When one positive integer is divided by another, we typically represent what's left over either as a REMAINDER or as a DECIMAL.
There is a relationship between the two representations:
\(\frac{remainder}{divisor} = decimal\)
When 5 is divided by 2:
Remainder representation: \(\frac{5}{2} =\) 2 R1
Decimal representations: \(\frac{5}{2} = 2.5\)
\(\frac{remainder}{divisor} = \frac{1}{2}\)
\(decimal = 0.5\)
Since the two values are equal:
\(\frac{remainder}{divisor} = decimal\)
In most cases, it is helpful to represent the decimal AS A FRACTION IN ITS MOST REDUCED FORM.
Rachit92 wrote:
If X/Y = 5.32, where x and y are positive integers, what is the sum of all the values of Y that yield a remainder less than 30, when X is divided by Y ?
A) 25
B) 50
C) 75
D) 100
E) 150
In the problem above:
remainder = R
divisor = Y
decimal \(= 0.32 = \frac{32}{100} = \frac{8}{25}\)
Plugging these values into \(\frac{remainder}{divisor} = decimal\), we get:
\(\frac{R}{Y }= \frac{8}{25}\)
Since R must be less than 30, the following options are possible for \(\frac{R}{Y}\):
\(\frac{R}{Y} = \frac{8}{25} = \frac{16}{50} = \frac{24}{75}\)
Sum of the options for Y = 25 + 50 + 75 = 150
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