperature is much lower than 98.6 degrees Fahrenheit, thus making it an inaccurate conversion.

Conclusion
The accurate conversion of 98.6 degrees Fahrenheit results in 37 degrees Celsius, affirming that this temperature is recognized as the normal body temperature. The other choices provided differ significantly from this correct conversion, demonstrating the importance of using the proper formula for temperature conversion.

Select an answer to continue →

Question 5

A woman received a bottle of perfume as a present. The bottle contains 3/4 oz of perfume. How many milliliters is this?

Your Answer: Option(s)

Correct Answer: Option(s) C

Rationale

3/4 oz of perfume is equivalent to 22.5 ml.

To convert ounces to milliliters, the conversion factor is approximately 29.57 ml per ounce. Therefore, multiplying 3/4 oz by this conversion factor yields the correct volume in milliliters.

A) 20.0 ml
This choice underestimates the conversion from ounces to milliliters. 3/4 oz converts to approximately 22.5 ml, making 20.0 ml significantly lower than the accurate calculation.

B) 23.0 ml
While this choice is closer to the correct answer, it still does not reflect the accurate conversion of 3/4 oz to milliliters. The precise calculation results in 22.5 ml, hence 23.0 ml is slightly too high.

C) 22.5 ml
This is the correct answer. By multiplying 3/4 by 29.57 ml/oz, the calculation yields approximately 22.5 ml, making this option the accurate conversion.

D) 22.0 ml
This choice, while close, is still an approximation and does not accurately represent the conversion from ounces to milliliters. The correct conversion yields 22.5 ml, thus making 22.0 ml incorrect.

Conclusion
The conversion of 3/4 oz to milliliters results in 22.5 ml, which is confirmed through the use of the appropriate conversion factor. All other options present values that either underestimate or overestimate the correct volume, emphasizing the importance of accurate unit conversions in measurement.

Select an answer to continue →

Free Preview Ended

You've seen the first 5 questions.
Subscribe to unlock the remaining 58 questions + full features.

Unlock Full Exam See Other Exams

14 & 11/12 is the result of adding 6 3/4 and 8 1/6.

Four cakes are needed to provide 24 servings for a class of 70 students and 3 staff members.

X equals 6.

98.6 degrees Fahrenheit is equivalent to 37 degrees Celsius.

3/4 oz of perfume is equivalent to 22.5 ml.

Free Preview Ended

Unlock Full Access

You are leaving this quiz

You're in the middle of a quiz

Report an Issue

Rate this Practice Test