Discussion
The difference between the largest and smallest fractions among \(\frac{4}{7}\), \(\frac{9}{16}\), \(1\frac{2}{7}\) and \(\frac{3}{5}\) is :
Answer: B
The difference is \(\frac{81}{112}\).
The mixed number \(1\frac{2}{7} = \frac{9}{7}\) is the only value above 1, so it is the largest. Among the others, \(\frac{4}{7} \approx 0.571\), \(\frac{9}{16} = 0.5625\) and \(\frac{3}{5} = 0.6\), so \(\frac{9}{16}\) is the smallest.
\[ \begin{aligned} \frac{9}{7} - \frac{9}{16} &= \frac{144 - 63}{112} \\ &= \frac{81}{112} \end{aligned} \]
Taking \(\frac{4}{7}\) as the smallest gives \(\frac{9}{7} - \frac{4}{7} = \frac{5}{7}\), which is not offered. \(\frac{25}{28}\) and \(\frac{31}{56}\) come from pairing the wrong fractions.
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