Tính

a) \[\frac{1}{4} + \frac{2}{4} + \frac{3}{4} = \frac{{..... + ..... + .....}}{{.....}} = \frac{{.....}}{{.....}}\]

b) \[2 + \frac{3}{5} + \frac{1}{5} = \frac{{..... + ..... + .....}}{{.....}} = \frac{{.....}}{{.....}}\]

Hướng dẫn giải

\[\frac{{13}}{{24}} + \left( {\frac{7}{{12}} + \frac{{11}}{{24}}} \right) + \frac{5}{{12}}\]

\( = \left( {\frac{{13}}{{24}} + \frac{{11}}{{24}}} \right) + \left( {\frac{7}{{12}} + \frac{5}{{12}}} \right)\)

= 1 + 1

= 2

Hướng dẫn giải

a)

\[3 - \frac{1}{2} = \frac{6}{2} - \frac{1}{2} = \frac{{6 - 1}}{2} = \frac{5}{2} = \frac{{10}}{4}\]

\[\frac{1}{4} + \frac{1}{2} = \frac{1}{4} + \frac{2}{4} = \frac{{1 + 2}}{4} = \frac{3}{4}\]

So sánh: \(\frac{{10}}{4} > \frac{3}{4}\) hay \[3 - \frac{1}{2} > \frac{1}{4} + \frac{1}{2}\]

b)

\[\frac{5}{7} + 2 = \frac{5}{7} + \frac{{14}}{7} = \frac{{5 + 14}}{7} = \frac{{19}}{7}\]

\[4 - \frac{1}{7} = \frac{{28}}{7} - \frac{1}{7} = \frac{{28 - 1}}{7} = \frac{{27}}{7}\]

So sánh: \(\frac{{19}}{7} < \frac{{27}}{7}\) hay\[\frac{5}{7} + 2 < 4 - \frac{1}{7}\]