Answer:
(1594/29) - (-233)/14
Explanation:
Simplify the following:
(6×7 - 1 + 16 - 1) - 1/29 - 1
6×7 = 42:
(42 - 1 + 16 - 1) - 1/29 - 1
42 - 1 + 16 - 1 = (42 + 16) - (1 + 1):
((42 + 16) - (1 + 1)) - 1/29 - 1
| 4 | 2
+ | 1 | 6
| 5 | 8:
(58 - (1 + 1)) - 1/29 - 1
1 + 1 = 2:
(58 - 2) - 1/29 - 1
| 5 | 8
- | | 2
| 5 | 6:
(56) - 1/29 - 1
(56) - 1/29 - 1 = (56 - 1/29 - 1):
(56 - 1/29 - 1)
Put 56 - 1/29 - 1 over the common denominator 29. 56 - 1/29 - 1 = (29×56)/29 - 1/29 - 29/29:
((29×56)/29 - 1/29 - 29/29)
| | 5 | 6
× | | 2 | 9
| 5 | 0 | 4
1 | 1 | 2 | 0
1 | 6 | 2 | 4:
(1624/29 - 1/29 - 29/29)
1624/29 - 1/29 - 29/29 = (1624 - 1 - 29)/29:
((1624 - 1 - 29)/29)
1624 - 1 - 29 = 1624 - (1 + 29):
((1624 - (1 + 29))/29)
| 1 |
| 2 | 9
+ | | 1
| 3 | 0:
((1624 - 30)/29)
| | 5 | 12 |
| 1 | 6 | 2 | 4
- | | | 3 | 0
| 1 | 5 | 9 | 4:
Answer: (1594/29)
_____________________________________________________
Simplify the following:
-7 - 10/(-28) - 10
The gcd of -10 and -28 is -2, so (-10)/(-28) = (-2×5)/(-2×14) = (-2)/(-2)×5/14 = 5/14:
-7 + 5/14 - 10
Put -7 + 5/14 - 10 over the common denominator 14. -7 + 5/14 - 10 = (14 (-7))/14 + 5/14 + (14 (-10))/14:
(14 (-7))/14 + 5/14 + (14 (-10))/14
14 (-7) = -98:
(-98)/14 + 5/14 + (14 (-10))/14
14 (-10) = -140:
(-98)/14 + 5/14 + (-140)/14
-98/14 + 5/14 - 140/14 = (-98 + 5 - 140)/14:
(-98 + 5 - 140)/14
-98 + 5 - 140 = 5 - (98 + 140):
(5 - (98 + 140))/14
| 1 | |
| 1 | 4 | 0
+ | | 9 | 8
| 2 | 3 | 8:
(5 - 238)/14
5 - 238 = -(238 - 5):
(-(238 - 5))/14
| 2 | 3 | 8
- | | | 5
| 2 | 3 | 3:
Answer: (-233)/14