Question

The smallest fraction which should be subtracted from the sum of $1\dfrac{3}{4}, 2\dfrac{1}{2}, 5 \dfrac{7}{12}, 3\dfrac{1}{3}$ and $2\dfrac{1}{4}$ to make the result a whole number, is…
A. $\dfrac{5}{12}$
B. $\dfrac{7}{12}$
C. $\dfrac{1}{2}$
D. 7

Answer 1

Hint: Whole Numbers: Whole numbers is a set of numbers containing zero and all positive integers. For example, 0, 1, 2, 3, …
In this question, to find the smallest fraction we first add all the numbers and then find the adjacent whole number to it. Then, by subtracting the whole number from the sum, we can get the required result.

Complete step-by-step answer:
In order to make the sum of given numbers a whole number, we need to subtract a fraction from the sum of given numbers.
Now, sum of given numbers is:
$1\dfrac{3}{4}+2\dfrac{1}{2}+5\dfrac{7}{12}+3\dfrac{1}{3}+2\dfrac{1}{4}=\dfrac{7}{4}+\dfrac{5}{2}+\dfrac{67}{12}+\dfrac{10}{3}+\dfrac{9}{4}$
Taking L.C.M in the denominator to simplify, we get,
$1\dfrac{3}{4}+2\dfrac{1}{2}+5\dfrac{7}{12}+3\dfrac{1}{3}+2\dfrac{1}{4}=\dfrac{21+30+67+40+27}{12}=\dfrac{185}{12}$
Now, writing the sum as mixed fraction, we get,
$\dfrac{185}{12}=15\dfrac{5}{12}$
Thus, $1\dfrac{3}{4}+2\dfrac{1}{2}+5\dfrac{7}{12}+3\dfrac{1}{3}+2\dfrac{1}{4}=15\dfrac{5}{12}$.
Now, it is clear that in order to make this sum a whole number the smallest number to be subtracted is $\dfrac{5}{12}$.
Hence, option A is correct.

Note: In this type of question, to find the smallest fraction to make a certain sum or value whole is done by writing the sum in the form of a mixed fraction which makes it easier to find the smallest fraction to be subtracted. If we try to convert these numbers in decimal form, it would make it difficult to find the number to be subtracted such that the sum is whole.