# Page 1 Elementary Algebra Study Guide for the ACCUPLACER® test

## How to prepare for the ACCUPLACER Elementary Algebra Test

Of the ACCUPLACER math tests, the Elementary Algebra test is the shortest, containing only 12 questions. This test requires you to have a basic working knowledge of algebra and its operations. There are only three types of questions. These include operations with integers and rational numbers, operations with algebraic expressions, and operations involving the solution of equations, inequalities, and word problems. Many algebraic expressions and functions are also covered in the other math exams but are not explored in as much depth.

### Operations with Integers and Rational Numbers

To solve this type of problem, you will need to be comfortable doing a variety of things with rational numbers and integers, including:

#### Computation with Integers and Negative Rational Numbers

Computation with integers entails the addition, subtraction, multiplication, or division of positive or negative whole numbers.

Consider the following examples:

$3 + 4$
Simply add 4 to 3: $3 + 4 = 7$

$-3 + 4$
This is the equivalent of beginning on the number line at the point -3 and then moving 4 spaces to the right. This expression can also be thought of as $4 + (-3)$ which is also $4 - 3$, all of which simplify to 1.

$3 - 4$
This is the same as starting at positive 3 on the number line and moving to the left 4 spaces. Notice that after moving left 3 spaces, you will arrive at 0. Moving 1 step further to the left ends at -1: $3 - 4 = -1$

$-3 - 4$
This is the same as beginning at the point -3 and moving left 4 spaces. The subtraction of a positive integer is the same as the addition of a negative integer: $-3 - 4 = -3 + (-4) = -7$

$-3 - (-4)$
The subtraction of a negative integer is the same as the addition of a positive integer. Consider why this is so. What is happening in the expression $- (-4)$? This is equivalent to $-1 \cdot (-4)$ which is equivalent to $+4$. The subtraction of a negative integer is the same as the product of negative one and the negative integer. The product of 2 negative integers is always positive. Consequently, the original expression can be rewritten as $-3 + 4 = 1$.

The general rules governing the addition and subtraction of positive and negative rational numbers are the same as those governing integers, but with the added caveat that you can only combine fractions through addition and subtraction when the fractions share a denominator.

To multiply and divide positive and negative integers, perform multiplication or division as usual, but pay attention to the signs of the numbers involved.

A positive times a positive is always positive. A positive times a negative is always negative. A negative times a negative is always positive.

A positive divided by a positive is always positive. A positive divided by a negative is always negative. A negative divided by a negative is always positive.

The same rules apply to positive and negative rational expressions, but with the additional rules governing multiplication and division of fractions.

To multiply fractions, calculate the product of the numerators and place this value over the product of the denominators:

To divide fractions, rewrite the problem as the multiplication of the reciprocal: