1.007. Вычислите: \(\dfrac{(\frac16+0{,}1+\frac1{15}):(\frac16+0{,}1-\frac1{15})\cdot2{,}52}{(0{,}5-\frac13+0{,}25-\frac15):(0{,}25-\frac16)\cdot\frac7{13}}\).

Question

1.007. Вычислите: \(\dfrac{(\frac16+0{,}1+\frac1{15}):(\frac16+0{,}1-\frac1{15})\cdot2{,}52}{(0{,}5-\frac13+0{,}25-\frac15):(0{,}25-\frac16)\cdot\frac7{13}}\).

Accepted Answer

\(\frac16+0{,}1+\frac1{15}=\frac25\), \(\frac16+0{,}1-\frac1{15}=\frac4{25}\), поэтому числитель равен \(\frac25:\frac4{25}\cdot\frac{63}{25}=\frac52\cdot\frac{63}{25}=\frac{63}{10}\).

Знаменатель: \(0{,}5-\frac13+0{,}25-\frac15=\frac{13}{60}\), \(0{,}25-\frac16=\frac1{12}\), значит \(\frac{13}{60}:\frac1{12}\cdot\frac7{13}=\frac{21}{5}\).

\(\frac{63}{10}:\frac{21}{5}=\frac32\).

Ответ: \(1\frac12\).