SIGNED NUMBERS SUBTRACTION

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 Subtraction

Step 1 | Rewrite the subtraction operation as an addition operation.
Step 2 | Change the sign of the number being subtracted.
Step 3 | If any negative number is between two absolute value symbols then change that number to a positive number.
Step 4 | Finish by using the Rules of Addition.

Example 1 Subtract: ( + 5 ) – ( – 2 )

Step 1 | Rewrite the subtraction operation as an addition operation. | ( + 5 ) – ( – 2 ) = becomes ( + 5 ) + ( – 2 ) =
Step 2 | Change the sign of the number being subtracted. | ( + 5 ) + ( – 2 ) = becomes ( + 5 ) + ( + 2 ) =
Step 3 | Finish by using the Rules of Addition. (Rule 1 of the Rules of Addition: If the numbers have like signs, add the numbers and give the answer the same sign as the numbers being added.) | ( + 5 ) + ( + 2 ) = + 7

Example 2 Subtract: ( + 7 ) – ( + 3 )

Step 1 | Rewrite the subtraction operation as an addition operation. | ( + 7 ) – ( + 3 ) becomes ( + 7 ) + (+ 3 ) =
Step 2 | Change the sign of the number being subtracted. | ( + 7 ) + ( – 3 ) =
Step 3 | Finish by using the Rules of Addition. (Rule 2 of the Rules of Addition: If the numbers have unlike signs, find the difference between the numbers without the signs [the absolute values] and give the answer the sign of the larger number.) | ( + 7) + ( – 3 ) = + 4