Không quy đồng, hãy so sánh các phân số dưới đây: a) 10/19 và 1 010/1 919

a)

Ta có: \[\frac{{1\,\,010}}{{1\,\,919}} = \frac{{10 \times 100 + 10}}{{19 \times 100 + 19}}\]

\[ = \frac{{10 \times (100 + 1)}}{{19 \times (100 + 1)}} = \frac{{10 \times 101}}{{19 \times 101}} = \frac{{10}}{{19}}\]

Vậy \(\frac{{10}}{{19}} = \frac{{1\,\,010}}{{1\,\,919}}\)

b)

Ta có: \(\frac{{2\,\,023}}{{2\,\,024}} + \frac{1}{{2\,\,024}} = 1\)

\(\frac{{2\,\,024}}{{2\,\,025}} + \frac{1}{{2\,\,025}} = 1\)

Mà: \(\frac{1}{{2\,\,024}} > \frac{1}{{2\,\,025}}\)

Nên \(\frac{{2\,\,023}}{{2\,\,024}}\) < \(\frac{{2\,\,024}}{{2\,\,025}}\)