Discussion
\(\dfrac{5}{7}\) of \(\dfrac{35}{12} \div \dfrac{28}{9}\) + \(\dfrac{96}{15} \div \dfrac{8}{5} \times \dfrac{3}{4}\) - \(\dfrac{7}{56}\) is equal to :
Answer: D
The expression equals \(3\dfrac{61}{112}\).
By the order of operations (BODMAS), 'of' is done first, then division and multiplication from left to right, then addition and subtraction.
\[ \begin{aligned} \tfrac{5}{7} \text{ of } \tfrac{35}{12} &= \tfrac{25}{12} \\ \tfrac{25}{12} \div \tfrac{28}{9} &= \tfrac{25}{12} \times \tfrac{9}{28} = \tfrac{75}{112} \end{aligned} \]
\[ \begin{aligned} \tfrac{96}{15} \div \tfrac{8}{5} &= \tfrac{96}{15} \times \tfrac{5}{8} = 4 \\ 4 \times \tfrac{3}{4} &= 3 \end{aligned} \]
\[ \begin{aligned} \tfrac{75}{112} + 3 - \tfrac{7}{56} &= 3 + \tfrac{75 - 14}{112} \\ &= 3\tfrac{61}{112} \end{aligned} \]
The order is what the question tests: 'of' binds the two fractions next to it before the division sign is applied, and the subtraction of \(\frac{7}{56}\) comes last. Working strictly left to right without these rules gives a different value, which is how the other options arise.
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