Operation with Real Numbers

The rules for the basic arithmetic operations, addition, subtraction, multiplication and division on signed numbers will be discussed in this section. No calculators should be used when practicing these operations—these are skills also required for future operations on the terms of algebraic expressions.

Addition/Subtraction

The real number line can be used to visualize the addition and subtraction of signed numbers, until one becomes comfortable with the operations. The following rules can be used:

— adding a positive number → move right
— subtracting a positive number → move left
— adding a negative number → move left (notice this is the same action as subtracting a positive number)
— subtracting a negative number → move right (notice this is the same action as adding a positive number)

Examples

1. $3+(-7)$ — in this case, a negative is being added. Use 3 as the starting point, then move 7 spaces to the left.

So,   $3+\left(-7\right)=-4$ .

 

2. $\left(-2\right)+\mathrm{3 }$ — in this case, a positive is being added. Use -2 as the starting point, then move 3 spaces to the right.

So,   $\left(-2\right)+3=1$ .

 

 

3. $2-(-6)$ — in this case, a negative is being subtracted. Use 2 as the starting point, then move 6 spaces to the right.

 

So,   $2-\left(-6\right)=8$ .

 

 

4. $-2-7=-2-(7)$ — in this case, a positive is being subtracted. Use -2 as the starting point, then move 7 spaces to the left.

 

So,   $-2-7=-2-\left(7\right)=-9$ .

 

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