Arithmetic for Praxis II ParaPro Test Prep Study Guide
The practice quiz for this study guide can be found at:
This section covers the basics of mathematical operations and their sequence. It also reviews whole numbers, integers, fractions, decimals, percents, and estimation.
The Number Line
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.
A number line can show the approximate values of certain numbers. For example, the following number line shows that –4.5 is halfway between –5 and –4 and that 2.2 is closer to 2 than it is to 3.
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
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
When two or more numbers are being multiplied, they are called factors. The answer that results is called the product. In the following example, 5 and 6 are factors and 30 is their product:
5 ×6 = 30
There are several ways to represent multiplication in this mathematical statement.
A dot between factors indicates multiplication:
5 · 6 = 30
Parentheses around any one or more factors indicate multiplication:
(5)6 = 30, 5(6) = 30, and (5)(6) = 30.
Multiplication is also indicated when a number is placed next to a variable: 5a = 30. In this equation, 5 is being multiplied by a.
In division, the number being divided by is called the divisor. The number being divided into is called the dividend. The answer to a division problem is called the quotient.
There are a few different ways to represent division with symbols. In each of the following equivalent expressions, 3 is the divisor and 8 is the dividend:
Prime and Composite Numbers
A positive integer that is greater than the number 1 is either prime or composite, but not both.
- A prime number is a number that has exactly two factors: 1 and itself. For example, 2, 3, 5, 7, 11, 13, 17, 19, and 23 are all prime numbers.
- A composite number is a number that has more than two factors. For example, 4, 6, 8, 9, 10, 12, 14, 15, and 16 are all composite numbers.
- The number 1 is neither prime nor composite since it has only one factor.
Whole numbers are the set of nonnegative numbers that are not expressed as a fraction or a decimal. For example, 0, 4, 39, and 3,318 are all whole numbers. For the ParaPro Assessment, you will be expected to know how to add, subtract, multiply, divide, compare, and order them.
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