Question

Найдите значение числового выражения: №1 11/15 * (4 1/2 - 3 2/5 : 17/20) + 1 11/20; №2 5 4/7 : 1 5/21 - (5 2/15 * 3/22 + 1 14/15); №3 7 2/3 + 4 1/6 * (6 2/7 - 3 5/7); №4 4 2/7 : 1 5/21 + ( 4 3/13 * 14/15 - 3 1/3). Помогите пожалуйста ответивший получит - 20 Баллов.Заранее спасибо!

Answer 1

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.

Answer 2

Конечный ответ для каждого выражения:

№1: 6 31/75 + 1 11/20 = 8 41/75

№2: 23/28 - (25/33 * 73/22 + 29/15) = -3441/2310 ≈ -1.488

№3: 7 2/3 + 25/6 = 12 5/6

№4: 30/19 + (59/13 * 14/15 - 10/3) = 1511/247 ≈ 6.120

Подробное решение:

№1: 4 1/2 - 3 2/5 : 17/20 = 9/2 - (17/5 * 20/17) / 2 = 9/2 - 2 = 13/2 11/15 * (13/2) + 1 11/20 = 143/30 + 31/20 = 289/60 = 6 31/75 И, наконец, добавляем 1 11/20: 6 31/75 + 1 11/20 = 8 41/75

№2: 5 4/7 : 1 5/21 - (5 2/15 * 3/22 + 1 14/15) = 39/7 : 26/441 - (76/33 * 3/22 + 29/15) = 39/7 : 26/441 - 608/7269 - 29/15 = 23/28 - (25/33 * 73/22 + 29/15) = 23/28 - 1825/7266 - 1161/7266 = 23/28 - 2986/7266 = -3441/2310

№3: 4 1/6 * (6 2/7 - 3 5/7) + 7 2/3 = 25/6 * (20/7 - 26/7) + 7 2/3 = 25/6 * (-6/7) + 22/3 = -25/14 + 22/3 = 450/84 + 308/84 = 12 5/6

№4: 4 3/13 * 14/15 - 3 1/3 + 4 2/7 : 1 5/21 = 59/13 * 14/15 - 10/3 + 30/19 = 826/195 - 650/195 + 570/195 = 746/195 = 1511/247 ≈ 6.120