Question

So sánh:

a) \(\frac{{123}}{7}\) và 17,75

b) \( - \frac{{65}}{9}\) và -7,125.

Answer 1

a) Ta có:

\(\begin{array}{l}\frac{{123}}{7} = \frac{{123.4}}{{7.4}} = \frac{{492}}{{28}}\\17,75 = \frac{{1775}}{{100}} = \frac{{71}}{4} = \frac{{71.7}}{{4.7}} = \frac{{497}}{{28}}\end{array}\)

Vì 492 < 497 nên \(\frac{{492}}{{28}} < \frac{{497}}{{28}}\) hay \(\frac{{123}}{7} < 17,75\)

b) Ta có:

\(\begin{array}{l} - \frac{{65}}{9} = \frac{{( - 65).8}}{{9.8}} = \frac{{ - 520}}{{72}}\\ - 7,125 = \frac{{ - 7125}}{{1000}} = \frac{{ - 57}}{8} = \frac{{ - 57.9}}{{8.9}} = \frac{{ - 513}}{{72}}\end{array}\)

Vì 520 > 513 nên -520 < -513. Do đó, \(\frac{{ - 520}}{{72}} < \frac{{ - 513}}{{72}}\) hay \( - \frac{{65}}{9}\) < -7,125