**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.

**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 : **

Add the rational number 2/3 and its additive inverse.

**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 : **

Add the rational number 4/9 and the additive inverse of 2/9.

**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 : **

Add the rational number -4/3 and the additive inverse of -1/3.

**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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