Упражнение 704

Решение:

Упростим выражение:

• \(\frac{a}{5{,}7-4{,}5}+\frac{a}{2{,}8+4{,}4}=\left(\frac{1^{\backslash6}}{1{,}2\phantom{^{\backslash6}}}+\frac{1^{\backslash1}}{7{,}2\phantom{^{\backslash1}}}\right)\cdot{a}=\left(\frac{6}{7{,}2}+\frac{1}{7{,}2}\right)\cdot{a}=\frac{7}{7{,}2}a=\frac{7\cdot10}{7{,}2\cdot10}a=\frac{70}{72}a=\frac{35}{36}a\)

• \({\largeа)}\ a=2\frac{1^{\backslash5}}{7\phantom{^{\backslash5}}}+1\frac{4^{\backslash7}}{5\phantom{^{\backslash7}}}=2\frac{5}{35}+1\frac{28}{35}=3\frac{33}{35}=\frac{138}{35}\)

Найдем значение выражения:

• \(\frac{35}{36}a=\frac{35}{36}\cdot\frac{138}{35}=\frac{\cancel{35}^{\backslash1}\cdot138}{36\cdot\cancel{35}^{\backslash1}}=\frac{138}{36}=3\frac{30}{36}=3\frac{5}{6}\)

• \({\largeб)}\ a=1{,}8\cdot(1-0{,}6)=1{,}8\cdot0{,}4=0{,}72\)

Найдем значение выражения:

• \(\frac{35}{36}a=\frac{35}{36}\cdot0{,}72=\frac{35}{36}\cdot\frac{72}{100}=\frac{\cancel{35}^{\backslash7}\cdot\cancel{72}^{\backslash2}}{\cancel{36}^{\backslash1}\cdot\cancel{100}^{\backslash20}}=\frac{7\cdot\cancel2^{\backslash1}}{\cancel{20}^{\backslash10}}=\frac{7}{10}=0{,}7\)