Упростите и найдите значение выражения: а) \(\frac47x+\frac5{14}x\) при \(x=5\frac14\); б) \(\frac5{16}y+y-\frac38y\) при \(y=1\frac1{15}\); в) \(\frac{17}{42}c-\frac27c+\frac7{18}c\) при \(c=3\frac12\); г) \(\frac34n+\frac23n-\frac4{18}n\) при \(n=1\frac{13}{23}\).

\[\frac47x+\frac5{14}x=\left(\frac8{14}+\frac5{14}\right)x=\frac{13}{14}x\]

\[x=5\frac14=\frac{21}{4},\quad \frac{13}{14}\cdot\frac{21}{4}=\frac{39}{8}=4\frac78\]

Ответ: \(4\frac78\).

\[\frac5{16}y+y-\frac38y=\left(\frac5{16}+\frac{16}{16}-\frac6{16}\right)y=\frac{15}{16}y\]

\[y=1\frac1{15}=\frac{16}{15},\quad \frac{15}{16}\cdot\frac{16}{15}=1\]

Ответ: \(1\).

\[\frac{17}{42}-\frac27+\frac7{18}=\frac{51}{126}-\frac{36}{126}+\frac{49}{126}=\frac{64}{126}=\frac{32}{63}\]

\[c=3\frac12=\frac72,\quad \frac{32}{63}\cdot\frac72=\frac{16}{9}=1\frac79\]

Ответ: \(1\frac79\).

\[\frac34n+\frac23n-\frac4{18}n=\left(\frac34+\frac23-\frac29\right)n=\frac{43}{36}n\]

\[n=1\frac{13}{23}=\frac{36}{23},\quad \frac{43}{36}\cdot\frac{36}{23}=\frac{43}{23}=1\frac{20}{23}\]

Ответ: \(1\frac{20}{23}\).