Question

Find the sum.

– 9 + 16 + (– 12) + 3

Short answer

Answer is – 2

Step-by-step solution

Apply the concept of adding or subtracting integers 

Rule: The sum of any integer and its opposite is equal to zero.

Explanation: Adding two positive integers always yields a positive sum; adding two negative integers always yields a negative sum. To find the sum of a positive and a negative integer, take the absolute value of each integer and then subtract these values.

Explanation: How to add or subtract the integers.

To add two numbers with the same sign, first add the two numbers ignoring the sign and then put their common sign before the answer.

To add two numbers with the opposite sign, ignore their signs and subtract the smaller number from the bigger number. Then put the sign of the bigger number before the answer.

Find the sum: – 9 + 16 + (– 12) + 3 

To add two integers, we need to check the signs of those two integers.

Rule: If they are with the same sign (positive or negative),first add the two numbers ignoring the sign and then put their common sign (positive or negative) before the answer.

First we rearrange the numbers with positive and negative separately and add them with same signs.

– 9 +16 + (– 12) + 3 = – 9 + (– 12) + 16 + 3 = – 9 – 12 + 16 + 3 = – 21 + 19

Now Evaluate:– 21 + 19

Rule: If they are with the opposite sign (one is positive and other is negative), subtract the smaller number from the bigger number ignoring the sign, then put the sign of bigger number before the answer.

Here 21 is bigger number and negative, so the answer will be negative.

Evaluate: – 21 + 19 = – 2

We can write: – 9 +16 + (– 12) + 3 = – 2