Find the sum.

$- 13 + (- 21)$

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

Rule: Adding two positive integers always gives a positive integer; adding two negative integers always gives a negative integer.

Rule: To find the sum of a positive and a negative integer, take the absolute value of each integer and then subtract these values.

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.

An example of addition is: 5 + 11 + 3 = 19.

Example: If a = 7 and b = 8, find the value of a + b and a – b

To evaluate the expressiona + b, substitute the value of a as 7 and the value of b as 8 and add the numbers as shown below,

$a+b = 7+8=15$and $a-b=7-8=-1$

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

Rule: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.

Now Evaluate:$- 13 + (- 21) = - (13 + 21) = - 34$

Thus, the sum of the numbers is $-34$.