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a, = 21.22.68 / 11.17.63
= 21. 22 .68 / 11.22.21.3
=68 / 33
b, =5.7.26 / 14.13.25
= 5 . 7 .13 .2/ 7 . 2.13. 5.5
= 1/5
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\(\frac{42}{17}\times\frac{68}{63}=\frac{8}{3}\)
\(\frac{5}{26}\times\frac{26}{25}=\frac{1}{5}\)
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a) \(\frac{21}{11}\cdot\frac{22}{17}\cdot\frac{68}{63}\)
\(=\frac{21\cdot22\cdot68}{11\cdot17\cdot63}\)
\(=\frac{3\cdot7\cdot2\cdot11\cdot4\cdot17}{11\cdot17\cdot7\cdot3\cdot3}\)
\(=\frac{2\cdot4}{3}\)
\(=\frac{8}{3}\)
b) \(\frac{5}{14}\cdot\frac{7}{13}\cdot\frac{26}{25}\)
\(=\frac{5\cdot7\cdot26}{14\cdot13\cdot25}\)
\(=\frac{5\cdot7\cdot2\cdot13}{2\cdot7\cdot13\cdot5\cdot5}\)
\(=\frac{1}{5}\)
=))
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\(\frac{21}{11}\cdot\frac{22}{17}\cdot\frac{68}{63}=\frac{21\cdot22\cdot68}{11\cdot17\cdot63}\)=\(\frac{1\cdot2\cdot4}{1\cdot1\cdot3}=\frac{8}{3}\)
\(\frac{5}{14}\cdot\frac{7}{13}\cdot\frac{26}{25}=\frac{5\cdot7\cdot26}{14\cdot43\cdot25}\)=\(\frac{1\cdot1\cdot2}{2\cdot1\cdot5}\)\(=\frac{2}{10}=\frac{1}{5}\)
A = 7 + 21 + 63 +... + 5103 + 15309
3\(\times\) A = 21 + 63 + 189 +...+15309 + 45927
3 \(\times\) A - A = (21+63 + 189 +..+45927) - (7+21 + 63+..+15309)
A \(\times\) (3 - 1) = 21 + 63 + 189 +...+ 45927 - 7 -21- 63 - ...- 15309
A \(\times\) 2 = (21 - 21) + (63 - 63) +...+(15309 - 15309) + (45927 - 7)
A \(\times\) 2 = 45920
A = 45920 : 2
A = 22960