MOST STUDENTS DON'T KNOW THIS BASIC MATHS TOPIC. HOW WELL DO YOU KNOW THIS?

Hello Everyone, In this post, I will explain everything you need to know about integers. After the end of this post, you will be able to solve almost every question based on Integers, whether it be addition, multiplication, subtraction or division of integers, you will be able to solve them easily.

Without any delay, let's get started with our topic.

What are integers?

In books, you may find complicated definitions of integers. But we will not go with those definitions. Integers are basically a collections of not so special types of numbers. You are well aware of those numbers, but you didn't knew them as Integers. So, what are integers?

These are basically numbers like 1, 56, 345, 68767, etc and also numbers like -3, 0, -4, -94, etc.

So, integers are just collection of positive and negative whole numbers (Not fractions).

More Examples of Integers: 0 , 54, 46, 27, -34532, 5634, etc

Note: Integers does not include fractions.

Representation of Integers on Number Line:

As you can See, Number line is just a line, with 0 at its centre. On the left side, we have negative integers. On the right side, we have positive integers.

After understanding Number Line, we can move to integer operations

Integer Operations:

How to add two numbers?

If I want to add 54 and 2, I will do 54 + 2 = 56

But, things get a little complicated when the two numbers to be added are of the opposite signs (positive and negative).

For example, how to add -3 and 1?

To do this, you first need to understand what addition means. Remember Number line, it will be easier to understand addition if you visualise numbers on the number line.

As you can See, if you want to add 2 and 3, you will do 2 + 3 = 5.

On number line 2 + 3 means to move 3 steps in the right direction from 2. If you move 3 steps, you will end up at 5. Hence, you have added 2 and 3. 

Similarly, for adding -3 and 1, we can use the same analogy. Adding -3 and 1 means moving 1 steps in the right direction from -3. You will end up at -2. The same in illustrated in the figure below:

NOTE: The reason we are moving to the right is because we want to add 1 (which is positive). Similarly if we want to add -10 to a number, we will move to the left (because -10 is negative).

So, can we extend the same analogy for subtraction also?

The answer is yes!

Consider the case: 5 - 1 = 4

Visualising this on the number line, we can see that 5 - 1 means moving one steps to the left from 5. Hence, we will end up at 4. The same in illustrated in the figure below:

Hence, for doing 1 - 2, we will move 2 steps to the left from 1. Doing this, we will end up at -1.

The same is illustrated in the figure below:

Hence, we can do subtraction of integers using this same analogy.

Having done this much, some more examples of these operations are:

Example One: -5 + 2 = -3

ILLUSTRATION :

Example Two: 2 - 5 = -3

ILLUSTRATION: 

OBERVATION: It is clear that -5 + 2 is same as 2 - 5. This is not a coincidence, in fact, this is true for every integer, and this property is known as commutative property.

Example Three: -2 - 1 = -3 (Move one step to the left from -2).

ILLUSTRATION:

TRICK TO SOLVE INTEGER ADDITION AND SUBTRACTION PROBLEMS:

As you have seen, the number line analogy is pretty simple, but it can be time consuming. So there are some basic rules that will help us to solve questions with number line analogy.

RULES: 

For example, Consider 3 + 5 = 8

first, the signs of both 3 and 5 is +. Hence , we will add the magnitude of 3 and 5 = 8, which is the answer.

For example, Consider 3 - 5 = -2

first, the sign of 3 is + and the sign of -5 is -. Hence, we have a configuration like + - . We know from the rule that + - = - . So, we will take the magnitude of -5 and 3 and then subtract them to get 2. Now, the magnitude of -5 > magnitude of 3. So, the final answer will have the same sign as that of -5. Hence, our answer is -2. (Because -5 also have a sign of -).

For example, Consider -3 + 5 = 2

first the sign of -3 is - and the sign of 5 is +. Hence we have a configuration like - +. We know from the rule that - + = -. So, we will take the magnitude of 5 and -3 and then subtract them to get 2. Now, the magnitude of 5 >  magnitude of -3. So, the final answer will have the same sign as that of 5. Hence, our answer is +2. (Because 5 also have a sign of + ).

For example, Consider -3 - 5 = -8

first the sign of -3 is - and the sign of -5 is -. Hence we have a configuration like - -. We know from the rule that - - = +. So, we will take the magnitude of -5 and -3 and then add them to get 8. Now, the magnitude of -5 >  magnitude of -3. So, the final answer will have the same sign as that of -5. Hence, our answer is -8. (Because -5 also have a sign of - ).

These all are the possible cases of Integer Addition and Subtraction. I will add another post for multiplication and division of integers. So stay tuned for future updates.

If you have any doubts or query, feel free to ask in the comment Box.

That's it for this post, Thank you!