## Learn with 98thPercentile, how to solve Hard Math Questions

There might be a question bugging you for a very long time. If that virus did not infect your brain cells, it will infiltrate now because I have a very basic and yet complex question.

Whenever we do addition, subtraction, or multiplication, we start from the right and progress toward the left. That is, you would add the right-most numbers first with the lowest place values and then keep on moving left until the problem is solved. But have you ever noticed that we do the opposite for division?

Indeed, when you are dividing a number, you start from the digit with the highest place value and then go down the line. But why?

Logic dictates that multiplication and division are similar, so they should share similar patterns, attributes, and processes. Or if we apply another skewed logic, we should say that subtraction and division are destructive and decreasing in nature and so they should share a similar pattern. But why does only division stand out as an anomaly from the rest of the crowd and why not any other operation? Let's find out.

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For a question about the fundamentals of mathematics, we need to look at the fundamentals of the number system. The number system that we follow depends on place values. A simplified explanation of place values can be given with candy. Let us assume that the ones place which can be assumed as loose candy. And tens place can be assumed as a group of ten candies. And the hundreds place can be assumed as the pack of hundred candies and so on. So now, let's start the operations.

When we add numbers, let's say we are adding two numbers 27 and 48. Let's go the wrong way around. Let's add the tens place first. We have 2 groups of ten candy in the first number and 4 groups in the second number which makes a total of 6 groups. Now, let's go to the lower place value and do the addition. We have 7 loose candies in the first number and 8 loose candies in the second number. Add them and we have 15 candy. But we know that we can pick out 10 candies and make it into a new group. So, we have to redo the tens place addition. Don’t you think it would have been convenient to start with one place and work your way up as the groups keep on piling? Hence, we add from the lowest place value to the highest place value. The same goes for subtraction and the same goes for multiplication.

Let's apply the same approach for division and go the wrong way around to see if the operation still works. Let us say that we are dividing the number 54 by 3. We know that dividing is distributing among people. Let's start with the one's place. We have 4 candies and we have to divide them among 3 people. We give one candy to each kid so we have one left as the remainder. Now, we move on to the tens place. We divide the 5 groups of ten candies in such a manner that each child gets one group of ten candies. Now, we have 2 groups of ten candy left. We have to break this group into loose candies and add the one remaining candy to make 21 loose candies. Now, we can divide it into 7 candies for each child. It feels better to go according to the convention and first divide the larger pool and break down the remaining into the smaller pool. Hence, the division has to go in the opposite direction.

In conclusion, if we go the wrong way around in these operations of addition, subtraction, multiplication, and division, we end up doing the process multiple times. This makes the process lengthy. Hence we follow the standard direction and convention to make our life easier.

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