Question

Найдите неизвестные члены пропорции (123-125): 1) 15 : 3 = x: 6; 2) у : 9 = 50 : 5; 3) 26 : 2 = 39 : 2; 4) 66 : t = 24 : 4.​

Answer 1

Свойство пропорции: произведение крайних членов пропорции равняется произведению средних.

 $\frac{a}{b}=\frac{c}{d}$   ⇒  $a*d = c*d$

№123

( 1 )

$\frac{15}{3}=\frac{x}{6}\\\\3*x=15*6\\\\3x= 90\\\\x=90:3\\\\x=30$

( 2 )

$\frac{y}{9}=\frac{50}{5}\\\\y*5=9*50\\\\5y= 450\\\\y=450:5\\\\y=90$

( 3 )

$\frac{26}{2}=\frac{39}{z}\\\\26*z=2*39\\\\26z=78\\\\z=78:26\\\\z=3$

( 4 )

$\frac{66}{t}=\frac{24}{4}\\\\t*24=66*4\\\\24t= 264\\\\t=264:24\\\\t= 11$

№124

( 1 )

$\frac{n}{4,7}=\frac{82}{4,1}\\\\n*4,1=4,7*82\\\\4,1n= 385,4\\\\n=385,4:4,1\\\\n=94$

( 2 )

$\frac{5,8}{29}=\frac{m}{3,4}\\\\29*m=5,8*3,4\\\\29m= 19,27\\\\m=19,27:29\\\\m= 0,68$

( 3 )

$\frac{60}{k}=\frac{46}{2,3}\\\\k*46=60*2,3\\\\46k= 138\\\\k=138:46\\\\k=3$

( 4 )

$\frac{4,2}{7}=\frac{9,6}{t}\\\\4,2*t=7*9,6\\\\4,2t=67,2\\\\t=67,2:4,2\\\\t= 16$

№125

( 1 )

$\frac{4}{a}=\frac{16}{20}\\\\a*16=4*20\\\\16a=80\\\\a=80:16\\\\a=5$

( 2 )

$\frac{c}{8}=\frac{25}{40}\\\\c*40=8*25\\\\40c=200\\\\c=200:40\\\\c= 5$

( 3 )

$\frac{39}{27}=\frac{b}{9}\\\\27*b=39*9\\\\27b=351\\\\b=351:27\\\\b= 13$

( 4 )

$\frac{49}{32}=\frac{12}{d} \\\\49*d=32*12\\\\49d=384\\\\d=384:49\\\\d=7\frac{41}{47}$