The number added to the numerator and the denominator is 2/3.
It is given in the question that when the same number is added to the numerator and denominator of fraction 5/7, the result is 17/23.
We have to find the number added to the numerator and the denominator.
Let the number be x.
Hence, according to the data given in the question, we get,
(5 + x)/(7 + x) = 17/23
By cross - multiplication, we get
23(5 + x) = 17 (7 + x)
Opening the bracket according to the distributive property of addition and multiplication, we get,
115 + 23x = 119 + 17x
23x - 17x = 119 - 115
6x = 4
x = 4/6
x = 2/3
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