i know how to divide but i dont quit understand why we use those steps told in schools.
like for example
____
3/450 150 quotient
3
-----
15
15
------
000
could someone please tell me why we do these steps is there any other method or can someone explain why?
Best Answer
To solve $450\div 3$ we are asking how many groups of 3 there are in 450. The obvious way to solve this is to subtract groups of 3 from 450, one at a time, and count each group as it is subtracted. Thus:
We have to repeat this 150 times, after which the 450 has been reduced to 0. So the answer is that 450 contains 150 groups of 3.
It should be clear that there is an easy way to speed up this process: instead of removing a single group of 3 each time, we could remove 10 or even 100 groups of 3 at once. So for example:
Here we have removed 150 groups of 3 as before, but instead of doing them one at a time, we removed 100 right away, and then five sets of 10 groups each, for a total of 150 groups.
We can abbreviate this further:
We begin by removing 100 groups of 3, as before:
Now we want to remove sets of 10 groups from 150. Removing a set of 10 groups of 3 will remove 30. Instead of removing the sets one at a time, we apply our knowledge of multiplication to see that 150 is big enough to remove 5 sets of 10 groups of 3, for a total of 150:
Since the total has reached 0, we do not need to remove any single groups, so we fill in the final 0 in the answer:
Added 2014-04-23: I learned today that my daughter is being explicitly taught this method in the fourth grade. The example she showed me was:
Here, she said, you might happen to know that $7\times 20=140$, so you remove the 140 from the dividend:
Then perhaps you remember that $7\times 5 = 35$, so you remove the 35:
Then you remove the remaining 7:
The remainder is now 0, so you add the right-hand column, $20+5+1$, to obtain the quotient 26.