tính tổng
\(A=\frac{4}{7\times31}+\frac{6}{7\times41}+\frac{9}{10\times41}+\frac{7}{10\times57}\)
\(B=\frac{7}{19\times31}+\frac{5}{19\times43}+\frac{3}{23\times43}+\frac{7}{10\times57}\)
Cho
A= \(\frac{4}{31\times7}+\frac{6}{7\times41}+\frac{9}{10\times41}+\frac{7}{10\times57}\)
B= \(\frac{7}{19\times31}+\frac{5}{19\times43}+\frac{3}{13\times43}+\frac{11}{23\times57}\)
Tính \(\frac{A}{B}\)
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Tính \(\frac{39}{7\times16}+\frac{65}{16\times31}+\frac{52}{31\times43}+\frac{26}{43\times49}\)
Tính:
\(\frac{\left(\frac{4}{7\cdot31}+\frac{6}{7\cdot41}+\frac{9}{10\cdot41}+\frac{10}{10\cdot57}\right)}{\left(\frac{7}{19\cdot31}+\frac{5}{19\cdot43}+\frac{3}{23\cdot43}+\frac{11}{23\cdot57}\right)}\)
\(\frac{1}{40\times41}+\frac{1}{41\times42}+\frac{1}{42\times43}+\frac{1}{43\times44}=\)
\(\frac{1}{40\times41}+\frac{1}{41\times42}+\frac{1}{42\times43}+\frac{1}{43\times44}\)
\(=\frac{1}{40}-\frac{1}{41}+\frac{1}{41}-\frac{1}{42}+\frac{1}{42}-\frac{1}{43}+\frac{1}{43}-\frac{1}{44}\)
\(=\frac{1}{40}-\frac{1}{44}=\frac{1}{440}\)
Tính tỷ số \(\frac{A}{B}\)
\(A=\frac{4}{9\times31}+\frac{5}{31\times12}+\frac{9}{36\times15}+\frac{13}{15\times58};B=\frac{5}{27\times8}+\frac{7}{8\times39}+\frac{9}{39\times12}+\frac{10}{12\times58}\)
1.tính giá trị biểu thức sau một cách hợp lí nếu có
a)\(\frac{1}{3}.\frac{4}{5}+\frac{1}{3}.\frac{6}{5}-\frac{5}{3}\)
b)\(\frac{4}{19}.\frac{-3}{7}+\frac{-3}{7}.\frac{15}{19}+\frac{5}{7}\)
c)\(\frac{6}{7}.\frac{10}{9}+\frac{1}{7}.\frac{10}{9}-\frac{8}{9}\)
a. \(\frac{1}{3}.\frac{4}{5}+\frac{1}{3}.\frac{6}{5}-\)
\(=\frac{1}{3}(\frac{4}{5}+\frac{6}{5})-\frac{5}{3}\)
\(=\frac{1}{3}.2-\frac{5}{3}\)
\(=\frac{2}{3}-\frac{5}{3}\)
\(=-\frac{1}{1}\)
c. \(\frac{6}{7}.\frac{10}{9}+\frac{1}{7}.\frac{10}{9}-\frac{8}{9}\)
\(=\frac{10}{9}\left(\frac{6}{7}+\frac{1}{7}\right)-\frac{8}{9}\)
\(=\frac{10}{9}.1-\frac{9}{8}\)
\(=\frac{10}{9}-\frac{9}{8}\)
\(=-\frac{1}{72}\)
\(b\).\(\frac{4}{19}.\frac{-3}{7}+\frac{-3}{7}.\frac{15}{19}+\frac{5}{7}\)
\(=\frac{-3}{7}\left(\frac{4}{19}+\frac{15}{19}\right)+\frac{5}{7}\)
\(=\frac{-3}{7}+\frac{5}{7}\)
\(=\frac{2}{7}\)
Tính tỉ số \(\frac{A}{B}\) biết : A = \(\frac{4}{7\cdot31}\)+\(\frac{6}{7\cdot41}\)+\(\frac{9}{10\cdot41}\)+\(\frac{7}{10\cdot57}\)và B = \(\frac{7}{19\cdot31}\)+ \(\frac{5}{19\cdot43}\) + \(\frac{3}{23\cdot43}\)+ \(\frac{11}{23\cdot57}\)
A=4/1.31+6/7.41+9/9.41+ 7/10.57
=20/35.31+30/35.41+45/45.41+35/50.57
=5(4/35.31+6/35.41+9/45.41+7/50.57)
=5(1/31-1/35+1/35-1/41+1/41-1/45+1/45-1/50+1/50-1/57)
=5(1/31-1/57)
B thì làm tương tự nhưng nhân với 2=> B=2(1/31-1/57)
=> A/B=5/2
Tính:
a)\(\frac{5\cdot18-10\cdot27+15\cdot36}{10\cdot36-20\cdot54+30\cdot27}\)
b)\(\frac{\frac{-6}{7}+\frac{6}{19}-\frac{6}{31}}{\frac{9}{7}-\frac{9}{19}+\frac{9}{31}}\)
\(\frac{5.18-10.27+15.36}{10.36-20.54+30.72\left(not27\right)}=\frac{5.18-10.27+15.36}{4\left(5.18-10.27+15.36\right)}=\frac{1}{4}\)
\(\frac{\frac{-6}{7}+\frac{6}{19}-\frac{6}{31}}{\frac{9}{7}-\frac{9}{19}+\frac{9}{31}}=\frac{-6\left(\frac{1}{7}-\frac{1}{19}+\frac{1}{31}\right)}{9\left(\frac{1}{7}-\frac{1}{19}+\frac{1}{31}\right)}=\frac{-6}{9}=\frac{-2}{3}\)
Tính giá trị biểu thức:
3) C= \(\frac{5}{18}+\frac{8}{19}-\frac{7}{21}+\left(\frac{-10}{36}+\frac{11}{19}+\frac{1}{3}\right)-\frac{5}{8}\)\(\frac{5}{8}\)
4) D= \(\frac{1}{9}-\left|\frac{-5}{23}\right|-\left(\frac{-5}{23}+\frac{1}{9}+\frac{25}{7}\right)+\frac{50}{4}-\frac{7}{30}\)
3) C thiếu đề
4) \(D=\frac{1}{9}-\left|\frac{-5}{23}\right|-\left(\frac{-5}{23}+\frac{1}{9}+\frac{25}{7}\right)+\frac{50}{4}-\frac{7}{30}\)
\(D=\frac{1}{9}-\frac{5}{23}+\frac{5}{23}-\frac{1}{9}-\frac{25}{7}+\frac{50}{4}-\frac{7}{30}\)
\(D=\frac{1}{9}-\frac{1}{9}-\frac{5}{23}+\frac{5}{23}+\frac{-25}{7}+\frac{50}{4}-\frac{7}{30}\)
\(D=0+0+\frac{125}{14}-\frac{7}{30}\)
\(D=\frac{913}{105}\)
\(C=\frac{5}{18}+\frac{8}{19}-\frac{7}{21}+\left(\frac{-10}{36}+\frac{11}{19}+\frac{1}{3}\right)-\frac{5}{8}\)
\(C=\frac{5}{18}+\frac{8}{19}-\frac{1}{3}+\frac{-5}{18}+\frac{11}{19}+\frac{1}{3}-\frac{5}{8}\)
\(C=\left(\frac{5}{18}+\frac{-5}{18}\right)+\left(\frac{8}{19}+\frac{11}{19}\right)+\left(\frac{-1}{3}+\frac{1}{3}\right)-\frac{5}{8}\)
\(C=0+1+0-\frac{5}{8}\)
\(C=\frac{3}{8}\)