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# Number Relations: GED Test Prep (page 3)

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Updated on Mar 9, 2011

### Sequence of Mathematical Operations

There is an order for doing a sequence of mathematical operations, which is illustrated by the acronym PEMDAS, which can be remembered by using the first letter of each of the words in the phrase: Please Excuse My Dear Aunt Sally. Here is what it means mathematically:

P: Parentheses. Perform all operations within parentheses first.

E: Exponents. Evaluate exponents.

M/D: Multiply/Divide. Work from left to right in your expression.

### Squares and Cube Roots

The square of a number is the product of a number and itself. For example, in the expression 32 = 3 × 3 = 9, the number 9 is the square of the number 3. If we reverse the process, we can say that the number 3 is the square root of the number 9. The symbol for square root is and it is called the radical. The number inside of the radical is called the radicand.

Example

52 = 25; therefore, = 5

Because 25 is the square of 5, it is also true that 5 is the square root of 25.

### Perfect Squares

The square root of a number might not be a whole number. For example, the square root of 7 is 2.645751311… It is not possible to find a whole number that can be multiplied by itself to equal 7. A whole number is a perfect square if its square root is also a whole number.

Examples of perfect squares:
1, 4, 9, 16, 25, 36, 49, 64, 81, 100…

### Odd and Even Numbers

An even number is a number that can be divided by the number 2: 2, 4, 6, 8, 10, 12, 14… An odd number cannot be divided by the number 2: 1, 3, 5, 7, 9, 11, 13… The even and odd numbers listed are also examples of consecutive even numbers and consecutive odd numbers because they differ by two.

Here are some helpful rules for how even and odd numbers behave when added or multiplied:

### Prime and Composite Numbers

A positive integer greater than the number 1 is either prime or composite, but not both. A factor is an integer that divides evenly into a number.

• A prime number has only itself and the number 1 as factors.
• Examples: 2, 3, 5, 7, 11, 13, 17, 19, 23…

• A composite number is a number that has more than two factors.
• Examples: 4, 6, 8, 9, 10, 12, 14, 15, 16…

• The number 1 is neither prime nor composite.