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\(\frac{1}{3}+\frac{1}{15}+\frac{1}{35}+\frac{1}{63}+\frac{1}{99}+\frac{1}{143}+\frac{1}{195}\)
\(=\frac{1}{1.3}+\frac{1}{3.5}+\frac{1}{5.7}+\frac{1}{7.9}+\frac{1}{9.11}+\frac{1}{11.13}+\frac{1}{13.15}\)
\(=\frac{1}{2}.\left(\frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}+\frac{2}{7.9}+\frac{2}{9.11}+\frac{2}{11.13}+\frac{2}{13.15}\right)\)
\(=\frac{1}{2}.\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+\frac{1}{9}-\frac{1}{11}+\frac{1}{11}-\frac{1}{13}+\frac{1}{13}-\frac{1}{15}\right)\)
\(=\frac{1}{2}.\left(1-\frac{1}{15}\right)\)
\(=\frac{1}{2}.\frac{14}{15}\)
\(=\frac{7}{15}\)
a) \(\frac{1}{1.3}+\frac{1}{3.5}+\frac{1}{5.7}+\frac{1}{7.9}+\frac{1}{9.11}+\frac{1}{11.13}+\frac{1}{13.15}\)
\(=\frac{1}{2}\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+...+\frac{1}{11}-\frac{1}{13}+\frac{1}{13}-\frac{1}{15}\right)\)
\(=\frac{1}{2}\left(1-\frac{1}{15}\right)=\frac{1}{2}.\frac{14}{15}\)\(=\frac{7}{15}\)
b)\(\frac{1414+1515+...+1919}{2020+2121+...+2525}\)
\(\Rightarrow\frac{101\left(14+15+16+17+18+19\right)}{101\left(20+21+22+23+24+25\right)}\)
\(=\frac{14+15+16+17+18+19}{20+21+22+23+24+25}\)
\(=\frac{\left(19+14\right).6:2}{\left(25+20\right).6:2}=\frac{19+14}{25+20}=\frac{33}{45}=\frac{11}{15}\)
a)\(\frac{1}{95}>\frac{1}{96}\Rightarrow\frac{91}{95}>\frac{91}{96}\Rightarrow\frac{93}{95}>\frac{91}{95}>\frac{91}{96}\Rightarrow\frac{93}{95}>\frac{91}{96}\)
b)\(\frac{37}{40}=1-\frac{3}{40}\)\(\frac{43}{46}=1-\frac{3}{46}\)
\(\frac{1}{40}>\frac{1}{46}\Rightarrow\frac{-3}{40}< -\frac{3}{46}\Rightarrow1-\frac{3}{40}< 1-\frac{3}{46}\Rightarrow\frac{37}{40}< \frac{43}{46}\)
c)
\(\frac{27}{55}=\frac{54}{110}< \frac{55}{110}=\frac{1}{2}\)
\(\frac{12}{23}=\frac{24}{46}>\frac{23}{46}=\frac{1}{2}\)
Vậy \(\frac{27}{55}< \frac{1}{2}< \frac{12}{23}\Rightarrow\frac{27}{55}< \frac{12}{23}\)
\(\frac{1010+1111+1212+1313+1414+1515+1616+1717}{2020+2121+2222+2323+2424+2525+2626+2727}\)
\(=\frac{101.10+101.11+...+101.17}{101.20+101.21+...+101.27}\)
\(=\frac{101.\left(10+11+...+17\right)}{101.\left(20+21+...+27\right)}\)
\(=\frac{108}{188}\)
\(=\frac{27}{47}\)
\(2>\left(\frac{1}{6}+\frac{2}{15}+\frac{3}{40}+\frac{4}{96}\right)\cdot5.y>\frac{5}{6}\)
\(\Rightarrow2>\left(\frac{1}{6}+\frac{2}{15}+\frac{3}{40}+\frac{1}{24}\right):5.y>\frac{5}{6}\)
\(\Rightarrow2>\left(\frac{20}{120}+\frac{16}{120}+\frac{9}{120}+\frac{5}{120}\right):5.y>\frac{5}{6}\)
\(\Rightarrow2>\frac{5}{12}:5.y>\frac{5}{6}\)
\(\Rightarrow2>\frac{1}{12}.y>\frac{5}{6}\)
Đặt :\(\frac{1}{12}.y=2\Rightarrow y=2:\frac{1}{12}=24\)
\(\frac{1}{12}.y=\frac{5}{6}\Rightarrow y=\frac{5}{6}:\frac{1}{12}=10\)
\(\Rightarrow24>y>10\)
\(\Rightarrow y\in\left\{11;12;...;23\right\}\)
tỉ số phần trăm của hs vắng mặt và số hs cả lớp là
(1+3):40x100%=10%
đs........
2
a)MC:84
\(\frac{3}{4}=\frac{3x21}{4x21}=\frac{63}{84}\)
\(\frac{5}{7}=\frac{5x12}{7x12}=\frac{60}{84}\)
\(\frac{13}{17}=\frac{8x28}{3x28}=\frac{224}{84}\)
tự kl
b)MC:1768
\(\frac{5}{8}=\frac{5x221}{8x221}=\frac{1105}{1768}\)
\(\frac{8}{13}=\frac{8x136}{13x136}=\frac{1088}{1768}\)
\(\frac{13}{17}=\frac{13x104}{17x104}=\frac{1352}{1768}\)
3
\(\frac{64}{96}=\frac{2}{3},\frac{27}{225}=\frac{3}{25},\frac{57}{18}=\frac{19}{6},\frac{72}{376}=\frac{9}{47}\)
tự suy luận nha
a) 123/127 = 123123/127127
Ta có 123123/127127 = 123 x 1001/127 x 1001
<=> 123123/ 127127 = 123 /127
Vậy 123/127 = 123123 /127127
b) 13/15 = 1313/1515 = 131313/151515
- Ta có 1313/1515 = 13 x 101 / 15 x 101
<=> 1313/1515 = 13/15
- ta cũng có : 131313/151515 = 13 x 10101 / 15 x10101
<=> 131313/151515 = 13/15
Vậy 13/15 = 1313/1515 = 131313 /151515
Chúc bạn học tốt <3
123/127=123123/127127=123 x 1001/127 x 1001=123/127
13/15=1313/1515=13 x 101/15 x 101=13 x 10101/15 x 10101=13/15
ung ho nhe
\(\frac{23}{12}\)
\(\frac{314}{105}\)
\(\frac{59}{60}\)
\(\frac{199}{90}\)
\(\frac{1}{18}\)
\(\frac{13}{36}\)
\(\frac{4}{221}\)
\(\frac{4}{85}\)