# Answer to Question #41091 in Algebra for maria

Question #41091

Dear Expert team Hi,We do addition ,subtraction and multiplication from right side (that is we take start from unit place) but for division we take start from left side.Why?Is there any reason why we do division from left side while others operations from right side.give some reasons to convince others.

best wishes

best wishes

Expert's answer

Let us consider all these operations. And we start from addition.

Suppose we have two numbers, for example, 258 and 387. We can expand them into the sum as 258=2*100+5*10+8 and 387=3*100+8*10+7. Then add them

258+387=2*100+5*10+8+3*100+8*10+7=(2+3)*100+(5+8)*10+(8+7). If we start from the left side we get at first five hundred then 13 tens, but it is 1 hundred and 3 tens and on this step we should return to the hundreds and add 1 to the 5. After that, we get 15 digits, which is equal to 1 ten and 5 digits, and again we should return to the previous step. It is not convenient because we need to return to the previous step often. That is why we start from the right side is the optimal way to find the sum.

The same situation we get with multiplying and subtraction (sometimes we need to borrow one hundred or ten, or something higher, and we have to return to subtract 1 from the previous step).

With the division we have the opposite situation. If we start our computations from the left side, we can get the remainder that we add to the next step. For example, 144/12. Let us try to start it from the right side. We take 44/12=3*12+8. This remainder we add to 100 and continue our division. 108/12 it is difficult now. And what do we get with larger numbers? Therefore, it is the optimal way for division started with the left side.

Suppose we have two numbers, for example, 258 and 387. We can expand them into the sum as 258=2*100+5*10+8 and 387=3*100+8*10+7. Then add them

258+387=2*100+5*10+8+3*100+8*10+7=(2+3)*100+(5+8)*10+(8+7). If we start from the left side we get at first five hundred then 13 tens, but it is 1 hundred and 3 tens and on this step we should return to the hundreds and add 1 to the 5. After that, we get 15 digits, which is equal to 1 ten and 5 digits, and again we should return to the previous step. It is not convenient because we need to return to the previous step often. That is why we start from the right side is the optimal way to find the sum.

The same situation we get with multiplying and subtraction (sometimes we need to borrow one hundred or ten, or something higher, and we have to return to subtract 1 from the previous step).

With the division we have the opposite situation. If we start our computations from the left side, we can get the remainder that we add to the next step. For example, 144/12. Let us try to start it from the right side. We take 44/12=3*12+8. This remainder we add to 100 and continue our division. 108/12 it is difficult now. And what do we get with larger numbers? Therefore, it is the optimal way for division started with the left side.

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