Tính rồi rút gọn phân số:

a) \[\frac{8}{{21}} + \frac{6}{{21}}\]       b) \[\frac{9}{{26}} + \frac{{11}}{{26}}\] c) \[\frac{{13}}{{30}} + \frac{7}{{30}}\]      d) \[\frac{5}{{12}} + \frac{1}{{12}}\]

e) \[\frac{7}{{16}} - \frac{5}{{16}}\]        f) \[\frac{{19}}{{50}} - \frac{9}{{50}}\] g) \[\frac{{19}}{{45}} - \frac{4}{{45}}\]       h) \[\frac{{27}}{{30}} - \frac{{12}}{{30}}\]

a)

Rút gọn phân số:

\[\frac{{10}}{{15}} = \frac{{10:5}}{{15:5}} = \frac{2}{3}\]

\[\frac{6}{{36}} = \frac{{6:6}}{{36:6}} = \frac{1}{6}\]

Quy đồng mẫu số hai phân số với mẫu số chung bằng 6

\[\frac{2}{3} = \frac{{2 \times 2}}{{3 \times 2}} = \frac{4}{6}\]

Giữ nguyên phân số \[\frac{1}{6}\]

 b)

Rút gọn phân số:

\[\frac{{20}}{{12}} = \frac{{20:4}}{{12:4}} = \frac{5}{3}\]

\[\frac{5}{{45}} = \frac{{5:5}}{{45:5}} = \frac{1}{9}\]

Quy đồng mẫu số hai phân số với mẫu số chung bằng 9

\[\frac{5}{3} = \frac{{5 \times 3}}{{3 \times 3}} = \frac{{15}}{9}\]

Giữ nguyên phân số \[\frac{1}{9}\]

c)

Rút gọn phân số:

\[\frac{4}{{16}} = \frac{{4:4}}{{16:4}} = \frac{1}{4}\]

\[\frac{5}{{10}} = \frac{{5:5}}{{10:5}} = \frac{1}{2}\]

Quy đồng mẫu số hai phân số với mẫu số chung bằng 4

\[\frac{1}{2} = \frac{{1 \times 2}}{{2 \times 2}} = \frac{2}{4}\]

Giữ nguyên phân số \[\frac{1}{4}\]

d)

Rút gọn phân số:

\[\frac{3}{9} = \frac{{3:3}}{{9:3}} = \frac{1}{3}\]

\[\frac{2}{{12}} = \frac{{2:2}}{{12:2}} = \frac{1}{6}\]

Quy đồng mẫu số hai phân số với mẫu số chung bằng 6

\[\frac{1}{3} = \frac{{1 \times 2}}{{3 \times 2}} = \frac{2}{6}\]

Giữ nguyên phân số \[\frac{1}{6}\]

a)

\[\frac{5}{3} + \frac{1}{6} = \frac{{10}}{6} + \frac{1}{6} = \frac{{11}}{6}\]

So sánh: \[\frac{{11}}{6} = \,\frac{{11}}{6}\]

Vậy: \[\frac{5}{3} + \frac{1}{6}\,\, = \,\,\frac{{11}}{6}\]       

b)

\[\frac{5}{{12}} + \frac{2}{3} = \frac{5}{{12}} + \frac{8}{{12}} = \frac{{13}}{{12}}\]

So sánh: \[\frac{{13}}{{12}}\,\, > \,\,\frac{{11}}{{12}}\]

Vậy: \[\frac{5}{{12}} + \frac{2}{3}\,\, > \,\,\frac{{11}}{{12}}\]  

c)

\[\frac{9}{5} + \frac{3}{{10}} = \frac{{18}}{{10}} + \frac{3}{{10}} = \frac{{21}}{{10}}\]

So sánh: \[\frac{{21}}{{10}}\,\, = \,\,\frac{{21}}{{10}}\]

Vậy: \[\frac{9}{5} + \frac{3}{{10}} = \frac{{21}}{{10}}\]

d)

\[\frac{7}{{15}} + \frac{1}{{15}} = \frac{8}{{15}}\]

So sánh: \[\frac{{14}}{{15}}\,\, > \,\,\frac{8}{{15}}\]

Vậy: \[\frac{{14}}{{15}}\,\, > \,\,\frac{7}{{15}} + \frac{1}{{15}}\]

e)

\[\frac{6}{5} + \frac{7}{{10}} = \frac{{12}}{{10}} + \frac{7}{{10}} = \frac{{19}}{{10}} = \frac{{38}}{{20}}\]

\[\frac{7}{4} + \frac{{11}}{{20}} = \frac{{35}}{{20}} + \frac{{11}}{{20}} = \frac{{46}}{{20}}\]

So sánh: \[\frac{{38}}{{20}} < \frac{{46}}{{20}}\]

Vậy: \[\frac{6}{5} + \frac{7}{{10}}\,\, < \,\,\frac{7}{4} + \frac{{11}}{{20}}\]

f)

\[\frac{3}{4} + \frac{7}{{12}} = \frac{9}{{12}} + \frac{7}{{12}} = \frac{{16}}{{12}}\]

\[\frac{1}{3} + \frac{5}{{12}} = \frac{4}{{12}} + \frac{5}{{12}} = \frac{9}{{12}}\]

So sánh: \[\frac{{16}}{{12}} > \frac{9}{{12}}\]

Vậy: \[\frac{3}{4} + \frac{7}{{12}}\,\, > \,\,\frac{1}{3} + \frac{5}{{12}}\]

g)

\[\frac{7}{8} + \frac{3}{2} = \frac{7}{8} + \frac{{12}}{8} = \frac{{19}}{8} = \frac{{38}}{{16}}\]

\[\frac{5}{4} + \frac{9}{{16}} = \frac{{20}}{{16}} + \frac{9}{{16}} = \frac{{29}}{{16}}\]

So sánh: \[\frac{{38}}{{16}} > \frac{{29}}{{16}}\]

Vậy: \[\frac{7}{8} + \frac{3}{2} > \,\,\frac{5}{4} + \frac{9}{{16}}\]

h)

\[\frac{5}{2} + \frac{7}{4} = \frac{{10}}{4} + \frac{7}{4} = \frac{{17}}{4} = \frac{{34}}{8}\]

\[\frac{3}{2} + \frac{5}{8} = \frac{{12}}{8} + \frac{5}{8} = \frac{{17}}{8}\]

So sánh: \[\frac{{34}}{8} > \frac{{17}}{8}\]

Vậy: \[\frac{5}{2} + \frac{7}{4}\,\, > \,\,\frac{3}{2} + \frac{5}{8}\]