MATHEMATICAL OPERATIONS ON INTEGERS

Mathematical operations are addition, subtraction, multiplication, and division. These are all basic and it is expected that the high school students already mastered these operations involving whole numbers even integers both positive and negative. But some students get confused when they see different signs (positive and negative). It's ok because I'm here to help you out. So, let's get started.

Let's start with addition first. There are only 3 rules in adding integers.

1) To add both (+) integers, add them and the answer is also (+).

Example:  5 + 7 = 12

2) To add both (-) integers: add them and the answer is also (-).

Example: -5 + (-7) = -12

3) To add (+) and (-) integers: subtract them and the answer should follow the sign of the larger number.

Example 1: -5 + 7 = 2
Example 2: 5 + (-7) = -2


Now, we go to multiplication and/or division of integers.

1) To multiply/divide two same signs i.e. both (+) or both (-) integers, multiply/divide the numbers and the answer is (+).

Example 1: 5 * 7 = 35

Example 2: (-49)/(-7) = 7

2) To multiply/divide two different signs, i.e. a (+) and a (-) integers, multiply/divide the numbers and the answer is (-).

Example 1: 5 * (-7) = -35

Example 2: (-49)/ 7 = -7


3) To multiply/divide two or more different signs, multiply/divide the numbers and count the (-) integers. If the number of (-) integers is even, the answer should be (+). If the number (-) integers is odd, then the answer should be (-).

Example 1: (-5) * (-7) * 1 * (-2) * (-1) = 70   [there are 4 (-) integers, 4 is even so the answer is (+)]

Example 2: (-5) * (-7) * 1 * (-2) = 70 [there are 3 (-) integers, 3 is odd so the answer is (-)]


For subtraction of integers, we have to follow the rules in multiplication and addition of integers.

Example 1: -7 - (-5) [since there are two (-) signs before 5, that will be (+) as per rule 1 of multiplication/division of integers] To make it simpler, it will be:
           -7 + 5 = -2 [from the rule 3 of addition of integers]

Example 2: -7 - 5  [will turn this into addition] To make it simpler, it will be
  -7 + (-5) = -12  [since there are (+) and (-) signs before 5, that will be (-) as per rule 2 of multiplication/division of integers]


To add/subtract a string of (+) and (-) integers, separate the (+) integers from the (-) integers first. Then, add all (+) integers and do the same for the (-) integers. You will come up with a (+) and a (-) integers so just do the rule 3 of addition of integers to come up with the final answer.

There you have it. Hope this will help high school students especially the seniors.