If $$A = \frac{1}{2} \div \frac{1}{3} \times \frac{1}{4} + \frac{1}{5} \times \frac{1}{6}$$ and $$B = \frac{1}{6} \div \frac{1}{3} \times \frac{1}{5} + \frac{1}{4} \times \frac{1}{2}$$, then what is the value of (A - B)?

Solution

$$A = \frac{1}{2} \div \frac{1}{3} \times \frac{1}{4} + \frac{1}{5} \times \frac{1}{6}$$

$$A=\frac{1}{2}\times\frac{3}{1}\times\frac{1}{4}+\frac{1}{5}\times\frac{1}{6}$$

$$A=\frac{3}{8}+\frac{1}{30}$$
$$A=\frac{45+4}{120}$$
$$A=\frac{49}{120}$$    Eq.(i)

$$B = \frac{1}{6} \div \frac{1}{3} \times \frac{1}{5} + \frac{1}{4} \times \frac{1}{2}$$

$$B=\frac{1}{6}\times\frac{3}{1}\times\frac{1}{5}+\frac{1}{4}\times\frac{1}{2}$$

$$B=\frac{1}{2}\times\frac{1}{1}\times\frac{1}{5}+\frac{1}{8}$$
$$B=\frac{1}{10}+\frac{1}{8}$$
$$B=\frac{4+5}{40}$$
$$B=\frac{9}{40}$$    Eq.(ii)
Value of (A - B) =  Eq.(i)- Eq.(ii)
= $$\frac{49}{120}-\frac{9}{40}$$
= $$\frac{49}{120}-\frac{27}{120}$$
= $$\frac{22}{120}$$
= $$\frac{11}{60}$$