HESI Math Review – The Absolute Most Important Topics

HESI Math Review - Six important and necessary topics, that if you know them well enough, will make all the difference in your exam.

The Hesi A2 math section has 6 key topics to pass. Six important and necessary topics, that if you know them well enough, will make all the difference in your exam. These 6 areas of knowledge are integral for anyone looking to successfully pass the Hesi A2 Math Section. After finish this HESI Math review, you can immediately check your Math knowledge with our free HESI practice test. Let’s start!

Fractions

The first topic this HESI Math Review reminds you of is fractions.

A number that results from dividing one whole number by another is called a fraction. It consists of two parts: numerators and denominators. For instance, a quarter is written as 1/4 where 1 is the numerator and 4 is the denominator. Please note that zero is never placed as the denominator.

Fractions can be mixed, like, unlike, or equivalent.

Number line

Fractions have many aspects such as like, unlike, improper, mixed, equivalence, value, and conversion to decimals. In order to learn these aspects, we will construct a number line.

Example: Place the following numbers on a line from smallest to largest:

1⁄4, 1⁄2, 2⁄4, 4⁄2, .3, 1 2⁄4

In the above example, we can see that:

  • 1⁄4 has a smaller value than .3 which can be converted to 1⁄3 in its fraction form
  • 1⁄2 and 2⁄4 are equivalent
  • 1 2⁄4 is a mixed fraction and has a value greater than 1. It can be rewritten as 6⁄4 or 3⁄2 or 1.5. 6⁄4 is the improper version of this fraction.
  • 1⁄4 and 2⁄4 are like
  • 2⁄4 and 4⁄2 are unlike

Adding & Subtracting

  • For like fractions: To add or subtract them, we just simply add or subtract the numerators while keeping the same denominators.

Example: 1⁄4 + 1⁄4 = 2⁄4 which is simplified to 1⁄2 by dividing the numerator and denominator by 2.

  • For unlike fractions: Firstly, you need to convert the fractions to equivalent fractions of the same denominators. Secondly, add or subtract the numerators while keeping the same denominator.

Example: 1⁄2 + 1⁄3 = 3⁄6 + 2⁄6 = 5⁄6

  • For mixed fractions: Firstly, you need to convert them to improper. Secondly, you may simply add the numerators if they are like. In case they are unlike, converting them to equivalent fractions before add or subtract them.

Example: 2 1⁄8 + 3 1⁄6 = 17⁄8 + 19⁄6 = 102⁄48 + 152⁄48 = 254⁄48 which is simplified to 127⁄24 or 5 7⁄24

Multiplication & Division

  • For simple fractions: 
  • To multiple them, you do not need to have like denominators. You simply multiple the numerators and multiple the denominators.

Example:  1⁄2 x 1⁄4 = 1⁄8

  • To divide them: flip the divisor and then multiple across. 

Example:  1⁄4 ÷ 1⁄2 should be rewritten as 1⁄4 x 2⁄1 = 2⁄4 or 1⁄2

  • For mixed fractions: You must convert to improper fractions and then follow the above rules.

 

hesi math review

Decimal

A decimal also represents part of a whole like a fraction. However, a decimal probably has an integer in front of it. For example, 1.5 has an integer of 1 and a decimal of .5 and .5 may be thought of as ½.

Decimals have positions, which are varied by 10. For instance, 74.289 has five positions:

  • Tens: 7
  • Ones: 4
  • Tenths: 2
  • Hundredths: 8
  • Thousandths: 9

To convert a decimal to a fraction, place the decimal number over its place value. 

For example 1.25

  • Ones: 1
  • Tenths: 2
  • Hundredths: 5

Rewrite as 1 + 2⁄10 + 5⁄100

Rewrite with a common denominator: 100⁄100 + 20⁄100 + 5⁄100 = 125⁄100

To convert a fraction to a decimal, divide the numerator by the denominator. If required, you can use a calculator to do this. This will give us our answer as a decimal.

Examples:

  • ⁴/₅ as a decimal is 4 ÷ 5 = 0.8
  • ⁷⁵/₁₀₀ as a decimal is 75 ÷100 = 0.75
  • ³/₆ as a decimal is 3 ÷ 6 = 0.5

Ratios

The relationship between two numbers that compare their quantities is called a ratio. The ratio of two terms “a” and “b” can be written as a:b, or “a is to b.”

For the terms of the same unit: You can compare by dividing

Example: Andrea has 40 pens and David has 20. By dividing each quantity by 20, we get a ratio of 2:1 describing Andrea’s pencils in comparison to David’s.

For the terms of different units: Before comparison, you must convert to the same units

Example: A football field is 200 yards, while a basketball court is 100 ft. When both are converted to feet, we can see that the ratio is 600ft:100ft which is simplified to a size of 6:1.

In some cases, the ratio is known and the terms are unknown

Example: Maria received a bouquet of three-dozen red and white roses for her birthday. The ratio of red to white roses was 3:1. How many red and how many white roses did she receive?

First, we must add the terms: 3 + 1 = 4. Then, we divide the total number of flowers by that: 36: 4 = 9. Then we multiply each term by that. Red: 3 x 9 = 27. White: 1 x 9 = 9. 

It is called a proportion when the ratio is set equal to other ratios. It is denoted by a:b::c:d, meaning the ratio of a & b is equal to the ratio of c & d. Usually, while the 3 terms are known, one of the terms is unknown. We just need to cross multiply the numerators and then solve.

Example: The patient’s weight has dropped 1.5 pounds over the last 4 days. If the rate of weight loss remains the same, how much more weight will be lost in the next 15 days?

1.5/4 = x/15 is solved to show that x = 5.625

Percentages

A ratio of a:b where b is always 100 is called a percentage.

For example, 60% is 60/100

The following are some of the uses of percentages

  • In proportions: 

Example: HPV was contracted at a 54.2% rate among adults 18-59 years of age. How many students in a university of 35,000 are expected to have had HPV?

54,2/100 = x/35,000 is solved to show that x = 18,970 people

  • In calculations:

Example: To prepare 1000mL of normal saline, a .9% NaCl, concentration is necessary: .9100 x 1000 shows that 9 grams of NaCl are required.

Simple Algebra

Algebra is a branch of mathematics dealing with symbols and the rules for manipulating those symbols. In these equations, we set the left-hand side equal to the right-hand side: LHS = RHS

Addition Law

The equation is still equal “A = B” if we add the same number to the LHS & RHS.

Example: Add c to both sides: A + c = B + c

Multiplication Law

The equation is still equal “A = B” if we multiply the LHS & RHS by the same number.

Example: Multiply by m: mA = mB

In algebra, we combine these laws to solve equations by:

  1. On  the side of equality (LHS), just let x
  2. On the other side of the equality (RHS), put the value 

Plugging in the answer choices for the variable and see if they make the equation true on multiple-choice exams is a trick to solving the equation. 

Example: What is the value of x for the equation 3(x-5)=3?

  1. a) 2 -> 3(2-5)≠3
  2. b) 3 -> 3(3-5)≠3
  3. c) 4 -> 3(4-5)≠3
  4. d) 6 -> 3(6-5)=3

The correct answer is d)

Metric system

The last topic in this HESI Math Review is the Metric system.

A standardized method of measuring weight, length, time, and mass is the metric system. 

  • For length, the meter (m) is used. 1m = 1.094yd, 3.281 ft, and 39.37 inches.
  • For mass, the gram (g) is used. 1g = .002 pounds
  • For volume, the liter (l) is used. 1l = 33.81oz
  • For temperature, Celsius (° C) is used. 1° C = 33.8F

The metric systems account for 12% of the HESI A2 math exam because it is an important part of science. Therefore, it’s necessary for you to have a deep knowledge of the metric systems. 

Knowing that each unit moves by a base of 10 is the key to understanding the metric system. For instance, study the table of grams below to see that each value is reduced 10-fold when moving from larger to smaller.

 

Kilogram 

Hectogram

Dekagram

Gram

Decigram

Centigram

Milligram

1000

100

10

1

.1

.01

.001

It is a must for you to know how to convert within the metric system.

Example: Convert 24, 68g to kg = .02468kg

You will also need to know how to convert from US Standard to the metric system.

Example: Given that 1m = .000621 mile, how many miles are in 45km?

First, solve that 1km = .621 mile by moving the decimal 3 places to the right (you may think of this as multiplying by 1000) as you move from meter to km. Next, multiply 45 x .621 to solve the equation = 27.945mi

In conclusion, to pass the Hesi A2 math exam, you must know how to solve the six topics in the above HESI Math review post. Remember to practice it before going to the Hesi A2 Math exam, it will help you become more familiar with these topics and can easily pass them.