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Module 1: Numbers and Whole Numbers

Applications to Addition/Subtraction

In addition and subtraction of signed numbers, the operation and the number sign of the number directly following will combine. This will be covered again in multiplication/division of signed numbers. If both signs are the same, the result is always positive. If the signs are different, the result is always negative.

Below is a more complete guide:

Addition

Description Examples

When the signs of all numbers are the same, the sum will always be the same sign.

+ 2 + + 4 = 2 + 4 = 6 {"version":"1.1","math":"+2++4=2+4=6"}

2 + 4 = 2 4 = 6 {"version":"1.1","math":"-2+-4=-2-4=-6"}

When the signs are different but the positive number is larger, subtract to get a positive result.

2 + + 4 = 2 + 4 = 2 {"version":"1.1","math":"-2++4=-2+4=2"}

+ 4 + 2 = 4 2 = 2 {"version":"1.1","math":"+4+-2=4-2=2"}

When the signs are different but the negative number is larger (smaller value), subtract to get a negative result.

+ 2 + 4 = 2 4 = 2 {"version":"1.1","math":"+2+-4=2-4=-2"}

4 + + 2 = 4 + 2 = 2 {"version":"1.1","math":"-4++2=-4+2=-2"}

Subtraction

Description Examples

When the signs are the same, the difference is positive so long as larger number is positive after combining signs.

The opposite applies when the larger number is negative.

+ 4 + 2 = 4 2 = 2 {"version":"1.1","math":"+4-+2=4-2=2"}

2 4 = 2 + 4 = 2 {"version":"1.1","math":"-2--4=-2+4=2"}

+ 2 + 4 = 2 4 = 2 {"version":"1.1","math":"+2-+4=2-4=-2"}

4 2 = 4 + 2 = 2 {"version":"1.1","math":"-4--2=-4+2=-2"}

When the signs are different, a sum is formed so long as the negatives combine to make a positive.

When the minus combines with a positive to make a negative, the difference is negative but appears as if the number were added.

+ 4 2 = 4 + 2 = 6 {"version":"1.1","math":"+4--2=4+2=6"}

+ 2 4 = 2 + 4 = 6 {"version":"1.1","math":"+2--4=2+4=6"}

4 + 2 = 4 2 = 6 {"version":"1.1","math":"-4-+2=-4-2=-6"}

2 + 4 = 2 4 = 6 {"version":"1.1","math":"-2-+4=-2-4=-6"}

Again, you’ll notice that there are certain interactions that occur with adjacent +/- where they combine. This has to do with multiplication of signs which can be checked out in the next section: Applications to Multiplication/Division.

You can think of adding a subtracting positive/negative numbers as movement along a number line. Any subtraction is movement to the left, and any addition is movement to right (after sign combining).