i know how to do long division, but confused as to why it works. can someone provide a good explanation?
for example 287/3 = 95 R2. I know how to do the problem, but I just do not know why that this algorithm works.
for example 287/3 = 95 R2. I know how to do the problem, but I just do not know why that this algorithm works.
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Long division works because of the question "how many" can be broken into hole units and portions of whole units.
Our number system sets long division as going left to right, where each place value to the right is smaller. As you "divide" the whole portion, the number which is written on top, represents how many times the divisor can subtract away from the dividend (starting number).The remainder after subtracting is how many parts remain that could not be subtracted away.
The reason why long division works occurs here - the remainder represent how many the next column has ------
For instance
115 divided by 5
In long division, 5 can not subtract away from the 1 (100's place), leaving that one as a remainder to attach to the next 1 (10's place) - this gives you 11 tens
5 can subtract away from 11 twice - putting the 2 in the column above the second 1.
2 5's produce a product of 10 - subtracting from 11 - leaves you a remainder of 1 - which attaches to the 5 (representing 15 in the one's column)
5 can be subtracted away from 15 three times - putting 3 next to the two up top, leaving no remainder left
Thus 115 divided by 5 equals 23.
Bit lengthy - but - since repeated subtraction is the essence of division (like repeated addition is for multiplication) - it does work!!!!
Our number system sets long division as going left to right, where each place value to the right is smaller. As you "divide" the whole portion, the number which is written on top, represents how many times the divisor can subtract away from the dividend (starting number).The remainder after subtracting is how many parts remain that could not be subtracted away.
The reason why long division works occurs here - the remainder represent how many the next column has ------
For instance
115 divided by 5
In long division, 5 can not subtract away from the 1 (100's place), leaving that one as a remainder to attach to the next 1 (10's place) - this gives you 11 tens
5 can subtract away from 11 twice - putting the 2 in the column above the second 1.
2 5's produce a product of 10 - subtracting from 11 - leaves you a remainder of 1 - which attaches to the 5 (representing 15 in the one's column)
5 can be subtracted away from 15 three times - putting 3 next to the two up top, leaving no remainder left
Thus 115 divided by 5 equals 23.
Bit lengthy - but - since repeated subtraction is the essence of division (like repeated addition is for multiplication) - it does work!!!!
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Because what we are really saying by remainder 2 is 2/3 so we have
3*[95+2/3] = 285+2 = 287
3*[95+2/3] = 285+2 = 287