Question

Сократите дроби: 3/10+1/6 , 5 7/12+3 9/20 , 1/2-1/5 1/4+2/15 , 11/12-1/3 , 5 9/14+2 11/35 3/44+5/56 , 10 4/77-3 8/11

Answer 1

3/10+1/6=9/30+5/30=14/30=7/15

5 целых 7/12 +3 целых 9/20= 67/12+69/20= 67*5/20*5+69*3/20*3=
=335+207=542=9*60+2 = 9 целых 2/60= 9 целых 1/30
  60    60    60      60                  
                  
 1/2-1/5= 1*5/2*5 - 1*2/5*2  = 5/10-2/10=3/10

1/4+2/15 = 15/60+8/60=23/60

11/12-1/3=11/12 - 4/12=7/12

5 целых 9/14+2целых 11/35=5ц.9*5/14*5+2ц.11*2/35*2=5ц.45/70+2ц.22/70=
=7 целых 67/70

3/44+5/56=3*14/44*14+5*11/56*11=42/616+55/616=97/616


10ц. 4/77-3ц. 8/11=10ц.4/77-3ц.56/77=9ц.81/77-3ц.56/77= 6 целых 25/77

Answer 2

Давайте упростим каждую из данных дробей:

1. 3/10 + 1/6 = (9/30) + (5/30) = 14/30 = 7/15

2. 5 7/12 + 3 9/20 = (5 + 3) + (7/12 + 9/20) = 8 + (35/60 + 27/60) = 8 + 62/60 = 8 31/30

3. 1/2 - (1/5 + 1/4 + 2/15) = 1/2 - (12/60 + 15/60 + 8/60) = 1/2 - 35/60 = 1/2 - 7/12 = 6/12 - 7/12 = -1/12

4. 11/12 - 1/3 = (11/12) - (4/12) = 7/12

5. 5 9/14 + 2 11/35 = (5 + 2) + (9/14 + 11/35) = 7 + (135/210 + 66/210) = 7 + 201/210 = 7 + 67/70

6. 3/44 + 5/56 = (6/88) + (5/56) = (3/44) + (5/56) = (12/176) + (5/56) = (12/176) + (55/176) = 67/176

7. 10 4/77 - 3 8/11 = (10 - 3) + (4/77 - 8/11) = 7 + [(4 * 11 - 8 * 77) / (77 * 11)] = 7 + (-308 / 847) = (7 * 847 - 308) / 847 = (5929 - 308) / 847 = 5621/847

Итак, дроби упрощены.