99/72 - 15/40 -1212/1616
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\(\frac{99}{72}-\frac{15}{40}-\frac{1212}{1616}\)= \(\frac{11}{8}-\frac{3}{8}-\frac{6}{8}\)
=\(\frac{11-3-6}{8}\)
=\(\frac{2}{8}=\frac{1}{4}\)
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a: 78/42-4/7=13/7-4/7=9/7
100/110-56/88=10/11-7/11=3/11
75/35-11/7+21/49=15/7-11/7+3/7=7/7=1
99/72-15/40-1212/1616=11/8-3/8-3/4=1-3/4=1/4
![](https://rs.olm.vn/images/avt/0.png?1311)
\(1,A=\dfrac{2}{3\cdot7}+\dfrac{2}{7\cdot11}+\dfrac{2}{11\cdot15}+...+\dfrac{2}{99\cdot103}\\ 2A=\dfrac{4}{3\cdot7}+\dfrac{4}{7\cdot11}+\dfrac{4}{11\cdot15}+...+\dfrac{4}{99\cdot103}\\ 2A=\dfrac{1}{3}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{11}+...+\dfrac{1}{99}-\dfrac{1}{103}\\ 2A=\dfrac{1}{3}-\dfrac{1}{103}=\dfrac{100}{309}\\ A=\dfrac{100}{309}\cdot\dfrac{1}{2}=\dfrac{50}{309}\)
\(2,A=\dfrac{7}{2}+\dfrac{7}{6}+\dfrac{7}{12}+\dfrac{7}{20}+\dfrac{7}{30}+\dfrac{7}{42}+\dfrac{7}{56}+\dfrac{7}{72}+\dfrac{7}{90}\\ A=7\left(\dfrac{1}{1\cdot2}+\dfrac{1}{2\cdot3}+\dfrac{1}{3\cdot4}+...+\dfrac{1}{9\cdot10}\right)\\ A=7\left(1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+...+\dfrac{1}{9}-\dfrac{1}{10}\right)\\ A=7\left(1-\dfrac{1}{10}\right)=7\cdot\dfrac{9}{10}=\dfrac{63}{10}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(1-\dfrac{1212}{1616}\)
\(=1-\dfrac{3}{4}\)
\(=\dfrac{4}{4}-\dfrac{3}{4}\)
\(=\dfrac{1}{4}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(\dfrac{360}{360}-\dfrac{1212}{1616}=1-\dfrac{3}{4}=\dfrac{4}{4}-\dfrac{3}{4}=\dfrac{1}{4}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(\frac{2323+1313+1414+1515+1616}{4141+2222+2323+2424+2525}\)
=\(\frac{8181}{13635}\)
\(=\dfrac{11}{8}-\dfrac{3}{8}-\dfrac{3}{4}=1-\dfrac{3}{4}=\dfrac{1}{4}\)
=11/8−3/8−3/4=1−3/4=1/4