Tính nhanh biếu thức sau: S = \(\frac{58}{89}\).\(\frac{51}{76}\)-\(\frac{28}{98}\).\(\frac{51}{76}\)+\(\frac{51}{89}\).\(\frac{23}{38}\)
Giúp mình với ạ :D
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a) \(\frac{9}{22}.\frac{33}{18}=\frac{9.33}{22.18}=\frac{297}{396}=\frac{3}{4}\)
b) \(\frac{12}{35}:\frac{36}{25}=\frac{12}{35}.\frac{25}{36}=\frac{12.25}{35.36}=\frac{300}{1260}=\frac{5}{21}\)
c) \(\frac{19}{17}:\frac{76}{51}=\frac{19}{17}.\frac{51}{76}=\frac{19.51}{17.76}=\frac{969}{1292}=\frac{3}{4}\)
\(A=-\frac{\frac{-6}{5}+\frac{6}{19}-\frac{6}{23}}{\frac{9}{5}-\frac{9}{19}+\frac{9}{23}}\)
\(=\frac{-6.\left(\frac{1}{5}-\frac{1}{19}+\frac{1}{23}\right)}{9.\left(\frac{1}{5}-\frac{1}{19}+\frac{1}{23}\right)}\)
\(=-\frac{6}{9}=-\frac{2}{3}\)
a) 31/23 - ( 7/32 + 8/22)
= 31/23 - 7/32 + 8/23
= ( 31/23 + 8/23 ) - 7/32
= 32/22 - 7/32
= 39/32
Ccá ý khác làm tương tự
a) \(\frac{31}{23}-\left(\frac{7}{32}+\frac{8}{23}\right)=\frac{31}{23}-\frac{7}{32}-\frac{8}{23}=1-\frac{7}{32}=\frac{25}{32}\)
b) \(\left(\frac{1}{3}+\frac{12}{67}+\frac{13}{41}\right)-\left(\frac{79}{67}-\frac{28}{41}\right)\)
\(=\frac{1}{3}+\frac{12}{67}+\frac{13}{41}-\frac{79}{67}+\frac{28}{41}\)
\(=\frac{1}{3}-\left(\frac{79}{67}-\frac{12}{67}\right)+\left(\frac{13}{41}+\frac{28}{41}\right)\)
\(=\frac{1}{3}-1+1=\frac{1}{3}\)
d) \(\frac{1}{7}.\frac{1}{3}+\frac{1}{7}.\frac{-1}{3}+\frac{17}{19}=\frac{1}{7}.\left(\frac{1}{3}-\frac{1}{3}\right)+\frac{17}{19}=\frac{17}{19}\)
e) \(\frac{3}{5}.\frac{7}{9}+\frac{7}{5}.\frac{2}{9}=\frac{7}{5}.\left(\frac{3}{9}+\frac{2}{9}\right)=\frac{7}{5}.\frac{5}{9}=\frac{7}{9}\)
=1/5+2/5+51/85+4/5
=7/5+51/85
=119/85+51/85
=170/85=2
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Ta có:
\(\frac{1}{51}>\frac{1}{100}\)
\(\frac{1}{52}>\frac{1}{100}\)
...
\(\frac{1}{99}>\frac{1}{100}\)
\(\frac{1}{100}=\frac{1}{100}\)
=> S = \(\frac{1}{51}+\frac{1}{52}+...+\frac{1}{99}+\frac{1}{100}>\frac{1}{100}+\frac{1}{100}+...+\frac{1}{100}+\frac{1}{100}\)
Mà số số hạng của S là: (100 - 51) : 1 + 1 = 50 (số)
=> S \(>\frac{1}{100}.50\)
=> S \(>\frac{1}{2}\)
Vậy S > 1/2.