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# Arithmetic for Praxis I: Pre-Professional Skills Test Study Guide

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Updated on Jul 5, 2011

This section covers the basics of mathematical operations and their sequence. It also reviews variables, integers, fractions, decimals, and square roots.

### Numbers and Symbols

#### Numbers and the Number Line

• Counting numbers (or natural numbers): 1, 2, 3,…
• Whole numbers include the counting numbers and zero: 0, 1, 2, 3, 4, 5, 6,…
• Integers include the whole numbers and their opposites. Remember, the opposite of zero is zero:…–3, –2, –1, 0, 1, 2, 3,…
• Rational numbers are all numbers that can be written as fractions, where the numerator and denominator are both integers, but the denominator is not zero. For example, is a rational number, as is . The decimal form of these numbers is either a terminating (ending) decimal, such as the decimal form of which is 0.75; or a repeating decimal, such as the decimal form of , which is 0.3333333…
• Irrational numbers are numbers that cannot be expressed as terminating or repeating decimals (i.e., nonrepeating, nonterminating decimals such as π, ).

The number line is a graphical representation of the order of numbers. As you move to the right, the value increases. As you move to the left, the value decreases.

If we need a number line to reflect certain rational or irrational numbers, we can estimate where they should be.

#### Comparison Symbols

The following table will illustrate some comparison symbols:

In addition, the numbers being added are called addends. The result is called a sum. The symbol for addition is called a plus sign. In the following example, 4 and 5 are addends and 9 is the sum:

4 + 5 = 9

#### Symbols of Subtraction

In subtraction, the number being subtracted is called the subtrahend. The number being subtracted from is called the minuend. The answer to a subtraction problem is called a difference. The symbol for subtraction is called a minus sign. In the following example, 15 is the minuend, 4 is the subtrahend, and 11 is the difference:

15 – 4 = 11