If $${\text{A}} = 3\frac{1}{4} \times 4\frac{1}{4} \div 34 - \frac{{47}}{{32}} + \frac{{47}}{{16}}$$      and $${\text{B}} = 2\frac{1}{2} + 5\frac{1}{2} \div 55 - \frac{{11}}{{10}}$$     then what is the value of A - B?

Solution(By Examveda Team)

$$\eqalign{ & {\text{A}} = 3\frac{1}{4} \times 4\frac{1}{4} \div 34 - \frac{{47}}{{32}} + \frac{{47}}{{16}} \cr & {\text{B}} = 2\frac{1}{2} + 5\frac{1}{2} \div 55 - \frac{{11}}{{10}} \cr & \therefore {\text{A}} - {\text{B}} = \left( {3\frac{1}{4} \times 4\frac{1}{4} \div 34 - \frac{{47}}{{32}} + \frac{{47}}{{16}}} \right) - \left( {2\frac{1}{2} + 5\frac{1}{2} \div 55 - \frac{{11}}{{10}}} \right) \cr & = \left( {\frac{{13}}{4} \times \frac{{17}}{4} \times \frac{1}{{34}} - \frac{{47}}{{32}} + \frac{{47}}{{16}}} \right) - \left( {\frac{5}{2} + \frac{{11}}{2} \times \frac{1}{{55}} - \frac{{11}}{{10}}} \right) \cr & = \left( {\frac{{13}}{{32}} - \frac{{47}}{{32}} + \frac{{47}}{{16}}} \right) - \left( {\frac{5}{2} + \frac{1}{{10}} - \frac{{11}}{{10}}} \right) \cr & = \left( {\frac{{13 - 47 + 94}}{{32}}} \right) - \left( {\frac{{25 + 1 - 11}}{{10}}} \right) \cr & = \frac{{60}}{{32}} - \frac{{15}}{{10}} \cr & = \frac{{15}}{8} - \frac{3}{2} \cr & = \frac{{15 - 12}}{8} \cr & = \frac{3}{8} \cr} $$