Вопрос:
9) Найти значение выражений: а) \((-15{,}64:4\frac{3}{5}+7{,}1)\cdot2\frac{2}{5}\); б) \((0{,}4-\frac{11}{15})\cdot1\frac{2}{7}-(\frac{7}{18}-0{,}5):1\frac{1}{6}\); в) \((2{,}17\cdot3{,}7)-(1{,}83\cdot2{,}3):19{,}1\); г) \(0{,}8:((\frac{2}{3})^2+\frac{5}{9})\); д) \(\frac{37{,}12-5{,}6:0{,}14}{1{,}21+3{,}4\cdot0{,}35}\); е) \(\frac{(3\frac{1}{3}-2\frac{2}{3})\cdot2{,}4}{(15{,}5+4{,}5):2\frac{1}{2}}\); ё) \(5\frac{3}{7}-(2\frac{1}{2}+1\frac{1}{3}):\frac{1}{6}\); ж) \((2\frac{7}{15}+1\frac{7}{12})\cdot1\frac{1}{9}-1\frac{7}{8}\); з) \(5\frac{4}{19}\cdot3\frac{4}{7}+1\frac{15}{19}:\frac{7}{25}-1\frac{2}{3}\); и) \((6\frac{1}{7}-5\frac{3}{4}):\frac{11}{14}+(3\frac{3}{4}-1\frac{5}{6}):\frac{1}{6}\).
Ответ:
- а) \(4\frac{3}{5}=4{,}6\), поэтому \((-15{,}64:4{,}6+7{,}1)\cdot2{,}4=(-3{,}4+7{,}1)\cdot2{,}4=3{,}7\cdot2{,}4=8{,}88\).
- б) \((0{,}4-\frac{11}{15})\cdot\frac{9}{7}-(\frac{7}{18}-\frac12):\frac76=-\frac35\cdot\frac97-(-\frac19)\cdot\frac67=-\frac{27}{35}+\frac{2}{21}=-\frac{73}{105}\).
- в) \(2{,}17\cdot3{,}7=8{,}029\), \(1{,}83\cdot2{,}3=4{,}209\), \(4{,}209:19{,}1=0{,}22\), значит \(8{,}029-0{,}22=7{,}809\).
- г) \(0{,}8:(\frac49+\frac59)=0{,}8:1=0{,}8\).
- д) \(\frac{37{,}12-40}{1{,}21+1{,}19}=\frac{-2{,}88}{2{,}4}=-1{,}2\).
- е) \(\frac{(\frac{10}{3}-\frac83)\cdot2{,}4}{20:2{,}5}=\frac{\frac23\cdot2{,}4}{8}=\frac{1{,}6}{8}=0{,}2\).
- ё) \(5\frac37-(\frac52+\frac43):\frac16=\frac{38}{7}-\frac{23}{6}\cdot6=\frac{38}{7}-23=-\frac{123}{7}=-17\frac47\).
- ж) \((\frac{37}{15}+\frac{19}{12})\cdot\frac{10}{9}-\frac{15}{8}=\frac{263}{60}\cdot\frac{10}{9}-\frac{15}{8}=\frac{263}{54}-\frac{15}{8}=\frac{689}{216}=3\frac{41}{216}\).
- з) \(\frac{99}{19}\cdot\frac{25}{7}+\frac{34}{19}:\frac{7}{25}-\frac53=\frac{2475}{133}+\frac{850}{133}-\frac53=25-\frac53=23\frac13\).
- и) \((\frac{43}{7}-\frac{23}{4}):\frac{11}{14}+(\frac{15}{4}-\frac{11}{6}):\frac16=-\frac{19}{28}\cdot\frac{14}{11}+\frac{23}{12}\cdot6=-\frac{19}{22}+\frac{23}{2}=\frac{117}{11}=10\frac7{11}\).
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