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# Number Relations: GED Test Prep (page 2)

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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.

### Number Lines and Signed Numbers

You have probably dealt with number lines before. The concept of the number line is simple: Less than is to the left and greater than is to the right.

### Absolute Value

The absolute value of a number or expression is always positive because it is the distance of a number from zero on a number line.

Example

|–1| = 1

|2 – 4| = |– 2| = 2

### Working with Integers

An integer is a positive or negative whole number. Here are some rules for working with integers:

### Multiplying and Dividing

(+) × (+) = +         (+) ÷ (+) = +
(+) × (–) = –         (+) ÷ (–) = –
(–) × (–) = +         (–) ÷ (–) = +

A simple way to remember these rules: If the signs are the same when multiplying or dividing, the answer will be positive, and if the signs are different, the answer will be negative.

Adding the same sign results in a sum of the same sign:

(+) + (+) = +
(–) + (–) = –

1. Subtract the absolute values of the numbers.
2. Keep the sign of the larger number.

Example

–2 + 3 =

1. Subtract the absolute values of the numbers: 3 – 2 = 1
2. The sign of the larger number (3) was originally positive, so the answer is positive 1.

Example

8 + –11 =

1. Subtract the absolute values of the numbers: 11 – 8 = 3
2. The sign of the larger number (11) was originally negative, so the answer is –3.