Номер 190
А))
1 2/3Х + 5/6Х = 2 1/2 + 7/12 - 4 1/4
(1•3+2)/3Х + 5/6Х=
( 2•2+1)/2+ 7/12- (4•4+1)/4
5/3Х+ 5/6Х= 5/2+ 7/12- 17/4
(5•2)/(3•2)Х+5/6Х =
(5•6)/(2•6)+ 7/12- (17•3)/(4•3)
10/6Х+5/6Х= 30/12+ 7/12- 51/12
15/6Х= -(51-30-7)/12
15/6Х= -14/12
Х= -14/12: 15/6
Х= -14/12• 6/15
Сокращаем 12 и 6 на 6
Х= -14/2• 1/15
Сокращаем 14 и 2 на 2
Х= -7/1• 1/15
Х= -7/15
Проверка
1 2/3Х + 5/6Х = 2 1/2 + 7/12 - 4 1/4
10/6Х+5/6Х= 30/12+ 7/12- 51/12
15/6Х= -(51-30-7)/12
15/6• (-7/15)= -14/12
Сокращаем 15 и 15 на -5; 14 и 12 на 2
1/6• (-7/1)= -7/6
-7/6= -7/6
Б))
1 3/5У - 2 4/15У= 1/10 - 3 11/30 + 1 7/15
(1•5+3)/5У - (2•15+4)/15У=
1/10- (3•30+11)/30+ (1•15+7)/15
8/5У- 34/15У= 1/10- 101/30+ 22/15
(8•3)/(5•3)У- 34/15У=
(1•3)/(10•3)- 101/30+ (22•2)/(15•2)
24/15У- 34/15У= 3/30- 101/30+ 44/30
-10/15У= -54/30
У= -54/30 : -10/15
У= -54/30• - 15/10
Сокращаем 54 и 10 на 2; 30 и 15 на 15;
У= 27/2• 1/5
У= 27/10= 2 7/10= 2,7
Проверка
1 3/5У - 2 4/15У= 1/10 - 3 11/30 + 1 7/15
24/15У- 34/15У= 3/30- 101/30+ 44/30
-10/15У= -54/30
Сокращаем 10/15 на 5; 54/30 на 2
-2/3У=-27/15
-2/3• (27/10)= -1 12/15
Сокращаем 3 и 27 на 3; 2 и 10 на 2;
12 и 15 на 3;
-1/1• 9/5= -1 4/5
-9/5= -1 4/5
-1 4/5= -1 4/5
В))
2 1/7а+ 3 9/14а = 11 1/7 -1 1/21 -2 3/14
(2•7+1)/7а + (3•14+9)/14а=
(11•7+1)/7 - (1•21+1)/21 - (2•14+3)/14
15/7а+ 51/14а= 78/7- 22/21- 31/14
(15•2)/(7•2)а+ 51/14а =
(78•2)/(7•2) - 31/14 - 22/21
30/14а + 51/14а= 156/14- 31/14- 22/21
81/14а= 125/14- 22/21
81/14а= (125•3)/(14•3)- (22•2)/(21•2)
81/14а= 375/42- 44/42
81/14а= 331/42
а= 331/42: 81/14
а= 331/42• 14/81
Сокращаем 42 и 14 на 14
а= 331/3• 1/81
а= 331/243
а= 1 88/243
Проверка
2 1/7а+ 3 9/14а = 11 1/7 -1 1/21 -2 3/14
15/7а+ 51/14а= 78/7- 22/21- 31/14
30/14а + 51/14а= (78•6)/(7•6) - (22•2)/(21•2)- (31•3)/(14•3)
81/14а= 468/42- 44/42- 93/42
81/14• 331/243= 331/42
Сокращаем 81 и 162 на 81
1/14• 331/3= 7 37/42
331/42= 7 37/42
7 37/42= 7 37/42