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Ta có:
\(\frac{3}{7}+\frac{4}{6}+\frac{9}{7}+\frac{8}{6}\)
\(=\left(\frac{3}{7}+\frac{9}{7}\right)+\left(\frac{4}{6}+\frac{8}{6}\right)\)
\(=\frac{3+9}{7}+\frac{4+8}{6}\)
\(=\frac{12}{7}+\frac{12}{6}\)
\(=\frac{72}{42}+\frac{84}{42}\)
\(=\frac{72+84}{42}\)
\(=\frac{156}{42}\)
\(=\frac{26}{7}\)
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\(\frac{1}{10}+\frac{2}{20}+\frac{3}{30}+\frac{4}{40}+\frac{5}{50}+\frac{6}{60}+\frac{7}{70}+\frac{8}{80}+\frac{9}{90}\)
\(=\frac{1}{10}+\frac{1}{10}+\frac{1}{10}+\frac{1}{10}+\frac{1}{10}+\frac{1}{10}+\frac{1}{10}+\frac{1}{10}+\frac{1}{10}\)
\(=\frac{9}{10}\)
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b, 3/5 + 4/7 + 2/8 + 10/25 + 9/21 + 28/16
= 3/5 + 4/7 + 2/8 + 2/5 + 3/7 + 14/8
= (3/5 + 2/5) + ( 4/7 + 3/7) + ( 2/8 + 14/8)
= 1 + 1 + 7/4
= 2 + 7/4 = 15/4
c , 8/7 + 7/6 + 5/8 + 10/12 + 24/28 + 6/16
= c , 8/7 + 7/6 + 5/8 + 5/6 + 6/7 + 1/2
= (8/7 + 6/7) + (7/6 + 5/6) + 5/8 + 1/2
= 14/7 + 12/6 + 5/8 + 1/2
= 2 + 2 + 5/8 + 1/2
= 4 + 9/8 = 41/8
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\(\dfrac{4}{5}\times\left(\dfrac{5}{4}-\dfrac{5}{7}\right)\)
\(=\dfrac{4}{5}\times\left(\dfrac{35}{28}-\dfrac{20}{28}\right)\)
\(=\dfrac{4}{5}\times\dfrac{15}{28}\)
\(=\dfrac{3}{7}\)
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\(\dfrac{5}{8}\times\dfrac{9}{7}+\dfrac{5}{8}\times\dfrac{5}{7}\)
\(=\dfrac{5}{8}\times\left(\dfrac{9}{7}+\dfrac{5}{7}\right)\)
\(=\dfrac{5}{8}\times2=\dfrac{10}{8}=\dfrac{5}{4}\)
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\(\frac{4}{9}+\frac{8}{9}+\frac{12}{9}+...+\frac{56}{9}\)
Tổng trên là tổng cách số hạng cách đều, số hạng sau hơn số hạng trước \(\frac{4}{9}\).
Dãy có số số hạng là: \(\left(\frac{56}{9}-\frac{4}{9}\right)\div\frac{4}{9}+1=14\)(số hạng)
GIá trị của tổng trên là: \(\left(\frac{56}{9}+\frac{4}{9}\right)\times14\div2=\frac{140}{3}\)
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\(\frac{3.6.2.7}{12.7.9.2}=\frac{3.6.2.7}{6.2.7.3.3.2}=\frac{1}{6}\)
\(\frac{3.4.30.56}{9.8.7.8.20}=\frac{3.4.5.6.7.8}{4.5.7.8.8.9}=\frac{1}{4}\)
a, \(\frac{3.6.2.7}{12.7.9.2}=\frac{3.6.2.7}{6.2.7.3.3.2}=\frac{1}{6}\)
b, \(\frac{3.4.30.56}{9.8.7.8.20}=\frac{3.4.3.10.7.8}{3.3.8.7.8.2.10}=\frac{1}{4}\)
Học tốt !