456 x 128 / 451 x 128 =58368/57728

123 x 451 / 128 x 451 = 55473/57728

so sánh : 58368/57728 ...>....  55473/ 57728 

vậy suy ra : 456/451 ....>.... 123/128 

tk mk nha mk nhanh nhất

\(\frac{456}{451}\) >    \(\frac{123}{128}\)tích cho mik nhé

Ta có:

\(\frac{124124}{125125}=\frac{124}{125}\)

Ta so sánh 2 phân số \(\frac{123}{124}và\frac{124}{125}\)

xét chữ số tận cùng khi quy đồng 2 phân số

123x125=.....5

124x124=......6

=> 123x125 < 124x124 

Vậy \(\frac{123}{124}< \frac{124124}{125125}\)

Ai thấy đúng thì nhấn vào chữ " đúng" cho mik nha thạnk you các bạn nhiều

Ta có:

\(\frac{124124}{125125}=\frac{124}{125}\)

Ta so sánh hai phân số \(\frac{123}{124}\)và \(\frac{124}{125}\)

\(1-\frac{123}{124}=\frac{1}{124}\)

\(1-\frac{124}{125}=\frac{1}{125}\)

Vì \(\frac{1}{124}>\frac{1}{125}\)nên suy ra \(\frac{123}{124}< \frac{124}{125}\)

1)

a) \(x+\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\frac{1}{32}+\frac{1}{64}+\frac{1}{128}=5\)

\(x+\frac{64}{128}+\frac{32}{128}+\frac{16}{128}+\frac{8}{128}+\frac{4}{128}+\frac{2}{128}+\frac{1}{128}=5\)

\(x+\frac{127}{128}=5\)

\(x=5-\frac{127}{128}=\frac{513}{128}\)

b) \(x+\frac{1}{3}+\frac{1}{9}+\frac{1}{27}+\frac{1}{81}+\frac{1}{243}+\frac{1}{729}+\frac{1}{2187}=3\)

\(x+\frac{729}{2187}+\frac{243}{2187}+\frac{81}{2187}+\frac{27}{2187}+\frac{9}{2187}+\frac{3}{2187}+\frac{1}{2187}=3\)

\(x+\frac{2186}{2187}=3\)

\(x=3-\frac{2186}{2187}=\frac{4375}{2187}\)

2)

a) \(\frac{1}{1\cdot2}+\frac{1}{2\cdot3}+\frac{1}{3\cdot4}+\frac{1}{4\cdot5}+\frac{1}{5\cdot6}\)

\(=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}\)

\(=1-\frac{1}{6}=\frac{5}{6}\)

b) \(5\frac{1}{2}+3\frac{5}{6}+\frac{2}{3}\)

\(=\left(5+3\right)+\left(\frac{1}{2}+\frac{2}{3}+\frac{5}{6}\right)\)

\(=8+\left(\frac{3}{6}+\frac{4}{6}+\frac{5}{6}\right)\)

\(=8+2=10\)

c) \(7\frac{7}{8}+1\frac{4}{6}+3\frac{3}{5}\)

\(=\left(7+1+3\right)+\left(\frac{7}{8}+\frac{2}{3}+\frac{3}{5}\right)\)

\(=11+\left(\frac{105}{120}+\frac{80}{120}+\frac{72}{120}\right)\)

\(=11+\frac{257}{120}=\frac{1577}{120}\)

3) Gọi số đó là x. Theo đề ta có :

\(\frac{16-x}{21+x}=\frac{5}{7}\)

\(7\left(16-x\right)=5\left(21+x\right)\)

\(112-7x=105+5x\)

\(112-105=7x-5x\)

\(7=2x\)

\(x=\frac{7}{2}=3,5\) ( vô lí )

Vậy không có số tự nhiên để thõa mãn điều kiện trên.

 a) \(\frac{{ - 3}}{8} = \frac{{ - 3.3}}{{8.3}} = \frac{{ - 9}}{{24}}\)

Vì -9 < -5 nên \(\frac{{ - 9}}{{24}} < \frac{{ - 5}}{{24}}\)

Vậy \(\frac{{ - 3}}{8} < \frac{{ - 5}}{{24}}\).

b) Cách 1: \(\frac{{ - 2}}{{ - 5}} = \frac{2}{5}; \frac{3}{{ - 5}} = \frac{-3}{{5}}\)

Vì 2 > -3 nên \(\frac{2}{5} > \frac{-3}{{5}}\)

Vậy \(\frac{{ - 2}}{{ - 5}} > \frac{3}{{ - 5}}\).

Cách 2: \(\frac{{ - 2}}{{ - 5}} = \frac{2}{5} > 0\) mà \(\frac{3}{{ - 5}} < 0\)

\(\Rightarrow\) \(\frac{{ - 2}}{{ - 5}} > \frac{3}{{ - 5}}\).

c) \(\frac{{ - 3}}{{ - 10}} = \frac{3}{{10}} = \frac{{3.2}}{{10.2}} = \frac{6}{{20}}\)

\(\frac{{ - 7}}{{ - 20}} = \frac{7}{{20}}\)

Vì 6 < 7 nên \(\frac{6}{{20}} < \frac{7}{{20}}\) nên \(\frac{{ - 3}}{{ - 10}} < \frac{{ - 7}}{{ - 20}}\).

d) \(\frac{{ - 5}}{4} = \frac{{ - 5.5}}{{4.5}} = \frac{{ - 25}}{{20}}; \frac{{ 23}}{{-20}}=\frac{{-23}}{{20}} \)

Vì -25 < -23 nên \( \frac{{ - 25}}{{20}} < \frac{{-23}}{{20}} \)

Vậy \(\frac{{ - 5}}{4} < \frac{{23}}{{ - 20}}\).

-2/3 và 4/-5

 Ta có:-2/3 = -10/15

           4/-5 = -12/15

Vì -10/15 > -12/15

Vậy -2/3 > 4/-5

\(\frac{-2}{3}<\frac{4}{-5}\)

Ta có: \(\frac{-2}{3}=\frac{-10}{15}\)

          \(\frac{4}{-5}=\frac{-12}{15}\)

Vì \(\frac{-10}{15}>\frac{-12}{15}nên\frac{-2}{3}>\frac{4}{-5}\)

Vậy \(\frac{-2}{3}>\frac{4}{-5}\)

a) $\frac{2}{3} = \frac{{2 \times 6}}{{3 \times 6}} = \frac{{12}}{{18}}$

Ta có $\frac{{12}}{{18}} > \frac{{11}}{{18}}$ nên $\frac{2}{3} > \frac{{11}}{{18}}$

b) $\frac{{36}}{{63}} = \frac{{36:9}}{{63:9}} = \frac{4}{7}$

Ta có $\frac{4}{7} < \frac{5}{7}$ nên $\frac{{36}}{{63}}$ < $\frac{5}{7}$

c)

$\frac{{55}}{{110}} = \frac{{55:55}}{{110:55}} = \frac{1}{2}$ ;  $\frac{4}{8} = \frac{1}{2}$

Vậy $\frac{{55}}{{110}}$ = $\frac{4}{8}$

a) Ta có: \( - 2 = \frac{{ - 2}}{1} = \frac{{ - 40}}{{20}}\)

\(\frac{{ - 11}}{5} = \frac{{ - 44}}{{20}} < \frac{{ - 40}}{{20}}\) nên \(\frac{{ - 11}}{5} < -2\).

\(\frac{{ - 7}}{4} = \frac{{ - 7.5}}{{4.5}} = \frac{{ - 35}}{{20}} > \frac{{ - 40}}{{20}}\) nên \(\frac{{ - 7}}{4} > -2\)

Vậy \(\frac{{ - 11}}{5} < \frac{{ - 7}}{4}\).

b) Ta có: \(\frac{{2020}}{{ - 2021}} = \frac{{ - 2020}}{{2021}} > \frac{{ - 2022}}{{2021}}\)

Vậy \(\frac{{2020}}{{ - 2021}} > \frac{{ - 2022}}{{2021}}\)