Four Operation Of Mathematics.

The operations that become the basis in the mathematics, in solving numbers. 

• Addition
• Subtraction
• Multiplication
• Division

In the mathematics and in calculating using formula, you will use these always because these operations can be considered as fundamental of mathematics.

Addition

Addition is when you combine the numbers of stuffs to one or more numbers of the same stuffs. For example:

The picture above shows how addition or plus operation is working. The first box shows 3 cars (🚗🚗🚙) available. Then, the addition come in place when the usage of + sign, that means add or plus. This symbol will add 3 cars to number after the + sign, that is 2 cars (🚗🚙). After the = sign (equal sign), write the answer of 3 plus 2. Thus, there is 5 cars (🚗🚗🚙🚗🚙).   

Even after swapping the 3 cars and 2 cars, it makes no difference to addition process. The answer is still 5 cars. Look at the picture below:

Let's look on another example:

From the example in the picture above, we can see that there are 2 planes (✈️✈️), then there is add sign (+). After the add sign there are 4 planes (✈️✈️✈️✈️). Then there is equal sign, which after that will give us the answer to 2 planes add with 4 planes. The answer is 6 planes (✈️✈️✈️✈️✈️✈️). 

The table below shows the addition processes from 0 to 9 with 0 to 9:

From the table above, we can calculate for addition. For example, take 5 from the upper side and 8 from the left side. Thus, they meet on 13, which is 5 plus 8 (5+8=13). Let's try another numbers. Take 3 from the upper side and take 6 from the right side. They meet on 9, which is 3 plus 6 (3+6=9). 

Let's add two digit numbers with two digit numbers.

The picture above shows the addition process between 25 and 19. First, we must add 5 and 9. It will be 14. Why 1 in 14 is blue, you may ask. It is because the number 1 will be carry forward to ten place, that has 2 and 1. Then, 2 plus 1 is 3, then 3 plus 1 (carry forward number) is 4. Thus, 25 plus 19 is 44 (25+19=44). 

Here is more information on addition process.

Subtraction

The subtraction is the opposite of addition. Instead of making the numbers more bigger, subtraction makes the numbers more smaller. Subtraction also called as additive inverse. Subtraction takes some numbers away from original numbers.  For example: 

From the picture above, we can see 4 apples. On the left of 4 apples, it is subtraction sign (-). After the subtraction sign, there are 2 apples. After the equal sign (=) it shows 2 apples, because 4 apples subtract with 2 apples equal 2 apples (or 4-2=2). 

What if 4 apples and 2 apples change place?

The picture above shows another subtraction process. at the front, there is 2 apples. Besides that, there is a subtraction sign or minus sign (-). At the left of minus sign, there are 4 apples. Then, after the equal sign, it shows the result of 2 apples minus 4 apples. But the answer is "need 2 apples more". Why did this happen?

Imagine you have 2 apples. Ahmad asks you for 4 apples. Then, you give Ahmad 2 apples and you say "I will give you 2 apples tomorrow". Ahmad agrees. Thus, that is why the answer is "need 2 apples more", or in mathematical terms: 

2-4=-2. 

Below is the table on subtraction (upper numbers subtracted by left numbers):

Let's take 6 from upper numbers and 2 from left numbers in the table. They meet on 4 because 6 subtracted by 2 is 4 (or 6-2=4). Then, take 4 from upper numbers and 8 from left numbers. They meet on -4, because 4 minus 8 is -4 (or 4-8=-4).

Below is the subtraction between 2 digit number to 2 digit number:

 

As we see the image above, 28 is minus by 15. The first step is to minus 8 by 5, the answer will be 3. Then, look at the ten place, that are 2 and 1. So, 2 subtracted by 1 is 1. Thus, the answer to 28 subtracted by 15 is 13 (28-15=13).

Let's look on another example of subtraction or minus operation:

From the image above, it shows 25 subtract by 18. First, we must subtract numbers in one place, that are subtract 5 with 8. But, it is not enough to subtract 5 with 8. So, we borrow 10 from ten place. Then, 10 plus 5 is 15, then 15 subtract with 8 is 7. At the ten place, there are two numbers, 1 and 1. 2 had become 1 because one place borrows 1 from 2. Thus, 1 minus 1 is 0. Thus, 25 subtracted with 18 is 7 (25-18=7).   

For more information regarding subtraction, look here.

Multiplication

Multiplication is how many times do you add the number. The process of multiplication called multiply or times. For example, 2 times 1 is 2, means 2 for 1 times. But 2 times 2 is 4, means 2 for 2 times, also 2+2. What is 2 times 3? It is same as 2+2+2, means 6. 

Let's look at the example below:

The picture above is a multiplication between 5 and 3. The multiplication symbol is x. 5 multiply by 3 equals to 15. Note that 5 times 3 (5x3) is same as 5 plus 5 plus 5 (5+5+5), which is 15. Thus, 5 times 3 is same as adding 5 for three times. What for 3 times 5 (3x5)? The answer would be the same, it is 15, because multiplication is commutative (eg 5x3=3x5). 

Next, below is the table on multiplication 0 to 9 with 0 to 9:

From the table above, we can see the results of multiplication. For example, take 4 from the upper numbers and 5 from the left numbers. They meet on 20, which is the result of 4 times 5 (4x5=20). From this table, it shows that 5 times 4 is also 20 (5x4=20). Let's look at another example. Take 7 from upper numbers and 8 from left numbers. They meet on 56, which is the answer to 7 times 8 (7x8=56). 

Below is the multiplication between two digit numbers and two digit numbers:

The picture above shows the multiplication between 17 and 34. First, multiply 17 to 4. 7 multiply by 4 is 28, then 4 multiply by 1 is 4. 4 will be added to 2 from 28 earlier. Thus, 17 times 4 is 68. Then, multiply 17 by 3. 7 times 3 is 21 and 1 times 3 is 3. 3 will be added to 2 from 21. Thus, 17 multiply by 3 is 51. Then, add 68 to 51, but put 1 in the same level as 6, like the picture above. The final answer to 17 times 34 is 578 (17x34=578). 

A lot of information regarding multiplication are present here.

Division

Division is how you divide the total stuffs in fair numbers. For example:

From the picture above, we can see that there are 9 pencils. Beside the division sign (÷), there are three persons. We must divide the pencils fairly. To be fair, 9 pencils had divided to 3 so each person has 3 pencils, which are the same for all 3 persons. From here we should know that 9 divided by 3 equals 3 (9÷3=3, or 9/3=3).

We know that 9÷3=3, but what does the name for each position of number? Look below:

The one that is divided (9) is dividend, the divider (3 after ÷) is divisor and the answer (3 after =) is quotient. The same case when 9/3=3, just change the symbol ÷ into /. 

Sometimes, there are remains that could not be divided. Let's look at the image below:

Let's say we want to divide 10 pencils fairly to each person. There are 3 persons. So, each person would get 3 pencils. But, 1 pencil is remaining. That pencil is what we called as remainder (R in the picture). Thus, 10 divided by 3 is 3 with the remainder 1. 

Division is the opposite of multiplying. Thus in division, everyone use multiplication table to solve it. Let's look at the picture below to solve long dividend:

From the picture above, it shows the process of 9405 divided by 9. First, we should solve the number in front, that is 9. 9x1 is 9, so write 1 on top of 9 in division, then minus 9 by 9. Then, bring down 4. There is no 4 in 9 multiplication table, so put 0 at the top of 4, then minus 4 by 0, equal 4. Then, bring down 0 to put it besides 4, becomes 40. 9 times 4 is 36, thus put 4 at the top of 0, then minus 40 by 36. The answer would be 4. Then, bring down 5 besides 4. 9x5 is 45, so write 5 on the top of 5 and 45 minus 45. Two dots below 45 represent zero. Thus, 9405 divided by 9 is 1045 (9405÷9=1045). 

There are a lot of information about division here.

The four basics operation of mathematics had been covered.

For the info regarding four operations, go here.

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