# HESI A2 Math Practice Test

The Health Education Systems, Inc. Admission Assessment (HESI A2) Mathematics Test consists of 50 mathematics questions covering several subsections. These subsections are: Basic Operations; Decimals, Fractions, and Percentages; Proportions, Ratios, Rate, and Military Time; and Algebra.

## Basic Operations

The subsection of the test covering basic operations will include questions related to the four basic mathematical operations: addition, subtraction, multiplication, and division. You will also face questions related to prime numbers, composite numbers, even and odd numbers, decimal points and places, rational numbers, and irrational numbers. Below are some sample problems.

**Addition, Subtraction, Multiplication, and Division**

- 5 + 4 = 9
- 9 – 5 = 4

In addition to basic subtraction problems, you might also face problems requiring regrouping. For instance:

- 721 – 435

You would set the problem up as:

721

__– 435__

In this case, you are looking at a problem in which the ones and tens columns for 721 contain smaller numbers, which means regrouping is necessary to get the correct answer. This requires borrowing. For the 1 in 721, you will borrow from the 2, which leaves that column with a 1. Then, you need to borrow from the 7 to increase the 1. This allows you to properly subtract the values and figure out the difference.

6 11 11

__– 4 3 5__

286

6 × 6 = 36

As you can see, if you add 6 together 6 times, you will receive a sum of 36— i.e. 6 + 6 + 6 + 6 + 6 + 6 = 36.

8 ÷ 2 = 4

In this case, you are dividing the 8 by 2, which leaves 4. In division problems, the order of operations matters, because changing the order changes the resulting value.

**Decimals, Fractions, and Percentages**

This subsection of the test covers adding, subtracting, multiplying, and dividing decimals, as well as identifying place values, and writing numbers in word form. It also covers adding, subtracting, dividing, and multiplying fractions, as well as converting fractions, decimals, and percentages. Below are a few sample problems.

**Adding, Subtracting, Multiplying, and Dividing Decimals and Fractions**

**5.6 + 3 = 8.6**

Because the first number has a decimal and the second does not, aligning is important; otherwise, you might end up with the incorrect answer of 5.9. In this problem, you can also think of the 3 as 3.0.

**5.6 – 2 = 3.6**

To ensure you are solving these problems correctly, add or subtract from the right to the left. If the column sums up to more than 9 when adding decimals, make sure to carry the number. For example: 5.8 + 2.2 = 8.0.

**2.3 × 1.61 = 3.703**

In this problem, multiply 23 by 161. The product is 3703. With numbers containing decimals, work the problem as if using whole numbers. Then, from the right of the decimal in the multiplicand and the multiplier, count the number of places. In this example, count three places from the right of the decimals to receive the correct product.

**22.5 ÷ 1.5 = 15**

In this problem, divide 225 into 15. The product is 15. In division problems with numbers containing decimals, convert the divisor into a whole number. Move the decimals in both numbers to the right.

**1/2 + 1/2 = 2/2 or 1**

**8/5 = 6/5 + 2/5 = 2 + 2/5 = 2 2/5**

To add fractions, if the two fractions have a common denominator, you can simply add the numerators. The same can be said for subtraction. Improper fractions are a bit different. These need to be written as mixed numbers, as seen in question number 6.

**1/4 + 1/5 = 4/5 + 1/5 = 5/5 or 1**

If the two fractions in the problem do not have a common denominator, they need to be changed in order to have the same denominator.

**2/5 × 2/5 = 4/25**

In multiplying fractions, multiply the two numerators for a new numerator, and multiply the two denominators for a new denominator.

**2/5 ÷ 2/5 = 2/5 × 5/2 = 10/10 or 1**

In dividing fractions, swap the numerator and denominator of the second fraction and then multiply.

**Converting Decimals, Fractions, and Percentages**

Percentages are essentially fractions based on a whole number of 100, which equals 100%. Fractions can be expressed as percentages and vice versa. In fact, decimals, fractions, and percentages are related concepts and can be converted to one another. Below are some sample problems.

**3/10 = 30/100 = 30%**

**3/10 = .3 = 30%**

**45% = .45 = 45/100**

## Proportions, Ratios, Rate, and Military Time

This subsection covers proportions, ratios, rate, and military time. In this section, you will see questions related to direct and inverse proportions, ratios, work/unit rate, and the 24-hour clock, often referred to as military time. Below are a few sample problems.

A vet clinic has 100 kennels, which are cleaned every two days. How many times will the kennels be cleaned in five days?

Ratios are comparisons between quantities in a specific order. For example: There are 12 cats in the clowder, and the clinic has 10 kennels. This means the cat to kennel ratio is 12 to 10, or 12:10. Reducing ratios is typical, which means this would become 6:5. The answer above, based on proportional reasoning, is 250. This is because 2.5 days would be half of 5 days. The equation below demonstrates how to get this answer:

**(100 kennels)/(2 days) = (x kennels)/(5 days) = 100(5) = 2(x) = 500 = 2(x) = 500 ÷ 2 = 2x ÷ 2 = 250**

Bob drives for a popular driving service. He made $50 during his first 2 hours driving tonight. He plans to drive for 2 more hours and then go home. Find out how much Bob makes per hour if his rate stays the same until the end of the night.

Unit rate is expressed as a quantity of something in terms of a unit of another. Here, unit rate is expressed in terms of an hour. In this case, Bob will make $100 in total, and his hourly rate is $25. This can be expressed as 50/2 = x/4 = 25. Cross-multiplying gives you 2x = 100, divided by 4 shows that x = 25.

**Convert 0031 hours on a 24-hour clock to time on a 12-hour clock**

**Convert 5:35 p.m. on a 12-hour clock to time on a 24-hour clock**

The answer to the first question is 12:31 a.m. The 24-hour clock expresses time in 4 figures, running from 0000 hour to 2359 hours. The second answer is 1735 hours. For a.m. times on a 12-hour clock, disregard the colon and add a zero to the beginning of the time, if the time has 3 digits. For p.m. times on a 12-hour clock, add 12 to the number. The exception is for times between 12:00 p.m. and 1:00 p.m.

## Algebra

The algebra subsection of the test covers Order of Operations; addition, subtraction, multiplication, and division of positive and negative numbers; as well as parentheses, exponents, and solving linear equations. An important component in this subsection is remembering the Order of Operations, or PEMDAS, which stands for Parentheses, Exponents, Multiplication, Division, Addition, and Subtraction. A couple sample questions can be found below.

**6 + 18 ÷ 3 × (2 + 4) – 3**

This problem can be solved by using PEMDAS. Solve the problem in parentheses first: (2 + 4) = 6; then, simplify the exponents. The equation now appears as: 6 + 18 ÷ 3 × 6 – 3. Next, perform multiplication and division, starting from the left: 18 ÷ 3 = 6; then 6 × 6 = 36. The equation now appears as: 6 + 36 – 3. Lastly, perform addition and/or subtraction starting from the right: 6 + 36 = 42; 42 – 3 = 39.

**6x + 12 = 0**

To solve for x, you need to look at this equation as a single variable linear equation wherein ax + b = 0 and a ≠ 0. So, in this case, reorder the problem: 12 + 6x = 0. Then, reorder the problem again by moving terms with an x to the left and everything else to the right: 12 + -12 + 6x = 0 + -12. Combining like terms gives you: 6x = -12. By dividing each side by 6, you get the answer: x = -2.

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