Mình nghĩ ra câu a rồi!

Ta có: 58/63 > 54/63=6/7

Mà 6/7=36/42 > 36/55

Vậy 58/63 > 36/55.

Mình làm câu b trước nha!

31/41 = 310/410

Ta có: 310/410 = 1-100/410 ; 313/413 = 1-100/413

Ta thấy: 100/410 > 100/413 => 1-100/410 < 1-100/413

Vậy 31/41 < 313/413.

\(\frac{58}{89}\)&   \(\frac{36}{53}\)

Ta có : 

  \(\frac{58}{89}\)=  \(\frac{58.53}{89.53}\)=\(\frac{3074}{4717}\)         ;              \(\frac{36}{53}\)=\(\frac{36.89}{53.89}\)=\(\frac{3204}{4717}\)

Vậy \(\frac{58}{89}\)<  \(\frac{36}{53}\)

\(\frac{58}{63}\)&   \(\frac{36}{55}\)

Ta có:

  \(\frac{58}{63}\)=\(\frac{58.55}{63.55}\)=\(\frac{3190}{3465}\)                  ;                   \(\frac{36}{55}\)=\(\frac{36.63}{55.63}\)=\(\frac{2268}{3465}\)

Vậy \(\frac{58}{63}\)>    \(\frac{36}{55}\)

58/89<36/89

58/63>36/55

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) \(\frac{1}{3}+\frac{1}{15}+\frac{1}{35}+\frac{1}{63}+\frac{1}{99}+\frac{1}{143}+\frac{1}{195}\)

\(=\frac{1}{1.3}+\frac{1}{3.5}+\frac{1}{5.7}+\frac{1}{7.9}+\frac{1}{9.11}+\frac{1}{11.13}+\frac{1}{13.15}\)

\(=\frac{1}{2}.\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{13}-\frac{1}{15}\right)\)

\(=\frac{1}{2}.\left(1-\frac{1}{15}\right)\)

\(=\frac{1}{2}.\frac{14}{15}\)

\(=\frac{14}{30}=\frac{7}{15}\)

a)

\(=\frac{1}{3.5}+\frac{1}{5.7}+\frac{1}{7.9}+\frac{1}{9.11}+\frac{1}{11.13}+\frac{1}{13.15}\)

\(=2\left(\frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}+\frac{2}{7.9}+\frac{2}{9.11}+\frac{2}{11.13}+\frac{2}{13.15}\right)\)

\(=2\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+\frac{1}{9}-\frac{1}{11}+\frac{1}{11}-\frac{1}{13}+\frac{1}{13}-\frac{1}{15}\right)\)

\(=2\left(1-\frac{1}{15}\right)\)

\(=2.\frac{14}{15}\)

\(=\frac{28}{15}\)

b)

\(=1+\frac{2}{6}+\frac{2}{12}+\frac{2}{20}+\frac{2}{30}+\frac{2}{42}+\frac{2}{56}+\frac{2}{72}+\frac{2}{90}+\frac{2}{110}+\frac{2}{132}\)

\(=1+\frac{2}{2.3}+\frac{2}{3.4}+\frac{2}{4.5}+\frac{2}{5.6}+\frac{2}{6.7}+\frac{2}{7.8}+\frac{2}{8.9}+\frac{2}{9.10}+\frac{2}{10.11}+\frac{2}{11.12}\)

                                                                                         \(...\)

câu a mình nhầm phải là ½.(…)

1. \(-2+\frac{-5}{8}=\frac{-16}{8}+\frac{-5}{8}=\frac{-21}{8}\)

2. \(\frac{55}{121}+\frac{36}{-63}=\frac{5}{11}+\frac{-4}{7}=\frac{35}{77}+\frac{-44}{77}=\frac{-9}{77}\)

-2+-5/8

=-2/1+-5/8            MSC:8

=-16/8+-5/8

=-21/8

CHÚC BẠN HC THẬT TỐT!

a: 58/63=3190/3465

36/55=2268/3465

=>58/63>36/55

b: 27/53=1998/3922

36/74=1908/3922

=>27/53>36/74

\(\frac{58}{89}\)\(< \)\(\frac{36}{53}\)

58/89<36/53

Ta có : \(\frac{58}{89}< \frac{58}{87}=\frac{2}{3}=\frac{36}{54}< \frac{36}{53}\)

Nên : \(\Rightarrow\frac{58}{59}< \frac{36}{53}\)

Chúc bạn học tốt -_<