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: First we’ll learn the concept of a mixed fraction, using it we’ll find the sum of the given fractions after simplifying them. Now we’ll convert the final answer into the mixed fraction as mixed fraction breaks a fraction into the sum of a whole number and a fraction that is less than 1, and since that fraction is always less than 1, that fraction will be the answer for our question.

Complete step by step answer:

Given data:Fractions $1\dfrac{3}{4},2\dfrac{1}{2},5\dfrac{7}{{12}},3\dfrac{1}{3}$ and $2\dfrac{1}{4}$
A mixed fraction is a whole number plus a fractional part. An improper fraction is a fraction where the numerator is larger than the denominator and if the numerator is smaller than the denominator then it is called a proper fraction, we can only interchange the improper fraction to mixed fraction and vice versa.
If we have a mixed fraction $a\dfrac{b}{c}$ then its form in improper fraction will be $\dfrac{{ac + b}}{c}$ or $a + \dfrac{b}{c}$
Now adding the given fractions
i.e. $1\dfrac{3}{4} + 2\dfrac{1}{2} + 5\dfrac{7}{{12}} + 3\dfrac{1}{3} + 2\dfrac{1}{4}$
From the form of mixed fractions, we mentioned we can write it as
 $ \Rightarrow \dfrac{{4 + 3}}{4} + \dfrac{{4 + 1}}{2} + \dfrac{{60 + 7}}{{12}} + \dfrac{{9 + 1}}{3} + \dfrac{{8 + 1}}{4}$
On simplifying the numerator
 $ \Rightarrow \dfrac{7}{4} + \dfrac{5}{2} + \dfrac{{67}}{{12}} + \dfrac{{10}}{3} + \dfrac{9}{4}$
Taking LCM of the denominator of the fractions, we get,
 $ \Rightarrow \dfrac{{7 \times 3}}{{4 \times 3}} + \dfrac{{5 \times 6}}{{2 \times 6}} + \dfrac{{67}}{{12}} + \dfrac{{10 \times 4}}{{3 \times 4}} + \dfrac{{9 \times 3}}{{4 \times 3}}$
Now adding the numerators as the denominators are constant
 $ \Rightarrow \dfrac{{21 + 30 + 67 + 40 + 27}}{{12}}$
On simplifying the numerators
 $ \Rightarrow \dfrac{{185}}{{12}}$
As it is also in improper fraction converting it to mixed fraction,
 $ \Rightarrow 15\dfrac{5}{{12}}$
 $ \Rightarrow 15 + \dfrac{5}{{12}}$ , therefore from this value, we can say that subtracting $\dfrac{5}{{12}}$ from the sum of the given fraction we will the result as a whole number i.e. 15
Option(A) is correct.

Note: Some of the students misinterpret this mixed fraction and just do the simple multiplication of the whole number and the fraction, which is wrong and will lead us to a wrong solution to the question. Some students write this mixed fraction $a\dfrac{b}{c}$ as $a \times \dfrac{b}{c}$ which is wrong and $a\dfrac{b}{c} = \dfrac{{ac + b}}{c} \ne a \times \dfrac{b}{c}$ .