Answer:
(-2579)/3400
Step-by-step explanation:
Simplify the following:
3/5 (7/10 + 2/5)/(5 + 2/3) + 1 + 3/8 - (2 + 1/4)
(3 (7/10 + 2/5)/(5 + 2/3))/5 = (3 (7/10 + 2/5))/(5 (5 + 2/3)):
(3 (7/10 + 2/5))/(5 (2/3 + 5)) + 1 + 3/8 - (2 + 1/4)
Put 5 + 2/3 over the common denominator 3. 5 + 2/3 = (3×5)/3 + 2/3:
(3 (7/10 + 2/5))/(5 (3×5)/3 + 2/3) + 1 + 3/8 - (2 + 1/4)
3×5 = 15:
(3 (7/10 + 2/5))/(5 (15/3 + 2/3)) + 1 + 3/8 - (2 + 1/4)
15/3 + 2/3 = (15 + 2)/3:
(3 (7/10 + 2/5))/(5 (15 + 2)/3) + 1 + 3/8 - (2 + 1/4)
15 + 2 = 17:
(3 (7/10 + 2/5))/(5×17/3) + 1 + 3/8 - (2 + 1/4)
Put 7/10 + 2/5 over the common denominator 10. 7/10 + 2/5 = 7/10 + (2×2)/10:
(3 7/10 + (2×2)/10)/((5×17)/3) + 1 + 3/8 - (2 + 1/4)
2×2 = 4:
(3 (7/10 + 4/10))/((5×17)/3) + 1 + 3/8 - (2 + 1/4)
7/10 + 4/10 = (7 + 4)/10:
(3 (7 + 4)/10)/((5×17)/3) + 1 + 3/8 - (2 + 1/4)
7 + 4 = 11:
(3×11/10)/(5×17/3) + 1 + 3/8 - (2 + 1/4)
5×17/3 = (5×17)/3:
(3×11/10)/((5×17)/3) + 1 + 3/8 - (2 + 1/4)
3×11/10 = (3×11)/10:
((3×11)/10)/((5×17)/3) + 1 + 3/8 - (2 + 1/4)
Multiply the numerator by the reciprocal of the denominator, ((3×11)/10)/((5×17)/3) = (3×11)/10×3/(5×17):
(3×11×3)/(5×17×10) + 1 + 3/8 - (2 + 1/4)
5×17 = 85:
(3×11×3)/(85×10) + 1 + 3/8 - (2 + 1/4)
85×10 = 850:
(3×11×3)/850 + 1 + 3/8 - (2 + 1/4)
3×11 = 33:
(33×3)/850 + 1 + 3/8 - (2 + 1/4)
33×3 = 99:
99/850 + 1 + 3/8 - (2 + 1/4)
Put 2 + 1/4 over the common denominator 4. 2 + 1/4 = (4×2)/4 + 1/4:
99/850 + 1 + 3/8 - (4×2)/4 + 1/4
4×2 = 8:
99/850 + 1 + 3/8 - (8/4 + 1/4)
8/4 + 1/4 = (8 + 1)/4:
99/850 + 1 + 3/8 - (8 + 1)/4
8 + 1 = 9:
99/850 + 1 + 3/8 - 9/4
Put 99/850 + 1 + 3/8 - 9/4 over the common denominator 3400. 99/850 + 1 + 3/8 - 9/4 = (4×99)/3400 + 3400/3400 + (425×3)/3400 + (850 (-9))/3400:
(4×99)/3400 + 3400/3400 + (425×3)/3400 + (850 (-9))/3400
4×99 = 396:
396/3400 + 3400/3400 + (425×3)/3400 + (850 (-9))/3400
425×3 = 1275:
396/3400 + 3400/3400 + 1275/3400 + (850 (-9))/3400
850 (-9) = -7650:
396/3400 + 3400/3400 + 1275/3400 + (-7650)/3400
396/3400 + 3400/3400 + 1275/3400 - 7650/3400 = (396 + 3400 + 1275 - 7650)/3400:
(396 + 3400 + 1275 - 7650)/3400
| 1 | 1 | 1 |
| 3 | 4 | 0 | 0
| 1 | 2 | 7 | 5
+ | | 3 | 9 | 6
| 5 | 0 | 7 | 1:
(5071 - 7650)/3400
5071 - 7650 = -(7650 - 5071):
(-(7650 - 5071))/3400
| | | 14 |
| | 5 | 4 | 10
| 7 | 6 | 5 | 0
- | 5 | 0 | 7 | 1
| 2 | 5 | 7 | 9:
Answer: (-2579)/3400
