How to add integers with different signs?

Integers are a combination of whole numbers along with negative numbers. Thus, the numbers -3, -2, -1, 0, 1, 2, 3 are called integers.

• The natural numbers 1, 2, 3 are called positive integers.
• The negative numbers -3, -2, -1 are called negative integers.
• The number 0 is also an integer but it is neither a positive integer nor a negative integer.

Representation of Integers on a Number Line

Step 1: Draw a line and label a point on it as zero.

Step 2: Select a unit of length. Start marking points on the line at unit length intervals on both sides of 0 (zero).

Step 3: To the right side of the zero, label the points as 1, 2, 3, … and the points to the left of the zero as -1, -2, -3, …

Step 4: Lastly, add arrows on either side of the line to show that the line continues indefinitely in both directions.

Addition of Positive and Negative integers using a Number Line

• To add a positive number, we need to move to the right of the number line.
• To add a negative number, we need to move to the left of the number line.

Examples

Question 1: Find (-4) + 2.

Solution:

Start from -4 on the number line. Move 2 units to the right. We reach -2.

Therefore, (-4) + 2 = -2

Question 2: Find 4 + (-2).

Solution:

Start from 4 on the number line. Move 2 units to the left. We reach +2.

Therefore, 4 + (-2) = 2

Adding integers with Different signs without the Number Line

Using the number line to add large integer numbers is a very tedious task. There is a better alternative, we have the following rules for the addition of integers with different signs.

To add a positive and negative number: 

Subtract the smaller number from the larger number and give the sign of the number which is larger.

Examples

Question 1: Evaluate (-130) + (+200)

Solution: 

As we can see here, one number is positive and another one is negative, so we need to subtract the smaller number from the larger number and give the sign of the larger number i.e. subtract 130 from 200 and give the sign as positive to the final sum.

Therefore, (-130) + (+200) = 200 – 130 = +70. 

Question 2: Evaluate (+500) + (-780)

Solution:

As we can see here, one number is positive and another one is negative, so we need to subtract the smaller number from the larger number and give the sign of the larger number i.e. subtract 500 from 780 and give the sign as negative to the final sum.

Therefore, (+500) + (-780) = 780 – 500 = -280.