Discussion
Find the value of question mark (?) in the following :
\[ \begin{aligned} &1\tfrac{3}{4} + 5\tfrac{1}{8} \\ &- (?) \times \tfrac{4}{3} \div 2\tfrac{2}{3} \\ &= 5\tfrac{3}{4} \end{aligned} \]
Answer: C
The missing value is \(2\frac{1}{4}\).
Follow BODMAS: the multiplication and division on (?) come before the addition and subtraction. First the known terms:
\[ \begin{aligned} 1\tfrac{3}{4} + 5\tfrac{1}{8} &= \tfrac{14}{8} + \tfrac{41}{8} = \tfrac{55}{8} \\ \tfrac{4}{3} \div 2\tfrac{2}{3} &= \tfrac{4}{3} \times \tfrac{3}{8} = \tfrac{1}{2} \end{aligned} \]
So \(\tfrac{55}{8} - \tfrac{1}{2}(?) = 5\tfrac{3}{4} = \tfrac{46}{8}\), giving \(\tfrac{1}{2}(?) = \tfrac{9}{8}\) and \((?) = \tfrac{9}{4} = 2\tfrac{1}{4}\).
The other options do not satisfy the equation; for example \(3\frac{1}{2}\) would make the left side \(5\frac{1}{8}\).
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