x = 1313/1010 - 1414/2828

x = 4/5

x = 1414/2828 - 1313/1010

x = -4/5 

4/5

G = \(\left(\dfrac{1313}{1414}+\dfrac{10}{160}\right)-\left(\dfrac{130}{140}-\dfrac{1515}{1616}\right)\)

= \(\left(\dfrac{13}{14}+\dfrac{1}{16}\right)-\left(\dfrac{13}{14}-\dfrac{15}{16}\right)\)

= \(\dfrac{13}{14}+\dfrac{1}{16}-\dfrac{13}{14}+\dfrac{15}{16}\)

= \(\dfrac{1}{16}+\dfrac{15}{16}=1\)

Bài làm

\(\frac{1313}{1010}+x=\frac{1414}{2828}\)

\(\Rightarrow\frac{13}{10}+x=\frac{14}{28}\)

\(x=\frac{14}{28}-\frac{13}{10}\)

\(x=\frac{1}{2}-\frac{13}{10}\)

\(x=\frac{10}{20}-\frac{26}{20}\)

\(x=-\frac{16}{20}\)

\(x=-\frac{4}{5}\)

Vậy \(x=-\frac{4}{5}\)

\(\frac{2323+1313+1414+1515+1616}{4141+2222+2323+2424+2525}\)

=\(\frac{8181}{13635}\)

18180,8               

a )   − 1212 − 2424 = ( − 1212 ) : ( − 1212 ) ( − 2424 ) : ( − 1212 ) = 1 2

b )   120120 − 240240 = 120120 : ( − 120120 ) − 240240 : ( − 120120 ) = − 1 2

c)  1313 − 1414 = 1313 : ( − 101 ) − 1414 : ( − 101 ) = − 13 14

\(\dfrac{121212}{131313}=\dfrac{121212:10101}{131313:10101}=\dfrac{12}{13}=1-\dfrac{1}{13}\)

\(\dfrac{1313}{1414}=\dfrac{1313:101}{1414:101}=\dfrac{13}{14}=1-\dfrac{1}{14}\)

Vì \(\dfrac{1}{13}>\dfrac{1}{14}\) nên \(\dfrac{12}{13}< \dfrac{13}{14}\) hay \(\dfrac{1212}{1313}< \dfrac{1313}{1414}\)

b) \(\dfrac{1717}{2525}=\dfrac{1717:101}{2525:101}=\dfrac{17}{25}=\dfrac{51}{75}\)

\(\dfrac{515151}{727272}=\dfrac{515151:10101}{727272:10101}=\dfrac{51}{72}\)

Vì \(\dfrac{51}{75}< \dfrac{51}{72}\) nên \(\dfrac{17}{25}< \dfrac{51}{72}\) hay \(\dfrac{1717}{2525}< \dfrac{515151}{727272}\)

a) \(\dfrac{1212}{1313}=\dfrac{101x12}{101x13}=\dfrac{12}{13}< \dfrac{12+1}{13+1}=\dfrac{13}{14}\)

\(\dfrac{1313}{1414}=\dfrac{101x13}{101x14}=\dfrac{13}{14}\)

Vậy \(\dfrac{1212}{1313}< \dfrac{1313}{1414}\)

Làm tương tự câu b

a) 1212/1313 = 12/13 = 1 - 1/13

1313/1414 = 13/14 = 1 - 1/14

Do 13 < 14 nên 1/13 > 1/14

⇒ 1 - 1/13 < 1 - 1/14

Vậy 1212/1313 < 1313/1414

b) 1717/2525 = 17/25

515151/727272 = 51/72 = 17/24

Do 25 > 24 nên 17/25 < 17/24

Vậy 1717/2525 < 515151/727272

\(\frac{1010+1111+1212+1313+1414+1515}{2020+2121+2222+2323+2424+2525}=\frac{10\times101+11\times101+12\times101+13\times101+14\times101+15\times101}{20\times101+21\times101+22\times101+23\times101+24\times101+25\times101}=\frac{101\times\left(10+11+12+13+14+15\right)}{101\times\left(20+21+22+23+24+25\right)}\)

\(=\frac{10+11+12+13+14+15}{20+21+22+23+24+25}=\frac{75}{135}=\frac{5}{9}\)

1010+1111+1212+1313+1414+1515= 7575

2020+2121+2222+2323+2424+2525= 13635

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A)1212/1313<1313/1414.B)1717/2525<515151/727272.23/28,7/9,5/7,11/18