**Adding rational numbers with different signs :**

To add rational numbers with different signs, find the difference of their absolute values. Then use the sign of the rational number with the greater absolute value.

**Example 1 : **

Add : (-4/5) + (+7/5)

**Solution : **

**Step 1 : **

Find the absolute difference of the rational numbers without the actual signs.

|4/5 - 7/5| = |-3/5| = 3/5

**Step 2 : **

In the given two rational numbers 4/5 and 7/5, the sign of the bigger number is positive. So, we have to take positive sign to the answer.

Hence, (-4/5) + (+7/5) = +3/5

**Example 2 : **

Add : (+5/9) + (-8/9)

**Solution : **

**Step 1 : **

Find the absolute difference of the rational numbers without the actual signs.

|5/9 - 8/9| = |-3/9| = 3/9 = 1/3

**Step 2 : **

In the given rational numbers 5 and 8, the sign of the bigger number is negative. So, we have to take negative sign to the answer.

Hence, (+5/9) + (-8/9) = -1/3

**Example 3 : **

Add : (+2.03) + (-2.3)

**Solution : **

**Step 1 : **

Find the absolute difference of the rational numbers without the actual signs.

|2.03 - 2.3| = |-0.27| = 0.27

**Step 2 : **

In the given rational numbers 2.03 and 2.3, the sign of the bigger number is negative. So, we have to take negative sign to the answer.

Hence, (+2.03) + (-2.3) = -0.27

**Example 4 :**

Add "3" and "-2" using a number line.

**Solution :**

Here, the rational numbers "3" and "-2" are having different signs.

To find the sum of rational numbers 3 and -2, we have to start at 3

Since the second number "-2" is negative, we have to move 2 units in the negative direction as given in the picture below.

After having move 2 units in the negative direction, we are in the position of "1"

Hence, 3 + (-2) = 1

**Example 5 :**

During the day, the temperature increases by 4.5 degrees. At night, the temperature decreases by 7.5 degrees. What is the overall change in temperature?

**Solution :**

**Step 1 : **

Use a positive number to represent the increase in temperature and a negative number to represent a decrease in temperature.

**Step 2 : **

Find 4.5 + (-7.5).

Let us use the real number line to add 4.5 and (-7.5).

**Step 3 : **

Start at 4.5.

**Step 4 :**

Move | -7.5 | = 7.5 units to the left because the second addend is negative.

The result is -3.

The temperature decreased by 3 degrees overall.

**Example 6 :**

Ernesto writes a check for $2.50. Then he deposits $6 in his checking account. What is the overall increase or decrease in the account balance?

**Solution :**

**Step 1 :**

Use a positive number to represent a deposit and a negative number to represent a withdrawal or a check.

**Step 2 : **

Find -2.5 + 6.

Let us use the real number line to add -2.5 and 6.

**Step 3 : **

Start at -2.5.

**Step 4 :**

Move | 6 | = 6 units to the right because the second addend is positive .

The result is 3.5.

The account balance will increase by $3.50.

After having gone through the stuff given above, we hope that the students would have understood "Adding rational numbers with different signs".

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