Question

The smallest fraction which should be subtracted from the sum of the following numbers: \[ 4\frac{1}{4}, \, 2\frac{1}{2}, \, \frac{9}{12}, \, 3\frac{1}{3}, \, 2\frac{3}{4} \quad \text{so as to make it a whole number is:} \]

• A. \( \frac{5}{12} \)
• B. \( \frac{7}{12} \)
• C. \( \frac{1}{2} \)
• D. \( \frac{3}{4} \)

Hint:

When adding mixed fractions, first convert them to improper fractions and then find a common denominator. The difference between the sum and the nearest whole number will give you the fraction to subtract.

Answer 1

The Correct Option is B

% Option (A) Convert mixed numbers to improper fractions:

\begin{align} 4\frac{1}{4} &= \frac{17}{4}
2\frac{1}{2} &= \frac{5}{2}
5\frac{9}{12} &= \frac{69}{12} = \frac{23}{4}
3\frac{1}{3} &= \frac{10}{3}
2\frac{3}{4} &= \frac{11}{4} \end{align} % Option (B) Find a common denominator (12) and convert the fractions:

\begin{align} \frac{17}{4} &= \frac{51}{12}
\frac{5}{2} &= \frac{30}{12}
\frac{23}{4} &= \frac{69}{12}
\frac{10}{3} &= \frac{40}{12}
\frac{11}{4} &= \frac{33}{12} \end{align} % Option (C) Add the fractions:

\[ \frac{51}{12} + \frac{30}{12} + \frac{69}{12} + \frac{40}{12} + \frac{33}{12} = \frac{223}{12} \] % Option (D) Convert the improper fraction to a mixed number:

\[ \frac{223}{12} = 18\frac{7}{12} \] % Option (E) Determine the fraction to subtract:

To make $18\frac{7}{12}$ a whole number, we need to subtract $\frac{7}{12}$. Answer: The smallest fraction to be subtracted is $\frac{7}{12}$.