# an algebraic question

• Dec 6th 2009, 12:12 AM
werepurple
an algebraic question
I haven't found an answer to that question, and certainly not sure if there is one. lol, I had nothing to do, so I was playing with my calculator, then I thought, "how do I find the remainder of a quotient using a calculator?".

I'm not really good in mathematics, and the question might be flawed, so if you were to find any fault in it, please correct it along with the answer.

Let a = b/c = d + R/c , where a, b, c, & R(remainder) are constants; b > c & R < c

Express R and d in terms of a, b, and c.

Thank you!!
• Dec 6th 2009, 05:42 AM
HallsofIvy
Quote:

Originally Posted by werepurple
I haven't found an answer to that question, and certainly not sure if there is one. lol, I had nothing to do, so I was playing with my calculator, then I thought, "how do I find the remainder of a quotient using a calculator?".

I'm not really good in mathematics, and the question might be flawed, so if you were to find any fault in it, please correct it along with the answer.

Let a = b/c = d + R/c , where a, b, c, & R(remainder) are constants; b > c & R < c

Express R and d in terms of a, b, and c.

Thank you!!

Given that b/c= d+ R/c, b/c- d= R/c. Finally, R= (b/c- d)c

For example, to determine the remainder after 132134 is divided by 233, first divide: 132134/233= 567.09871244635193133047210300429. Subtract the "integer part", 567, which is "d": 0.09871244635193133047210300429 and multiply by c= 233: (0.09871244635193133047210300429)(233)= 23.

If 132134 is divided by 233, the quotient is 567 and the remainder is 23.

Again, to determine the remainder when 213 is divided by 8, divide 213 by 8 to get 26.625. Subtract 26 from that to get 0.625, and multiply by 8: (0.625)8= 5.

If 213 is divided by 8, the quotient is 26 and the remainder is 5.
• Dec 6th 2009, 05:45 AM
werepurple
oh ok lol
What I really want to know is how to find the remainder using just its numerator and denominator. :D
• Dec 6th 2009, 05:58 AM
HallsofIvy
Well, there is this way: Given any b and a, there exist an integer n such that an< b< a(n+1). After you know n, the remainder is R= b- an. One way of finding that "n" is repeated multiplication:
To find the remainder with 832 is divided by 37, I might try 2(37)= 74, 3(37)= 111, 4(37)= 148, ..., 22(37)= 814, 23(37)= 851. Since 814< 832< 851, 37 divides into 832 with quotient 22 and remainder 832- 814= 18.

But since you are using a calculator, it is much easier to find that "n" by dividing! 832/37= 22.486486486486486486486486486486. Subtracting the quotient, 22, gives 0.486486486486486486486486486486. Multiplying that by 37 gives the remainder, 18.
• Dec 6th 2009, 06:14 AM
werepurple
But I have to use a number(22) other than the numerator or denominator to do that.

I want an expression for R(remainder), so that when I have to find the remainder of a quotient, I have to simply use its numerator and denominator. haha.

How do I do that? :o