05. Упростите и найдите значение выражения: а) 4/7x + 5/14x при x = 5 1/4; б) 5/16y + y − 3/8y при y = 1 1/15; в) 17/42c − 2/7c + 7/18c при c = 3 1/2; г) 3/4n + 2/3n − 4/18n при n = 1 13/23

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Accepted Answer

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

При \(x=5\frac14=\frac{21}{4}\): \(\frac{13}{14}\cdot\frac{21}{4}=\frac{39}{8}=4\frac78\).

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

При \(y=1\frac1{15}=\frac{16}{15}\): \(\frac{15}{16}\cdot\frac{16}{15}=1\).

в) \(\frac{17}{42}c-\frac27c+\frac7{18}c=\left(\frac{51}{126}-\frac{36}{126}+\frac{49}{126}\right)c=\frac{64}{126}c=\frac{32}{63}c\).

При \(c=3\frac12=\frac72\): \(\frac{32}{63}\cdot\frac72=\frac{16}{9}=1\frac79\).

г) \(\frac34n+\frac23n-\frac4{18}n=\left(\frac34+\frac23-\frac29\right)n=\left(\frac{27+24-8}{36}\right)n=\frac{43}{36}n\).

При \(n=1\frac{13}{23}=\frac{36}{23}\): \(\frac{43}{36}\cdot\frac{36}{23}=\frac{43}{23}=1\frac{20}{23}\).

Ответ: а) \(4\frac78\); б) \(1\); в) \(1\frac79\); г) \(1\frac{20}{23}\).