Adding integers

There are 2 conditions to remember when adding integers:


1.  When adding integers having the same sign, add the numbers and then copy the sign.


Adding Integer
Example 1
 –31

Explanation:

–14 and –17 are both negative integers.

14 + 17 = 31

Copy the negative sign.

The sum is –31.

Example 2
 42

Explanation:

23 and 19 are both positive integers.

23 + 19 = 42

The sum is 42.


2.  When adding two integers having different signs, subtract the numbers and copy the sign of the integer with the larger number.


Adding Integer with different sign
Example 1
 -3

Explanation:

4 is a positive integer and –7 is a negative integer.

Since both integers have different signs, subtract the numbers: 7 – 4 = 3

Since 7 is greater than 4, copy the sign of the integer with 7.

The sum is –3.


Additive inverse


Additive inverse of a number is the number that when added to that number will yield zero. It can also be defined as the opposite of a number.

Additive Inverse
Simple example with explanation

 -4

Explanation:

Think about a number that when added to 4 will give us 0.

That number is the negative of 4.

4 + (-4) = 0

So, the additive inverse of 4 is - 4.

Problems

 The additive inverse of 77 is - 77. We get - 22 if it is added to 55.

Explanation:

First we write the additive inverse of 77, which is -77.

Then we think about the number that when added to -77 will yield 55.

Mathematically,

-77 + ? = 55

- 77 + 22 = 55

 -120

Explanation:

First we add the integers without the minus sign.

80 + 40 = 120

Now, we put the minus sign.

So, (-80)- 40 = - 120

 372

Explanation:

(-200) - (-572)

= - 200 + 572

When we subtract the integers, we get 372.






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