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# Positive and Negative Numbers Study Guide for McGraw-Hill's ASVAB

By McGraw-Hill Professional
Updated on Mar 16, 2011

Positive numbers are numbers that are greater than 0, such as +6. Negative numbers are numbers that are less than 0, such as –4. (See number line at bottom of page.)

The absolute value of a number is the distance of the number from 0 on a number line. For example, the absolute value of +6 is 6. The absolute value of –4 is 4.

Operations with Positive and Negative Numbers   For the ASVAB, you'll need to know how to add, subtract, multiply, and divide with positive and negative numbers.

Adding Positive and Negative Numbers   To add numbers with the same sign, add their absolute values. The sum will have the same sign as the numbers you added.

Examples

To add numbers with different signs, first find their absolute values. Subtract the lesser absolute value from the greater absolute value. Give the sum the same sign as the number with the greater absolute value.

Examples

Subtracting Positive and Negative Numbers   Look again at the number line. (See number line at bottom of page.)

• When you subtract a positive number, you move left on the number line a distance equal to the absolute value of the number being subtracted.
• When you subtract a negative number, you move right on the number line a distance equal to the absolute value of the number being subtracted.

Examples

Subtract positive numbers (move left on the number line):

Subtract negative numbers (move right on the number line):

Note that when you subtract negative numbers, all you really need to do is change the sign of the number being subtracted from negative to positive, and then add.

Absolute Value   A number regardless of its sign (+ or –) is called the absolute value. The absolute value of a number is shown as the number placed between two vertical parallel lines; for example, |–4| or |4|. In each of these cases, the absolute value of the number is 4. When using absolute values, just ignore the sign.

Examples

Multiplying and Dividing Negative Numbers   These operations are easy if you use just one trick. To multiply or divide negative numbers, first treat all the numbers as positive and perform the operation is normally.

• If there is an odd number of negative signs, the answer will be negative.
• If there is an even number of negative signs, the number will be positive.

Examples

(–5)(+6)(+2) = –60

This expression has 1 negative sign. Since 1 is an odd number, the result is negative.

(–5)(–6)(+2) = +60

This expression has 2 negative signs. Since 2 is an even number, the result is positive.

This expression has 2 negative signs. Since 2 is an even number, the result is positive.

This expression has 1 negative sign. Since 1 is an odd number, the result is negative.

Subtracting Numbers within Parentheses   If there is a minus sign in front of parentheses, change the sign of all the numbers within the parentheses and then add.

Examples

Multiplying and Dividing by Zero

Remember the following rules:

• Any number multiplied by zero = zero.
• Zero divided by any number = zero.
• Dividing by zero is considered to be "undefined."

Examples