Directed Numbers

# Directed Numbers

Practice Quiz

Many of the numbers you use represent situations which have directions as well as size

A number which has a direction and a size is called directed number.

A directed number can either be negative or positive. Directed numbers are real numbers.

They are used for counting. Positive numbers are numbers that are larger than zero and are sometimes written

with a small plus(+) sign placed in front of them. For example +3 and +7 are positive numbers.

Most times we leave the "+" sign off the positive number.Therefore, +3 and 3 mean positve 3.

Negative numbers are numbers that are smaller than zero and are always written

with a mnus (-) signed placed in front of them. For example, -3 and -5 are negative numbers.

Rules for adding negative and positive numbers

1. A posive number + a positive number = a positve number

For example: 3 + 6 = 9

2. A negative number + a negative number = a negative number

For example, -3 + -5 = -8

The above example could also be written as

-3 - 5 = -8. They give the same result.

So, what we got from these rules is that, if both numbers have the same sign we must

Rule for subtracting negative and positive numbers

A positive number - negative number = postive + postive

For example, 7 - (-5) is the same as 7 - -5 and is equal to 7 + 5 = 12.

The two negatives running together equal to a postive. That is why - -5 = +5.

Rules for multiplying and dividing negative and positive numbers

1. A positive number × a positive number = a positive number

For example, 4 × 5 = 20

2. A negative number × a negative number = a positive number

For example, -3 × -4 = -12

3. A positive number ÷ a positive number = a positive number

For example, 8 ÷ 4 = 2

4. A negative number ÷ a negative number = a positive number

For example, -12 ÷ -3 = 4

So, what we got from rules 1-4 is that, if both numbers have the same sign we must

get a positive number for our answer.

5. A positive number × a negative number = a negative number

For example, 5 × -3 = -15 and is the same as -5 × 3 = -15

6. A positive number ÷ a negative number = a negative number

For example, 16 ÷ -2 = -8 and is the same as -16 ÷ 2 = -8.

So, what we got from rules 5 and 6 is that, if one number is negative and the other is postive

then our answer has to be negative.

By now you should have noticed that the rules for multiplication and division are the same.