Adding and Subtracting a Negative Integer

Adding a negative integer - b to an integer a requires changing the addition sign to a subtraction sign and changing - b to its additive inverse, b. To illustrate this, consider a= 4 and - b= - 5. a= 4, - b= - 5 ⇓ 4+( -5)=? Next, this process is shown with these pair of integers.

2

Plot a on a Number Line

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The process now is similar to subtracting one positive integer from another. First, plot a on a number line. The value of a, in this case, is 4.

3

Move b Units to the Left-Hand Side of a

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Now move b units to the left-hand side of a to subtract b from a. In this example, move 5 units to the left of 4 to subtract 5 from 4.

The point is now at -1. This means that the subtraction of 5 from 4 is -1. This is also the result of adding -5 to 4. 4+( -5)=-1

Subtracting a negative integer - b from an integer a requires changing the subtraction sign to an addition sign and changing - b to its additive inverse. To illustrate this, consider a= -2 and - b= - 6 a - ( - b) ⇔ a + b -2 - ( -6) ⇔ -2 + 6 The result is the sum of an integer and a positive integer.

The point is now at 4. The result of subtracting - 6 from -2 is 4. -2 - ( -6)=4 ⇔ -2 + 6=4 This process applies to adding or subtracting any netative integer - b from a positive or negative integer a. The result can be a negative integer, a positive integer, or 0.