Задание № 1029
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а) $\frac{20:2\frac2{15}+25\frac57:1\frac1{35}}{21\frac79:4\frac23-1}=\frac{\frac{20}1\ast\frac{15}{32}+\frac{180}7\ast\frac{35}{36}}{\frac{196}9\ast\frac3{14}-1}=\frac{\frac{4\ast5}1\ast\frac{15}{4\ast8}+\frac{36\ast5}7\ast\frac{7\ast5}{36}}{\frac{14\ast14}{3\ast3}\ast\frac3{14}-1}=\frac{\frac{75}8+25}{\frac{14}3-1}=\frac{\frac{78}8+\frac{200}8}{\frac{14}3-\frac33}=\frac{\frac{275}8}{\frac{11}3}=\frac{275}8\ast\frac3{11}=\frac{25\ast11}8\ast\frac3{11}=\frac{25}8\ast\frac31=\frac{75}8=9\frac38$
б) $\frac{6\frac34:9+24:\frac67-\frac19:\frac4{21}}{53\frac23-22\frac{14}{15}:2\frac23}=\frac{\frac{27}4\ast\frac19+\frac{24}1\ast\frac76-\frac19\ast\frac{21}4}{53\frac23-\frac{344}{15}\ast\frac38}=\frac{\frac{9\ast3}4\ast\frac19+\frac{6\ast4}1\ast\frac76-\frac1{3\ast3}\ast\frac{3\ast7}4}{53\frac23-\frac{43\ast8}{3\ast5}\ast\frac38}=\frac{\frac34+28-\frac7{12}}{53\frac23-\frac{43}5}=\frac{28\frac9{12}-\frac7{12}}{53\frac23-8\frac35}=\frac{28\frac2{12}}{45\frac{10-9}{15}}=\frac{28\frac16}{45\frac1{15}}=\frac{169}6\ast\frac{15}{676}=\frac{169}{3\ast2}\ast\frac{3\ast5}{4\ast169}=\frac58$
в) $\frac{20\frac3{10}-(2\frac1{10}\ast4+\frac{19}{20}\ast10)}{1:5}=\frac{20\frac3{10}-(\frac{21}{10}\ast4+\frac{19}{20}\ast10)}{1\ast\frac15}=\frac{20\frac3{10}-(\frac{21\ast2\ast2}{2\ast5}+\frac{19\ast10}{2\ast10})}{\frac15}=\frac{20\frac3{10}-(\frac{42}5+\frac{19}2)}{\frac15}=\frac{20\frac3{10}-\frac{84+95}{10}}{\frac15}=\frac{20\frac3{10}-\frac{179}{10}}{\frac15}=\frac{19\frac{13}{10}-17\frac9{10}}{\frac15}=2\frac4{10}\ast5=10\frac{20}{10}=12$
г) $\frac{4\frac25-2\frac34+7\frac7{15}-8\frac7{60}}{7\frac14-5\frac34}=\frac{4\frac{24}{60}-2\frac{45}{60}+7\frac{28}{60}-8\frac7{60}}{6\frac54-5\frac34}=\frac{3\frac{84}{60}-2\frac{45}{60}+7\frac{28}{60}-8\frac7{60}}{1\frac24}=\frac{1\frac{39}{60}+7\frac{28}{60}-8\frac7{60}}{1\frac12}=\frac{8\frac{67}{60}-8\frac7{60}}{\frac32}=\frac{8\frac{60}{60}}{\frac32}=9\ast\frac23=\frac{18}3=6$
д) $\frac{(\frac16+\frac1{10}+\frac1{15}):(\frac16+\frac1{30})}{(\frac16+\frac14-\frac15):(\frac14-\frac16)}=\frac{(\frac5{30}+\frac3{30}+\frac2{30}):(\frac5{30}+\frac1{30})}{(\frac{10}{60}+\frac{15}{60}-\frac{12}{60}):(\frac6{24}-\frac4{24})}=\frac{\frac{10}{30}:\frac6{30}}{\frac{13}{60}:\frac2{24}}=\frac{\frac{10}{30}\ast\frac{30}6}{\frac{13}{60}\ast\frac{24}2}=\frac{\frac{10}6}{\frac{13\ast12}{12\ast5}}=\frac53\ast\frac5{13}=\frac{25}{39}$
е) $\frac{5\frac15:\frac{39}{40}}{2\frac45:\frac7{10}\ast\frac34}+\frac{(2-1\frac3{20})\ast48}{\frac14\ast20+1:10}=\frac{\frac{26}5\ast\frac{40}{39}}{\frac{14}5\ast\frac{10}7\ast\frac34}+\frac{(1\frac{20}{20}-1\frac3{20})\ast48}{\frac{20}4+1\ast\frac1{10}}=\frac{\frac{13\ast2}5\ast\frac{8\ast5}{13\ast3}}{\frac{7\ast2}5\ast\frac{5\ast2}7\ast\frac3{2\ast2}}+\frac{\frac{17}{20}\ast48}{5+\frac1{10}}=\frac{\frac21\ast\frac83}3+\frac{\frac{17}{4\ast5}\ast\frac{4\ast12}1}{5\frac1{10}}=\frac{\frac{16}3}3+\frac{\frac{17\ast12}5}{\frac{51}{10}}=\frac{16}3\ast\frac13+\frac{204}5\ast\frac{10}{51}=\frac{16}9+\frac{51\ast4}5\ast\frac{5\ast2}{51}=1\frac79+8=9\frac79$
