## Let’s add in the correct rules, subtract out the wrong rules, and work towards scoring 100%!

Knowing the basics (and tricks of the trade) of basic math are essential to passing the HESI A2 Math section. We will tell you exactly which topics you MUST know how to solve. The HESI A2 Math section will cover six vital areas including fractions, decimals, ratios, percentages, simple algebra, and conversions.

We will go over the top six math tips that are crucial to passing the HESI A2. Knowing how to solve these equations will prepare you to ace the math section of the HESI A2 exam. Let’s get started!

**1. Fractions**

A fraction means a part of a whole. Fractions have numerators and denominators. For example, one half is written as 1⁄2 where 1 is the numerator and 2 is the denominator. Note that the denominator can never be zero.

Like any regular integer, fractions have values that are larger or smaller relative to other numbers. Fractions can be added, subtracted, multiplied, divided, and converted to decimals.

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

#### Number line

We shall construct a number line to learn some basic aspects of fractions including *value, conversion to decimals, equivalence, like, unlike, improper, and mixed*

**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

To add or subtract *like* fractions, simply add or subtract the numerators while keeping the same denominator.

**Example:** ^{1}⁄_{4} + ^{1}⁄_{4} = ^{2}⁄_{4} which is simplified to ^{1}⁄_{2} by dividing the numerator and denominator by 2.

To add or subtract *unlike* fractions, convert the fractions to equivalent fractions of the same denominator, and then simply add or subtract the numerators while keeping the same denominator.

**Example:** ^{1}⁄_{2} + ^{1}⁄_{3} = ^{3}⁄_{6} + ^{2}⁄_{6} = ^{5}⁄_{6}

To add or subtract *mixed* fractions, first convert them to *improper * Then if they are *like*, you may simply add the numerators. If they are *unlike*, you will need to convert to *equivalent like* fractions and then add or subtract.

**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

To multiply simple fractions, you do not need to have like denominators. You simply multiply the numerators and multiply the denominators.

**Example:** ^{1}⁄_{2} x ^{1}⁄_{4} = ^{1}⁄_{8}

To divide simple fractions, flip the divisor and then multiply across.

Example: ^{1}⁄_{4} ÷ ^{1}⁄_{2} should be rewritten as ^{1}⁄_{4} x ^{2}⁄_{1} = ^{2}⁄_{4} or ^{1}⁄_{2}

To multiply or divide mixed fractions, you must convert to improper fractions and then follow the above rules.

**2. Decimals**

A decimal, like a fraction, represents part of a whole. A decimal may have 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 example, 53.264 has five positions:

- Tens: 5
- Ones: 3
- Tenths: 2
- Hundredths: 6
- Thousandths: 4

To convert a decimal to a fraction, separate the integer and decimal into their *positions*, and then find the common denominator.

### 1.25

- Ones: 1
- Tenths: 2
- Hundredths: 5

Rewrite as 1 + ^{2}⁄_{10} + ^{5}⁄_{100}

Rewrite with common denominator: ^{100}⁄_{100} + ^{20}⁄_{100} + ^{5}⁄_{100} = ^{125}⁄_{100}

If you need to convert a fraction to a decimal, and no calculator is available, a trick is to convert the denominator to 10, 100, 1000, etc. Whichever number you multiplied the denominator by to get to 10, 100, 1000 needs to also be multiplied to the numerator. Then, use the numerator as the value and put the decimal in the correct *position*.

^{4}⁄_{5} = ^{8}⁄_{10} = .8

**3. Ratios**

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

If the terms have the same units, you can compare by dividing.

**Example:** Samuel has 20 pencils and Maria has 10. By dividing each quantity by 10, we get a ratio of 2:1 describing Samuel’s pencils in comparison to Maria’s.

If the terms have different units, conversion to the same units must happen before comparison.

**Example:** A football field is 100 yards, while a basketball court is 50 ft. When both are converted to feet, we can see that the ratio is 300ft:50ft which is simplified to a size of 6:1.

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

**Example:** Jordan received a bouquet of two-dozen pink and yellow roses for her birthday. The ratio of pink to yellow roses was 3:1. How many pink and how many yellow roses did she receive?

First, we must add the terms: 3 + 1 = 4. Then we divide the total number of flowers by that: 24 ÷ 4 = 6. Then we multiply each term by that. Pink: 3 x 6 = 18. Yellow: 1 x 6 = 6.

Ratios may be set equal to other ratios – this is called a *proportion*. It is denoted by a:b::c:d, meaning the ratio of a & b is equal to the ratio of c & d. Usually, one of the terms is unknown, while the other 3 terms are known. This is very simple to solve – just cross multiply the numerators and solve

**Example:** The patient’s weight has dropped by 1.5 pounds over the last 3 days. If the rate of weight loss remains the same, how much more weight will be lost in the next 10 days? ^{1.5}⁄_{3} = ^{x}⁄_{10} is solved to show that x = 5.

**4. Percentages**

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

40% is ^{40}⁄_{100}

Percentages may be used in proportions.

**Example:** HPV was contracted at a 42.5% rate among adults 18-59 years of age. How many students in a university of 40,000 are expected to have had HPV? ^{42.5}⁄_{100} = ^{x}⁄_{40000} is solved to show that x = 17,000 people.

Percentages are also used in calculations.

**Example:** To prepare 1000mL of normal saline, a .9% NaCl, concentration is necessary: ^{.9}⁄_{100} x 1000 shows that 9 grams of NaCl are required.

**5. Simple Algebra**

In algebra, we assign letters to unknown quantities to help us solve an equation. In these equations, we set the left-hand side equal to the right-hand side: *LHS = RHS*

#### Addition Law

If we add the same number to the LHS & RHS, the equation is still equal. *A = B*

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

#### Multiplication Law

If we multiply the LHS & RHS by the same number, the equation is still equal. *A = B*

**Example:** Multiply by m: *mA = mB*

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

1. Isolating x on one side of the equality (LHS)

2. Isolating the value on the other side of the equality (RHS)

*On multiple-choice exams, a trick to solving the equation (and checking your work) is to plug in the answer choices for the variable and see if they make the equation true.*

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

a) 2 -> 3(2-5)≠3

b) 3 -> 3(3-5)≠3

c) 4 -> 3(4-5)≠3

**d) 6 -> 3(6-5)=3**

**6. Metric system**

The metric system is a standardized method of measuring length, weight, mass and time.

- 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 system is an integral part of science that comprises 12% of your HESI A2 math exam. It is worth your time to gain a solid understanding of it now.

The key to understanding the metric system is to grasp that each unit moves by a base of 10. Using gram as an example, study the table 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 |

You will need to know how to convert within the metric system.

**Example:** Convert 13.86g to kg = .01386kg

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

These six topics will consist the majority of your HESI A2 Math exam questions.