Answer:
197/60 Exact result or 3 17/60 as Mixed Fractions
Step-by-step explanation:
Simplify the following:
75/40 + 16/30 + 35/40
The gcd of 75 and 40 is 5, so 75/40 = (5×15)/(5×8) = 5/5×15/8 = 15/8:
15/8 + 16/30 + 35/40
The gcd of 16 and 30 is 2, so 16/30 = (2×8)/(2×15) = 2/2×8/15 = 8/15:
15/8 + 8/15 + 35/40
The gcd of 35 and 40 is 5, so 35/40 = (5×7)/(5×8) = 5/5×7/8 = 7/8:
15/8 + 8/15 + 7/8
Put 15/8 + 8/15 + 7/8 over the common denominator 120. 15/8 + 8/15 + 7/8 = (15×15)/120 + (8×8)/120 + (15×7)/120:
(15×15)/120 + (8×8)/120 + (15×7)/120
| 1 | 5
× | 1 | 5
| 7 | 5
1 | 5 | 0
2 | 2 | 5:
225/120 + (8×8)/120 + (15×7)/120
8×8 = 64:
225/120 + 64/120 + (15×7)/120
15×7 = 105:
225/120 + 64/120 + 105/120
225/120 + 64/120 + 105/120 = (225 + 64 + 105)/120:
(225 + 64 + 105)/120
| | 1 |
| 2 | 2 | 5
| 1 | 0 | 5
+ | | 6 | 4
| 3 | 9 | 4:
394/120
The gcd of 394 and 120 is 2, so 394/120 = (2×197)/(2×60) = 2/2×197/60 = 197/60:
Answer: 197/60
