Найдите значение числового выражения:
№1 11/15 * (4 1/2 - 3 2/5 : 17/20) + 1 11/20
= 2 5/11.
1)) 3 2/5 : 17/20= (3•5+2)/5 • 20/17=
17/5• 20/17=
сокращаем 17 и 17 на 17; 5 и 20 на 5.
1/1• 4/1= 4.
2)) 4 1/2- 4= 1/2.
3)) 1 11/15 • 1/2= (15•1+11)/15• 1/2=
26/15• 1/2=
Сокращаем 26 и 2 на 2.
13/15• 1/1= 13/15.
4)) 13/15+ 1 11/20= 13/15+ (1•20+11)/20=
13/15+ 31/20=
(13•4)/(15•4)+ (31•3)/(20•3)=
52/60+ 93/60= 145/60=
2 25/60= 2 5/12.
Сократили 25/60 на 5.
№2 5 4/7 : 1 5/21 - (5 2/15 *3/22 +1 14/15) = -5 2/15.
1)) 5 2/15• 3/22= (5•15+2)/15• 3/2=
77/15• 3/2=
Сокращаем 15 и 3 на 3.
77/5•1/2= 77/10= 7 7/10
2)) 7 7/10+ 1 14/15=
7 (7•3)/(10•3)+ 1 (14•2)/(15•2)=
7 21/30+ 1 28/30= 8 49/30= 9 19/30
3)) 5 4/7: 1 5/21= (5•7+4)/7: (21•1+5)/21=
39/7: 26/21= 39/7• 21/26=
Сокращаем 39 и 26 на 13; 7 и 21 на 7.
3/1• 3/2= 9/2= 4 1/2
4)) 4 1/2 - 9 19/30 =
4 (1•15)/(2•15)- 9 19/30=
-(9 19/30 - 4 15/30)=
-( 5 4/30)= - 5 2/15.
Сократили 4/30 на 2.
№3 7 2/3 + 4 1/6 * (6 2/7 - 3 5/7)=
= 15 8/21.
1)) 6 2/7- 3 5/7= 5 (1•7+2)/7 - 3 5/7=
5 9/7- 3 5/7= 2 4/7.
2)) 4 1/6• 2 4/7= (4•6+1)/6• (2•7+4)/7=
25/6• 18/7=
Сокращаем 6 и 18 на 6
25/1• 3/7= 75/7= 7 5/7.
3)) 7 2/3+ 7 5/7=
7 (2•7)/(3•7)+ 7 (5•3)/(7•3)=
7 14/21+ 7 15/21= 14 29/21= 15 8/21.
№4 4 2/7 : 1 5/21 + ( 4 3/13 * 14/15 - 3 1/3). = 4 1/13.
1)) 4 3/13• 14/15= (4•13+3)/13• 14/15=
55/13• 14/15=
Сокращаем 55 и 15 на 5.
11/13• 14/3= 154/39= 3 37/39.
2)) 3 37/39- 3 1/3=
3 37/39- 3 (1•13)/(3•13)=
3 37/39- 3 13/39= 24/39.
3)) 4 2/7: 1 5/21= (4•7+2)/7: (1•21+5)/21=
30/7: 26/21= 30/7• 21/26=
Сокращаем 30 и 26 на 2; 7 и 21 на 7.
15/1• 3/13= 45/13= 3 6/13.
4)) 3 6/13 + 24/39=3 (6•3)/(13•3)+24/39=
3 18/39+24/39= 3 42/39=
4 3/39= 4 1/13.
Сократили 3/39 на 3.