Question

Which of the following fractions is the greatest of all?
$\frac{7}{8},\frac{6}{7},\frac{4}{5},\frac{5}{6}$

(a) $\frac{6}{7}$
(b) $\frac{4}{5}$
(c) $\frac{5}{6}$
(d) $\frac{7}{8}$

Answer 1

(d) $\frac{7}{8}$
The LCM of 8, 7, 6 and 5 is 840, so we can convert each fraction into an equivalent fraction with denominator 840.
$$\begin{gathered} \frac{7}{8}=\frac{7}{8}\times \frac{105}{105}=\frac{735}{840} \\ \frac{6}{7}=\frac{6}{7}\times \frac{120}{120}=\frac{720}{840} \\ \frac{4}{5}=\frac{4}{5}\times \frac{168}{168}=\frac{672}{840} \\ \frac{5}{6}=\frac{5}{6}\times \frac{140}{140}=\frac{700}{840} \end{gathered}$$

When denominator is the same, the fraction with the largest numerator is the greatest.

Thus, $\frac{7}{8}$ is the greatest fraction among all.