Simplify the following:
(4/5 + 5)/(1/5 + 26)
Put 26 + 1/5 over the common denominator 5. 26 + 1/5 = (5×26)/5 + 1/5:
(4/5 + 5)/((5×26)/5 + 1/5)
5×26 = 130:
(4/5 + 5)/(130/5 + 1/5)
130/5 + 1/5 = (130 + 1)/5:
(4/5 + 5)/((130 + 1)/5)
130 + 1 = 131:
(4/5 + 5)/(131/5)
Put 5 + 4/5 over the common denominator 5. 5 + 4/5 = (5×5)/5 + 4/5:
((5×5)/5 + 4/5)/(131/5)
5×5 = 25:
(25/5 + 4/5)/(131/5)
25/5 + 4/5 = (25 + 4)/5:
((25 + 4)/5)/(131/5)
25 + 4 = 29:
(29/5)/(131/5)
Multiply the numerator by the reciprocal of the denominator, 29/(5×131/5) = 29/5×5/131:
(29×5)/(5×131)
(29×5)/(5×131) = 5/5×29/131 = 29/131:
Answer: 29/131
