Reference

Adding and Subtracting Integers

Method

Adding and Subtracting a Positive Integer

To add a positive integer b to an integer a, move b units to the right-hand side of a on a number line. Consider a= 3 and b= 7. a= 3, b= 7 ⇓ 3+ 7=? The process of adding a and b will be illustrated using these values.

Plot a on a Number Line

Begin by graphing a on a number line. In this case, the value of a= 3. Move 3 units to the right side of 0 to plot 3.

Move b Units to the Right-Hand Side of a

Starting from a, move b units to the right to add b units to a. For this example, move seven units to the right of 3 to add 7 to 3.

Moving 7 units to the right-hand side of 3.

The point is now at 10. This means that the sum of 3 and 7 is 10. 3+ 7=10

Subtracting a positive integer b from a is similar. In this case, move b units to the left-hand side of a on a number line. Consider the subtraction of b from a using the same example values. a= 3, b= 7 ⇓ 3- 7=? This process can be performed on the number line.

Moving seven units to the left-hand side of 3 to subtract 7 from 3.

Now the point is at -4. The result of subtracting 7 from 3 is -4. 3- 7=-4 This process applies to adding or subtracting any positive integer b from a positive or negative integer a. The result can be a negative integer, a positive integer, or 0.

Method

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.

Change the Addition Sign to a Subtraction Sign and Change - b to b

Change the addition sign to a subtraction sign and then change - b to its opposite b. In this example, - b = -5 and its opposite is 5. 4 + ( -5) ⇔ 4 - 5 The addition of an integer and a negative integer is now turned into a subtraction of an integer and a positive integer.

Plot a on a Number Line

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.

Move b Units to the Left-Hand Side of a

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.

Moving five units to the left-hand side 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.

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