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MAT081 :: Lecture Note :: Week 15
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### Signed Numbers

Numbers that are prefixed with a dash are negative numbers and all negative numbers are less than zero. [Note: zero is neither negative nor positive.]

On the number line, negative numbers are to the left of zero.

Negative numbers are the opposite of positive numbers. For example, `-5` is the opposite of `+5` and vice versa.

The absolute value of a number is its distance from zero on the number line. For example, `-5` is five ones to the left of zero; therefore, its absolute value is `5`.

If both terms have the same sign, then add their respective absolute values and use the common sign as the sign for the sum.

```   -5 + -3
|-5| + |-3|  =  5 + 3  =  8
common sign is -
```

If the terms have differing signs, subtract the smallest absolute value from the largest absolute value. The sum is given the sign of the largest absolute value.

```   -5 + 15
|15| > |-5|
15 - 5 = 10
sign on 15 is +

-5 + 3
|-5| > |3|
5 - 3 = 2
sign on -5 is -
```
##### Subtracting Signed Numbers

Subtracting signed numbers is performed by converting the problem into an addition problem.

If `a` and `b` are numbers, then `a - b` equals `a + (-b)`. In other words, subtraction equals the first number added to the opposite of the second number.

```   general formula:  a - b = a + (-b)

5 -  3 =  5 + (-3) =  2
5 - -3 =  5 + ( 3) =  8
-5 -  3 = -5 + (-3) = -8
-5 - -3 = -5 + ( 3) = -2
```
##### Multiplying Signed Numbers

The product of two factors having the same sign is positive. The product of two factors having different signs is negative. In other words, a negative number times a positive number results in a negative number and vice versa. Any number (regardless of sign) times zero is zero.

```   "Minus times minus equals plus; the reason for this we won't discuss."
--anonymous
```
##### Dividing Signed Numbers

The quotient of two terms having the same sign is positive. The quotient of two terms having different signs is negative. In other words, a negative number divided by a positive number results in a negative number and vice versa. Any number (regardless of sign) cannot be divided by zero.

##### Exercise
1. Graph the numbers `5, -2, -4.7`.

```   -5   -4   -3   -2  -1     0    1    2    3    4    5
+----+----+----+----+----+----+----+----+----+----+
^            ^                                  ^
-4.7          -2                                  5

-4.7 is less than -2 which is less than 5
-4.7 < -2 < 5
```

PurpleMath.com:: Introduction to Negative Numbers
UGA.edu::Why is a negative number times a negative number a positive number?