**Adding and subtracting negative numbers :**

Whenever we want to simplify two numbers, first we have to check if numbers are having same sign or different sign.

- If both numbers are having same signs, then add both numbers and tag greater number sign for the answer.
- If both numbers are having different signs, then subtract the smaller number from the greater number and tag the greater number sign for the answer.

Let us see some example problems to understand the concept.

**Example 1 :**

Simplify (–10) + (+17)

**Solution :**

= –10 + 17

By considering the above numbers, both are having different signs. So,

Subtract the smaller number from greater number and tag greater number sign.

= +7

Hence, 7 is the answer.

**Example 2 :**

Simplify (+20) + (–13)

**Solution :**

= (+20) + (–13)

= +20 –13

By considering the above numbers, both are having different signs.

Subtract the smaller number from greater number and tag greater number sign.

= +7

Hence, 7 is the answer.

**Example 3 :**

Simplify (–50) + (–20)

**Solution :**

= (–50) + (–20)

= –50 – 20

By considering the above numbers, both are having same signs.

Add both numbers and tag greater number sign.

= -70

Hence, -70 is the answer.

**Example 4 :**

Simplify (+40) + (+70)

**Solution :**

= (+40) + (+70)

= + 40 + 70

By considering the above numbers, both are having same signs.

Add both numbers and put greater number sign.

= + 110

Hence, 110 is the answer.

**Example 5 :**

Simplify (+18) + (–75)

**Solution :**

= (+18) + (–75)

= +18 –75

By considering the above numbers, both are having different signs.

Subtract the smaller number from greater number, put greater number sign.

= - 57

Hence, -57 is the answer.

**Example 6 :**

Simplify (+75) + (–75)

**Solution :**

= (+75) + (–75)

= + 75 – 75

By considering the above numbers, both are having different signs.

Subtract the smaller number from greater number, put greater number sign.

= 0

Hence, 0 is the answer.

**Example 7 :**

Simplify (–30) + (12)

**Solution :**

= (–30) + (12)

= –30 + 12

By considering the above numbers, both are having different signs.

Subtract the smaller number from greater number, put greater number sign.

= -18

Hence, -18 is the answer.

**Example 8 :**

Simplify (–30) + (–22)

**Solution :**

= (–30) + (–22)

= –30 – 22

By considering the above numbers, both are having same signs.

Add both numbers and put greater number sign.

= - 52

Hence, -52 is the answer.

After having gone through the stuff given above, we hope that the students would have understood "Adding and subtracting negative numbers".

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