**Adding rational numbers with the same sign :**

To add rational numbers with the same sign, add the absolute values of the rational numbers and use the sign of the rational numbers for the sum.

**Example 1 : **

Add : (-2/3) + (-1/3)

**Solution : **

**Step 1 : **

Find the absolute values.

|-2/3| = 2/3 and |-1/3| = 1/3

**Step 2 : **

Find the sum of the absolute values :

2/3 + 1/3 = (2+1) / 3

2/3 + 1/3 = 3/3

2/3 + 1/3 = 1

**Step 3 : **

Use the sign of the rational numbers to write the sum.

(-2/3) + (-1/3) = -1

**Example 2 : **

Add : (+2/5) + (+1/5)

**Solution : **

**Step 1 : **

Find the absolute values.

|+2/5| = 2/5 and |+1/5| = 1/5

**Step 2 : **

Find the sum of the absolute values :

2/5 + 1/5 = (2+1)/5

2/5 + 1/5 = 3/5

**Step 3 : **

Use the sign of the rational numbers to write the sum.

(+2/5) + (+1/5) = +3/5

**Example 3 : **

Malachi hikes for 2.5 miles and stops for lunch. Then he hikes for 1.5 more miles. How many miles did he hike altogether?

**Solution : **

**Step 1 : **

Use positive numbers to represent the distance Malachi hiked.

**Step 2 : **

Find 2.5 + 1.5.

Let us use the real number line to add 2.5 and 1.5.

**Step 3 : **

Start at 2.5.

**Step 4 : **

Move 1.5 units to the right because the second addend is positive.

The result is 4.

Malachi hiked 4 miles.

**Example 4 : **

Kyle pours out 3/4 liter of liquid from a beaker. Then he pours out another 1/2 liter of liquid. What is the overall change in the amount of liquid in the beaker?

**Solution : **

**Step 1 : **

Use negative numbers to represent amounts the change each time Kyle pours liquid from the beaker.

**Step 2 : **

Find -3/4 + (-1/2).

Let us use the real number line to add -3/4 and -1/2.

**Step 3 : **

Start at -3/4.

**Step 4 : **

Move | -1/2 | = 1/2 unit to the left because the second addend is negative.

The result is -1 1/4.

The amount of liquid in the beaker has decreased by 1 1/4 liters.

After having gone through the stuff given above, we hope that the students would have understood "How to add rational numbers with the same sign".

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