Numbers - Session 1

What is the first number you ever learned to count? Most likely, it was one. Natural numbers are the basic numbers we use for counting. When a child starts learning how to count fingers, they usually begin with one, two, three, and so on. These numbers are called natural numbers because they come naturally when we start counting things in real life. For example, if you are counting apples, chairs, or days, you use natural numbers.

One important thing to remember is that natural numbers do not include zero, negative numbers, or any fractions or decimal points. So numbers like -1, 0, 3.5, or 2.7 are not natural numbers. Only the whole positive numbers like 1, 2, 3, 4, and so on are included.

Natural numbers are used in many simple math operations. When you add two natural numbers, like 5 and 7, you get another natural number, which is 12. The same is true for multiplication. If you multiply 3 and 4, you get 12, which is also a natural number. So natural numbers are what we call closed under addition and multiplication. That simply means when you use these two operations, you always stay within the natural number set.

But things change when you try subtraction or division. If you subtract a bigger number from a smaller one, like 3 minus 5, you get a negative number, which is not a natural number. And if you divide 3 by 2, you get 1.5, which is a decimal, not a natural number. So natural numbers are not closed under subtraction or division.

Whole numbers are the numbers we use when we count and include zero. So, whole numbers are 0, 1, 2, 3, 4, 5, and so on. They go-on forever, similar to natural numbers, but the main difference is that whole numbers start from zero, not from one. Think of it this way. When you count fingers, you usually start from 1, which is a natural number. But if you want to include the idea of “nothing,” like having zero apples or zero rupees, then you are using whole numbers. So whole numbers include all natural numbers, plus zero.

Even numbers are whole numbers that can be divided exactly by 2. That means when you divide them by 2, there is no remainder. These numbers make perfect pairs. Even numbers always end in 0, 2, 4, 6, or 8. Let us take 8 as an example. If you have 8 candies and you want to share them between 2 people, each person gets 4. That is fair and equal. So 8 is an even number.

Odd numbers are whole numbers that cannot be divided exactly by 2. When you try to divide them by 2, there is always 1 left-over. These numbers do not make perfect pairs. Odd numbers always end in 1, 3, 5, 7, or 9. For example, if you have 7 cookies and try to split them between 2 people, each gets 3, and 1 cookie is left. That leftover means 7 is an odd number. How can you tell the difference between odd number and even number quickly? Simply look at the last digit of the number. If it ends in 0, 2, 4, 6, or 8, it is even. If it ends in 1, 3, 5, 7, or 9, it is odd. This trick works for any number, no matter how big it is.

Prime numbers are special numbers in math. They are whole numbers that can only be divided exactly by 1 and themselves. This means they have only two factors. For example, the number 5 is a prime number because the only numbers that divide it evenly are 1 and 5. You cannot divide 5 by 2, 3, or 4 without getting a remainder or a decimal. 2, 3, 5, 7, 11, 13, and 17, all of these numbers can only be divided by 1 and by the number itself. If you try dividing them by any other number, it will not work out evenly. That is what makes them prime.

Now here is something important. 2 is the only even number that is a prime number. Every other even number can be divided by 2, so they are not prime. For example, 4 can be divided by 1, 2, and 4, which gives it more than two factors, so it is not a prime number. After 2, all other prime numbers are odd.

Integers are a bigger group of numbers that include more than simply the counting numbers. Natural numbers like 1, 2, 3 are part of the integers, but integers also include zero and the negative numbers. So the full set of integers looks like this. -3, -2, -1, 0, 1, 2, 3, and so on in both directions. They go-on forever to the left-side and to the right-side.

Imagine a number line. In the center, you have 0. On the right-side, you have the positive numbers like 1, 2, 3. On the left-side, you have the negative numbers like -1, -2, -3. This whole line is filled with integers. So if you move forward, you get bigger numbers, and if you move backward, you go-into the negative side. That is how integers help us represent values in both directions.

Integers are used when we need to indicate both gains and losses. For example, in temperature, if it is five degrees above zero, we write plus five. If it is five degrees below zero, we write negative five. In sports, if a team loses points or gets a penalty, we use negative numbers. Bank-accounts also use integers. If you spend more money than you have, your account-balance might become negative. That is how integers show-up in real-life situations where values can go-up or go-down.

Positive Integers are the numbers greater than zero. These are numbers like 1, 2, 3, 10, and 100. They indicate an increase, a gain, or movement in the forward or upward direction. For example, saving 500 rupees or earning 10 points in a game is shown using positive integers. These always appear on the right-side of zero on the number line.

Negative Integers are the numbers less than zero. These include numbers like negative one, negative 3, and negative ten. We use them when we want to indicate a loss, a drop, or something going below a starting point. If the temperature drops below zero or someone owes money, we use negative integers. These numbers are always shown to the left-side of zero on the number line.

When it comes to math operations, integers behave in specific ways. Adding or subtracting two integers will gives you another integer. For example, -3 plus 5 gives 2. Or if you subtract 10 from 7, you get -3. Multiplication also works the same way. But with division, sometimes you might get a fraction or decimal, which is not an integer anymore.