# ADDITIVE INVERSE OF A RATIONAL NUMBER

Additive inverse of a rational number :

The opposite, or additive inverse, of a number is the same distance from 0 on a number line as the original number, but on the other side of 0. Zero is its own additive inverse.

In other words, the additive inverse of a rational number is the same number with opposite sign.

For example : Additive inverse of 2/3 is -2/3.

## Additive inverse of a rational number - Examples

Example 1 :

A football team loses 3.5 yards on their first play. On the next play, they gain 3.5 yards. What is the overall increase or decrease in yards?

Solution :

Step 1 :

Use a positive number to represent the gain in yards and a negative number to represent the loss in yards.

Step 2 :

Find -3.5 + 3.5.

Step 3 :

Start at -3.5.

Step 4 :

Move | 3.5 | = 3.5 units to the right, because the second addend is positive.

The result is 0. This means the overall change is 0 yards.

Example 2 :

Solution :

Step 1 :

The additive inverse of 2/3 is -2/3.

Then, we have to find (2/3) + (-2/3).

Step 2 :

In the above addition, since the two rational numbers have different signs, we have to find the absolute difference of them without the actual signs.

|2/3 - 2/3|  =  |0|  =  0

Hence, (2/3) + (-2/3)  =  0

Example 3 :

Solution :

Step 1 :

The additive inverse of 2/9 is -2/9.

Then, we have to find (4/9) + (-2/9).

Step 2 :

In the above addition, since the two rational numbers have different signs, we have to find the absolute difference of them without the actual signs.

|4/9 - 2/9|  =  |2/9|  =  2/9

Step 3 :

In (4/9) + (-2/9), the sign of the bigger number is positive. So, we have to take positive sign to the answer.

Hence, (+4/9) + (-2/9)  =  +2/9

Example 3 :

Solution :

Step 1 :

The additive inverse of -1/3 is +1/3.

Then, we have to find (-4/3) + (+1/3).

Step 2 :

In the above addition, since the two rational numbers have different signs, we have to find the absolute difference of them without the actual signs.

|4/3 - 1/3|  =  |3/3|  =  1

Step 3 :

In (-4/3) + (+1/3), the sign of the bigger number is negative. So, we have to take negative sign to the answer.

Hence, (-4/3) + (+1/3)  =  -1.

After having gone through the stuff given above, we hope that the students would have understood "Additive inverse of rational numbers".

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