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RonPurewal
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Remainder question (from a student)

by RonPurewal Mon Apr 19, 2010 6:26 am

the following problem is modeled after one of the official problems:

When the positive integer x is divided by the positive integer y, the remainder is 20. If x/y = 87.625, what is y?


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BACKGROUND

the first thing you should know here is the following:
when you get a DECIMAL ANSWER to a DIVISION PROBLEM:

* the WHOLE NUMBER part of the answer corresponds to the QUOTIENT only (not the remainder).

* the DECIMAL part of the answer corresponds to the REMAINDER only (not the quotient).
furthermore,
DECIMAL PART = REMAINDER / DIVISOR


it's easier to understand this by looking at an example. i don't really want to provide a formula with four letters in it (unless any other posters really, really want that); it's easier to just look at the example and make an analogy.

the example:

22 / 8
= quotient 2, remainder 6
= 2 6/8 (as a mixed number with UNREDUCED fraction)
= 2.75
notice that 0.75 (the decimal part) corresponds to 6/8 (REMAINDER/DIVISOR).

if all you are concerned with is the remainder, you can actually ignore the quotient part (i.e., the whole-number part of the result) completely.

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once you've got the foregoing background, you can return to the above problem.

in that problem, you can ignore the "20", since we are only concerned with the remainder.
therefore,
DECIMAL PART = REMAINDER / DIVISOR
.625 = 20 / y
5/8 = 20/y (note: this step assumes that you know 5/8 = .625; if you don't, you'll have to divide 20 by .625 to solve the problem, which is annoying but not untenable)
y = 32