Discussion
The value of
\[ \begin{aligned} & 5\frac{1}{4} \div 3\frac{1}{2} \times \frac{5}{6} - \frac{3}{8} \\ & + \frac{2}{5} \div \frac{2}{15}\text{ of }1\frac{3}{5} - \frac{3}{4} \div \frac{5}{12} \end{aligned} \]
is:
Answer: C
The value is 19/20. Using BODMAS, 'of' is done first, then division and multiplication, then addition and subtraction. The first part is the division and multiplication:
\[ \frac{21}{4} \div \frac{7}{2} \times \frac{5}{6} \]
\[ = \frac{21}{4} \times \frac{2}{7} \times \frac{5}{6} \]
\[ = \frac{5}{4} \]
Next, the 'of' term and the divisions that follow it:
\[ \frac{2}{15} \text{ of } 1\frac{3}{5} \]
\[ = \frac{2}{15} \times \frac{8}{5} = \frac{16}{75} \]
\[ \frac{2}{5} \div \frac{16}{75} = \frac{15}{8} \]
\[ \frac{3}{4} \div \frac{5}{12} = \frac{9}{5} \]
Combining all the terms:
\[ \frac{5}{4} - \frac{3}{8} + \frac{15}{8} - \frac{9}{5} \]
\[ = \frac{11}{4} - \frac{9}{5} = \frac{19}{20} \]
The other options, 9/10, 3/5 and 39/40, come from a wrong order of operations.
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