a) $(\frac{1}{3}+\frac{1}{5}) \times \frac{1}{2}$

Cách 1:

$(\frac{1}{3}+\frac{1}{5}) \times \frac{1}{2} = (\frac{1\times 5}{3\times 5} + \frac{1\times 3}{5\times 3})\times \frac{1}{2}$ (quy đồng mẫu số)

$= (\frac{5}{15} + \frac{3}{15})\times \frac{1}{2} = \frac{8}{15}\times \frac{1}{2} = \frac{8\times 1}{15\times 2} = \frac{4\times 2\times 1}{15\times 2} = \frac{4}{15}$ (rút gọn cả tử và mẫu cho 2)

Cách 2:

$ (\frac{1}{3}+\frac{1}{5}) \times \frac{1}{2} = \frac{1}{3}\times \frac{1}{2} + \frac{1}{5}\times \frac{1}{2} = \frac{1\times 1}{3\times 2} + \frac{1\times 1}{5\times 2} = \frac{1}{6}+\frac{1}{10} = \frac{1\times 10}{6\times 10} + \frac{1\times 6}{10\times 6}$ (quy đồng mẫu số)

$= \frac{10}{60}+\frac{6}{60}= \frac{16}{60} = \frac{16:4}{60:4} = \frac{4}{15}$

b) $(\frac{1}{3}-\frac{1}{5}) \times \frac{1}{2}$

Cách 1:

$(\frac{1}{3}-\frac{1}{5}) \times \frac{1}{2} = (\frac{1\times 5}{3\times 5} - \frac{1\times 3}{5\times 3})\times \frac{1}{2}$

$= (\frac{5}{15} - \frac{3}{15})\times \frac{1}{2} = \frac{2}{15}\times \frac{1}{2} = \frac{2\times 1}{15\times 2}  = \frac{1}{15}$ (rút gọn cả tử và mẫu cho 2)

Cách 2:

$ (\frac{1}{3}-\frac{1}{5}) \times \frac{1}{2} = \frac{1}{3}\times \frac{1}{2} - \frac{1}{5}\times \frac{1}{2} = \frac{1\times 1}{3\times 2} - \frac{1\times 1}{5\times 2} = \frac{1}{6}-\frac{1}{10} = \frac{1\times 10}{6\times 10} - \frac{1\times 6}{10\times 6}$

$= \frac{10}{60}-\frac{6}{60}= \frac{4}{60} = \frac{4:4}{60:4} = \frac{1}{15}$