Tính S: 7 + 7/3 + 7/6 + 7/10 + 7/15 + 7/21 + 7/28 + 7/36 + 7/45 + 7/55
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S=7(1+1/3+1/6+...+1/55)
=7(2/2+2/6+...+2/110)
=14(1/2+1/6+...+1/110)
=14(1-1/2+1/2-1/3+...+1/10-11)
=14*10/11=140/11
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A=4/3+7/6+11/10+16/15+22/21+29/28+37/36+46/45
A = ( 1 + 1/3 ) + ( 1 + 1/6 ) + ( 1 + 1/10 ) + ( 1 + 1/15 ) + ( 1 + 1/21 ) + ( 1 + 1/28 ) + ( 1 + 1/36 ) + ( 1 + 1/45 )
A = ( 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 ) + - ( 1/3 + 1/6 + 1/10 + 1/15 + 1/21 + 1/28 + 1/36 + 1/45 )
A = 8 + 4/5
A = 44/5
A = 4/3 + 7/6 + 11/10 + 16/15 + 22/21 + 29/28 + 37/36 + 46/45
A = ( 1 + 1/3 ) + ( 1 + 1/6 ) + ( 1 + 1/10 ) + ( 1 + 1/15 ) + ( 1 + 1/21 ) + ( 1 + 1/28 ) + ( 1 + 1/36 ) + ( 1 + 1/45 )
A = ( 1 + 1 + 1 + ... + 1 ) - ( 1/3 + 1/6 + 1/10 + 1/15 + 1/21 + 1/28 + 1/36 + 1/45 )
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\(=2-\left(\dfrac{5}{3}-\dfrac{7}{6}+\dfrac{9}{10}-...-\dfrac{19}{45}\right)\)
\(=2-2\left(\dfrac{5}{6}-\dfrac{7}{12}+\dfrac{9}{20}-...-\dfrac{19}{90}\right)\)
\(=2-2\left(\dfrac{1}{2}+\dfrac{1}{3}-\dfrac{1}{3}-\dfrac{1}{4}+\dfrac{1}{4}+\dfrac{1}{5}-...-\dfrac{1}{9}-\dfrac{1}{10}\right)\)
\(=2-2\cdot\dfrac{4}{10}=2-\dfrac{8}{10}=2-\dfrac{4}{5}=\dfrac{6}{5}\)
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a) \(\dfrac{7}{-25}+\dfrac{8}{25}=\dfrac{-7}{25}+\dfrac{8}{25}=\dfrac{1}{25}\)
\(\dfrac{4}{5}+\dfrac{4}{-18}=\dfrac{4}{5+\left(-18\right)}=\dfrac{4}{-13}=\dfrac{-4}{13}\)
\(\dfrac{7}{21}+\dfrac{9}{-36}=\dfrac{1}{3}+\dfrac{1}{-4}=\dfrac{1}{3+\left(-4\right)}=\dfrac{1}{-1}=1\)
b) \(\dfrac{12}{20}-\dfrac{2}{5}=\dfrac{12}{20}+\left(\dfrac{-2}{5}\right)=\dfrac{3}{5}+\dfrac{-2}{5}=\dfrac{3+\left(-2\right)}{5}=\dfrac{1}{5}\)
\(\dfrac{2}{3}-\dfrac{-5}{6}=\dfrac{2}{3}+\dfrac{5}{6}=\dfrac{4}{6}+\dfrac{5}{6}=\dfrac{9}{6}=\dfrac{3}{2}\)
\(6-\dfrac{3}{20}=6+\dfrac{-3}{20}=\dfrac{60}{60}+\dfrac{-9}{60}=\dfrac{51}{60}\)
c) \(\dfrac{2}{21}.\dfrac{-7}{3}=\dfrac{2.\left(-1\right)}{7.3}=\dfrac{-2}{21}\)
\(\dfrac{27}{28}.\left(-21\right)=\dfrac{27.\left(-21\right)}{28}=\dfrac{-567}{28}\)
\(\dfrac{-15}{7}.\dfrac{-14}{25}=\dfrac{-3.\left(-2\right)}{1.5}=\dfrac{6}{5}\)
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6 ´ 8= 48 |
28 : 4 = 7 |
35 : 5 = 7 |
7 ´ 9 = 63 |
56 : 7 = 8 |
4 ´ 6 = 24 |
5 ´ 4 = 20 |
42 : 6 = 7 |
36 : 6 = 6 |
3 ´ 8 = 24 |
45: 5 = 9 |
49 :7 = 7 |
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7 x 2 = 14 7 x 4 = 28 7 x 6 = 42 7 x 3 = 21
2 x 7 = 14 4 x 7 = 28 6 x 7 = 42 3 x 7 = 21
14 : 7 = 2 28 : 7 = 4 42 : 7 = 6 21 : 7 = 3
14 : 2 = 7 28 : 4 = 7 42 : 6 = 7 21 : 3 = 7
\(S=7.\left(1+\dfrac{1}{3}+\dfrac{1}{6}+...+\dfrac{1}{55}\right)\)
\(=7.\left(\dfrac{2}{2}+\dfrac{2}{6}+\dfrac{2}{12}+...+\dfrac{2}{110}\right)\)
\(=14.\left(\dfrac{1}{2}+\dfrac{1}{6}+\dfrac{1}{12}+...+\dfrac{1}{110}\right)\)
\(=14.\left(1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+...+\dfrac{1}{10}-\dfrac{1}{11}\right)\)
\(=14.\dfrac{10}{11}=\dfrac{140}{11}.\)
\(S=7\left(1+\dfrac{1}{3}+\dfrac{1}{6}+...+\dfrac{1}{55}\right)\)
\(S=14\left(\dfrac{1}{2}+\dfrac{1}{6}+\dfrac{1}{12}+..+\dfrac{1}{110}\right)\)
\(S=14\left(\dfrac{1}{1\cdot2}+\dfrac{1}{2\cdot3}+\dfrac{1}{3\cdot4}+...+\dfrac{1}{10\cdot11}\right)\)
\(S=14\)\(\left(\dfrac{1}{1}-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+..+\dfrac{1}{10}-\dfrac{1}{11}\right)\)
S\(=14\left(\dfrac{1}{1}-\dfrac{1}{11}\right)=14\cdot\dfrac{10}{11}=\dfrac{140}{11}\)