SIGNED NUMBERS DIVISION

Concept: Signed numbers are whole numbers, their negatives, and zero. To show the complete set of numbers call signed numbers, we extend the positive number line to the left of zero to include the negative numbers. See the graph after the Absolute value definition.

Absolute value: These are numbers, whether they are positive or negative, that are between two of the following symbols “|“. It is a way of telling how far a number is away from zero.

Example "5" is 5 away from zero, but "-5" is also 5 away from zero.
So, the absolute value of 5 is 5 and the absolute value of -5 is also 5.
The symbol "|" is placed on both sides of a number to mean "Absolute Value", so we can write: |-5| = 5.

Steps for Division

Step 1 | If any negative number is between two absolute value symbols then change that number to a positive number.
Step 2 | Divide both numbers, paying no attention to the signs. Record your answer.
Step 3 | Now take note of the signs of the numbers.
| If the signs of both numbers are the same, the sign of the answer is positive.
| If the signs of both numbers are different, the sign of the answer is negative.

Example 1 Divide ( + 24 ) ÷ ( + 6 ) =

Step 1 | Divide numbers, paying no attention to the signs. Record your answer. | (24 ) ÷ ( 6 ) = 4
Step 2 | Now take note of the signs of the numbers. | (+ 24 ) ÷ (+ 6 )
| If the signs of both numbers are the same, the sign of the answer is positive. | (+ 24 ) ÷ (+6 ) = +4
| If the signs of both numbers are different, the sign of the answer is negative. | (Does not apply.)

Example 2 Divide ( – 24 ) ÷ ( – 6 ) =

Step 1 | Divide numbers, paying no attention to the signs. Record your answer. | (24 ) ÷ (6 ) = 4
Step 2 | Now take note of the signs of the numbers. | (– 24 ) ÷ (– 6 )
| If the signs of both numbers are the same, the sign of the answer is positive. | (–24 ) ÷ (–6 ) = +4
| If the signs of both numbers are different, the sign of the answer is negative. | (Does not apply.)

Example 3 Divide ( – 24 ) ÷ ( + 6 ) =

Step 1 | Divide numbers, paying no attention to the signs. Record your answer. | (–24 ) ÷ (+6 ) = 4
Step 2 | Now take note of the signs of the numbers. | (–24 ) ÷ (+6 )
| If the signs of both numbers are the same, the sign of the answer is positive. | (Does not apply.)
| If the signs of both numbers are different, the sign of the answer is negative. | (–24 ) ÷ (+6 ) = –4

Example 4 Divide ( + 24 ) ÷ ( – 6 ) =

Step 1 | Divide numbers, paying no attention to the signs. Record your answer. | (+24) ÷ (– 6 ) = 4
Step 2 | Now take note of the signs of the numbers. | (+24 ) ÷ (– 6 )
| If the signs of both numbers are the same, the sign of the answer is positive. | (Does not apply.)
| If the signs of both numbers are different, the sign of the answer is negative. | (+24) ÷ (– 6 ) = –4

Example 5 Divide ( |– 24| ) ÷ ( + 6 ) =

Step 1 | Change the sign of the absolute value number | (+24 ) ÷ (+6 )
Step 2 | Divide numbers, paying no attention to the signs. Record your answer. | (+24 ) ÷ (+6 ) = 4
Step 3 | Now take note of the signs of the numbers. | (+24 ) ÷ (+6 )
| If the signs of both numbers are the same, the sign of the answer is positive. | (+24 ) ÷ (+6 ) = +4
| If the signs of both numbers are different, the sign of the answer is negative. | (Does not apply.)

Division Rules

Rule 1 | If the signs are the same, the answer is positive.
Rule 2 | If the signs are different, the answer is negative.

Examples 1 to 5:

1: ( + 24 ) ÷ ( + 6 ) = + 4 | The sign of the answer here is positive, because the signs of both numbers are the same.
2: ( – 24 ) ÷ ( – 6 ) = + 4 | The sign of the answer here is positive, because the signs of both numbers are the same.
3: ( – 24 ) ÷ ( + 6 ) = – 4 | The sign of the answer here is negative, because the signs of the numbers are different.
4: ( + 24 ) ÷ ( – 6 ) = – 4 | The sign of the answer here is negative, because the signs of the numbers are different.
5: ( |– 24| ) ÷ ( + 6 ) = + 4 | The sign of the answer here is negative, because the signs of the numbers are different due to the absolute symbols.