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# Page 1 Mathematics Study Guide for the TEAS

## How to Prepare for the ATI TEAS Math Test

### General Information

About 72% of the 32 total scored questions on the ATI TEAS math test come from the areas of arithmetic and algebra. The remaining 28% cover measurement and data skills. There are also 4 unscored “pretest” ites that can come from any category. Some of the questions ask you to solve a numerically presented math problem, while others involve dealing with a “word problem.” The word-type problems present a “real-world” scenario, for which you must use math to find a solution.

Here, we have divided our study guide into the four main areas of math dealt with on the test. Under each area, there is a quick review of the major math procedures and concepts with which you need to be familiar. You need to seek further practice in areas in which you have trouble, such as that provided in workbooks or on Internet practice sites. If you search for the mathematical term, you will find plenty of this practice available online.

### Arithmetic

Arithmetic questions on the ATI TEAS deal with basic number concepts, such as the four basic operations and how numbers work when they are applied. The word problems related to this area of math will also require you to know when and how to use these operations. The numbers dealt with in arithmetic questions include positive and negative whole numbers, as well as fractions, percentages, and decimals. Be sure you are familiar with all of these concepts and can manipulate all of the number types accurately using each operation.

#### Place Value

Numerical values are written using one or more digits. There are a total of ten digits: 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. The reason an infinite range of values can be represented, using so few symbols, is that the quantity represented by a given digit changes, depending on its placement within a number. Hence, each position is given its own name, such as tens, hundreds, hundred-thousandths, etc. This is known as “place value.”

A dot, called a decimal point, separates digits that represent whole units from digits representing partial units. Whole units, more commonly referred to as whole numbers, fall to the left of the decimal point, whereas partial units are located to the right. Values that include partial units are commonly referred to as decimal numbers.

Here are the first place values on both sides of the decimal in a number:

So, this number would be read, “34 thousand, one hundred sixty-nine and 257 ten thousandths.”

#### Number Order and Comparison

To determine the correct arrangement when putting numbers in sequential order, position their digits one below the other so that their corresponding place values are aligned. Then compare their values column-by-column, moving from left to right.

10.407
10.0407

Evaluating each place, beginning at the left, we can see that the two numbers are equal until we reach the tenths place. Then, it becomes obvious which number is greater: the top one is larger because it has a 4 in the tenths place, while the bottom number contains a 0 in that place.

The largest number is the number whose leftmost digit has the greatest value. The second largest is the one whose leftmost digit has the second greatest value, and so on. If two or more digits have the same value, find the larger number by comparing the digits in the column that immediately follows. This manner of ordering numbers applies both to whole numbers and decimal numbers.

Another method of ordering numbers is to compare their positions on a number line. Here, the values increase as one moves from left to right. To find numbers that are not marked on a number line, approximate their location by evaluating where they are most likely positioned, relative to values that are marked.

For example, you could determine approximately where 16.5 would fall on this number line, even though that value is not specifically marked. It would be about halfway between 15 and 18.

#### Positive Whole Numbers

Positive whole numbers, also known as nonnegative integers, involve two concepts. The term positive conveys the idea that their values are greater than zero, whereas whole number reflects the fact that they represent one or more complete units. Positive whole numbers are essentially counting numbers. They are unlike fractions and decimals in that they do not include “in between” values.

#### Negative Numbers

Negative numbers are those numbers whose values are less than zero. They are, therefore, located to the left of zero on the number line. In most cases they are preceded by a minus sign. However, in certain contexts, such as on spreadsheets and some bank statements, their negative status is designated by the color red, by enclosing them in parentheses, or both.

The product of a negative number multiplied by another negative number is positive, so:

$–8 \;\cdot \;–3 = 24$

whereas the product of a negative number multiplied by a positive number is negative, thus:

$–8 \cdot 3 = \;–24$

Similarly, the quotient of a negative number divided by another negative number is positive, so:

$–24 \;\div \;–8 = 3$

but the quotient of a negative number divided by a positive number (or vise versa) is negative, hence:

$–24 \div 8 =\; –3$

Adding a group of all negative numbers is carried out by initially adding them as if they were positive, and then labeling the resulting sum with a minus sign.

To add a combination of negative and positive numbers, first add the two types of numbers separately.
Then subtract the smaller sum from the larger sum and label the resulting difference with the sign that matches the larger sum. Hence:

$–8 + 3 + 7 + (–9) =\; –17 + 10 = \;–7$

To solve a subtraction problem involving a negative number or negative numbers, reverse the sign of the number that is being subtracted and then add. For example:

$–8 \,– 4 = \;–8 + (–4) = \;–12$

whereas

$–9\, – (–3) =\; –9 + 3 =\; –6$

Also:

$5\, – (–6) = 5 + 6 = 11$

If you are asked to multiply a series of negative and positive numbers, you can shorten the process by first multiplying the numbers and disregarding the signs. Then, add the sign according to the number of negative signs in the original group.

If the number of negative signs is even, the answer will be positive.
If the number of negative signs is odd, the answer will be negative.

So:

$(-3)(4)(2)(-5) = 120$

but

$(-3)(4)(-2)(-5) = -120$