Basic Math #1 : 4 Basic Arithmetic

Understanding math

What is math?

Definition

"Math is an area of knowledge, which includes the study of such topics as numbers (arithmetic and number theory), formulas and related structures (algebra), shapes and spaces in which they are contained (geometry), and quantities and their changes (calculus and analysis)." - Wikipedia

The point is, math is a way to calculate. Math is used around the world on our daily life.

Who invented math?

This is an indescribable question. You see, math is not an object, it's a collection of ways to calculate. Which mean, there isn't only 1 person who invented "math". It's different people creating various of ways to calculate something.

Arithmetic

What are arithmetic?

"Arithmetic is a branch of mathematics that consists of the study of numbers, especially concerning the properties of the traditional operations on them—addition, subtraction, multiplication, division, exponentiation, and extraction of roots" - Wikipedia

Arithmetic is the most basic of math, besides knowing the concept of numbers and counting. With arithmetic, you could do other kind of calculation such as algebra and others.

As written in the Wikipedia article, there are 6 kinds of traditional operations in arithmetic : addition, subtraction, multiplication, division, exponentiation, and extraction of roots. But today, we will learn 4 of them, addition, subtraction, multiplication, and division.

Addition

The concept of addition is basically the same as manual counting (1, 2, 3...). But instead, of counting one by one, you could count it instantly. Let's take an example of a line consisting number 1 until 5

 

Let's say, I want to count 1 + 3. How do I do it? Let's see the image below

 

We start counting from number 1, we keep adding +1 until 3 times, because we are doing 1 + 3. And after adding +1 to number 1 for 3 times, we get number 4. Which concludes, 1 + 3 = 4. Simple, isn't it?

Two digits addition

It's easy to use that concept of addition on small numbers addition such as 1 + 3 or 4 + 5. But what if the number is more than 1 number? Example, 12 + 3, 10 + 11, etc. We can't always use that way! See the image below for how to add 2 digit numbers. Take an example for 3 + 11

We stack the numbers like this. We then add the back of the eleven, which is 1, with 3.

And then, we pull the front of the eleven, which is 1 down to the result section.

 So the conclusion is, 11 + 3 = 14. Easy, right? If you are adding 2 digit numbers with 2 digit numbers, then just add the front number together!

 It's just an easy concept! But, what if the added number resulted a 2 digit number?

 We want to add 17 + 13, but 7 + 3 = 10, so how are we going to put the 10? Look at the image below

 7 + 3 = 10. We put the 0 in the result section and keep the 1 to be added later. How to add the 1 then? Look at the image below

 

 We add the 1 with the 1 from the 17. So now, we add 1 + 1 + 1 = 3. You could also add the 1 + 1 first before adding it to the 1 in the 13 so it'll just do 2 + 1 = 3. Both do the same. It also applies on 3 digits and 4 digits numbers and above it. It is suggested to remember 1 digit addition to make >1 digits addition easier

 Subtraction

I don't have to explain the concept of subtracting, because it is the same with addition, but you are subtracting it. You count it backwards instead of front. Example this 4 - 3.

Basically the same, but you are doing it backwards. So you are doing -1 3 times. So it will be -3.So 4 - 3 = 1. It's just the same.

2 digits subtraction

This is a little bit different from 2 digits addition. Example of 17 - 3.

So for this case, it's just the same like addiction but it's backwards. But what if it's this case?

You can't subtract 0 with 3! It's smaller! So, we do this.

We subtract -1 from 1 from the front of the 10 so now it's 0. And we borrow the -1 and add it to 0 from the back of the 10. You may think it will be 0 + 1 = 1 and it will still being less than needed to subtract with 3, but borrowing 1 is not adding it, but it is being merged with the number and it forms the number from 1 digit into 2 digits number. So instead of 1, it will be 10. And now, we could subtract 10 - 3 = 7. If there's a number left in the front, then just pull it down to the answer section. Easy? How about the number next to the number need to borrow a digit, is 0? Look at the image below.

You borrow the from both 0 and 1. So now it will do 10 - 1 = 9. Understand? Okay, let's move on.

Multiplication

Multiplication is basically addition, but instead of adding with another number, you are multiplying the own number. Meaning you are adding a number with it's own self number over and over depending on how many it's being multiplied. Take an example of 2 x 2.

2 + 2 = 4. There are 2 times 2 in there. Which means, 2 x 2 is equal to 2 + 2, both results 4. It is advised to memorize 1 - 10 multiplication to make >10 multiplications easier.

Small notes

Anything multiplied by 0 results 0

2 digits multiplication

In multiplication, we multiply all numbers above to the numbers below. So how if there's 2 digits?

First, we will multiply all numbers above to the back of the number below.

Then, we will multiply all numbers above to the front of the numbers below. The result of this is put below the result of back number but leave 1 digit space.

And add the numbers from the results and you're now done! And just like addition, if you it results 2 digits, then keep it to get it added later.

Division

Last basic arithmetic you need to learn. Division is just multiplication but the reverse of it. Let's take example of 10 / 5.

Take a look at this. 10 divided by 5 results 2. And 2 times 5 is 10. It's basically just the reverse of it. To make it easier, how about we use boxes and cookies. I have 10 cookies and 5 boxes. I want to divide the 10 cookies into 5 boxes fairly. Which mean there will be 2 cookies each on every boxes in the 5 boxes I have. Here is also a representation of division

As you see, there are 2 times "-5" that subtracts 10. Quite simple, isn't it? Suggested to remember both 1 digit multiplication and division to make other process easier.

2 digits division

You may be able to calculate 12 / 2 = 6 or 36 / 6 = 6 because it's a 1 digit result multiplication, but what if the result is more than >10? Then here's how you calculate it

This is how you calculate a 2 digits division. The blank section above the cap is where we will write our final answer section.

So first, we will divide the first number in the 22, in this case, 2. Now we need to figure out what multiplication 2 has the result 2 or near it. We have 2 x 1 = 2. So now, we write 1 on the answer part.

Then, we subtract the front 2 with the result of 2 x 1 which means, 2. In this case, it results 0. And then, we pull down the back 2 from the 22. And do the same as the front 2 from the 22. Search for same or near, then subtract it. This time, I'll let you count the end result, the result of the 22 / 2. Write the result in the comment below!

Closing

I really hope you learn these 4 basic arithmetic first. Because next math tutorials will require these 4 basics. If you still need assistance, write down in the comment below!