When we combine a positive and a negative integer, we always obtain a negative integer. When we add two negative numbers, we get a positive integer. However, when we add a negative number and a positive number, we get a negative number.

Thus, adding two negative integers gives us a number where both the positive and the negative parts contribute to the total. This is different from how addition works for **positive integers** where only positive numbers can be combined with each other to produce **another positive number**.

An example will make this clear. Suppose we add -5 and 6. We know that addition of two negatives yields **a positive number** so our answer should be positive right? Well, no. -5 + 6 = 1. So even though both 5 and 6 were used in the addition, only 1 was contributed by 5+6.

Now, what if we had added 5 and -6? Here, only -6 would have made a contribution to the sum because 5 is too small compared to -6. In fact, only numbers greater than or equal to 0 can contribute to the sum of two negatives.

So, adding two negatives gives us a number where both the positive and the negative parts contribute to the total.

When two positive integers are added, the result is always a positive sum; when two negative integers are added, the result is always a negative sum. Take the absolute value of **each integer** and then subtract these values to determine the total of a positive and a negative integer. The sum of any integer with its inverse equals zero.

Example 1: Find the sum of -5 and 8. -5 + 8 = 3. 3 is a positive number so the sum is positive. Example 2: Find the sum of 5 and -8. 5 - 8 = -3. -3 is a negative number so the sum is negative. Example 3: Find the sum of 17 and -17. 17 - 17 = 0. 0 is a zero number so the sum is equal to zero.

Summation and subtraction are both associative and commutative. This means that the order in which operations are performed does not matter and that subtraction can be replaced by addition or multiplication depending on what other operators are needed to perform the entire calculation. For example, multiplying numbers together or adding them after taking the absolute value of each number will produce **the same result** as adding them before taking the absolutes.

Summation is defined for **all types** of numbers including integers, fractions, decimals, and negatives. If you have problems using **this technique** with numbers that cannot be represented exactly, use mathematics methods instead.

The integer principles are as follows: the sum of two integers equals an integer. The difference between **two numbers** is also an integer. The product of two or more numbers is an integer. Also, the quotient of one number by another number is an integer.

(ii) A negative integer is the product of three negative integers. (iii) If one of the two numbers is negative, their product must be positive. (iv) aandb, axb is always bigger than either aorb for all non-zero integers. Therefore the product of **two positive integers** is always positive.