Question

Which of the following fractions is the smallest?
$\frac{1}{2},\frac{3}{7},\frac{3}{5},\frac{4}{9}$

(a) $\frac{4}{9}$
(b) $\frac{3}{5}$
(c) $\frac{3}{7}$
(d) $\frac{1}{2}$

Answer 1

(c) $\frac{3}{7}$
The LCM of numerators is 12, so we can convert each fraction into an equivalent fraction with numerator 12.
$$\begin{gathered} \frac{1}{2}=\frac{1}{2}\times \frac{12}{12}=\frac{12}{24} \\ \frac{3}{7}=\frac{3}{7}\times \frac{4}{4}=\frac{12}{28} \\ \frac{3}{5}=\frac{3}{5}\times \frac{4}{4}=\frac{12}{20} \\ \frac{4}{9}=\frac{4}{9}\times \frac{3}{3}=\frac{12}{27} \end{gathered}$$
When numerator is the same, the fraction with greater denominator is the smallest.
Thus, $\frac{3}{7}$ is the smallest fraction.