Question

Mark the correct alternative in each of the following:

Which of the following fractions is more than one-third?

(a) $\frac{23}{70}$ (b) $\frac{205}{819}$ (c) $\frac{26}{75}$ (d) $\frac{118}{335}$

Answer 1

Let $\frac{a}{b}$ and $\frac{c}{d}$ be two fractions. Then, $\frac{a}{b}>\frac{c}{d}$ if $a\times d>b\times c$.

Consider the fractions $\frac{23}{70}$ and $\frac{1}{3}$.
$$\begin{gathered} 23\times 3=69 \\ 1\times 70=70 \\ \therefore 23\times 3<1\times 70 \\ \Rightarrow \frac{23}{70}<\frac{1}{3} \end{gathered}$$

Consider the fractions $\frac{205}{819}$ and $\frac{1}{3}$.
$$\begin{gathered} 205\times 3=615 \\ 1\times 819=819 \\ \therefore 205\times 3<1\times 819 \\ \Rightarrow \frac{205}{819}<\frac{1}{3} \end{gathered}$$

Consider the fractions $\frac{26}{75}$ and $\frac{1}{3}$.
$$\begin{gathered} 26\times 3=78 \\ 1\times 75=75 \\ \therefore 26\times 3>1\times 75 \\ \Rightarrow \frac{26}{75}>\frac{1}{3} \end{gathered}$$

Consider the fractions $\frac{118}{335}$ and $\frac{1}{3}$.
$$\begin{gathered} 118\times 3=354 \\ 1\times 335=335 \\ \therefore 118\times 3>1\times 335 \\ \Rightarrow \frac{118}{335}>\frac{1}{3} \end{gathered}$$

Thus, the fractions $\frac{26}{75}$ and $\frac{118}{335}$ are more than the fraction $\frac{1}{3}$.

Hence, the correct answers are options (c) and (d).


Disclaimer: There are two correct options in the question. One of the two options among (c) and (d) must be changed accordingly to get only one correct answer.