Answer: the number is x = 1 + 21/52
Step-by-step explanation:
we have
(5 + 5/12) - x = (6 + 1/6) - (2 + 2/13)
this means that x is smaller than 5 + 5/12 by the same amount as (2 + 2/13) is smaller than (6 + 1/6)
We can solve it directly, first solve the parentheses, put the whole numbers at one side and the fractions in the other side:
5 - 6 + 2 - x = -5/12 + 1/6 - 2/13
1 - x = -5/12 + 2/12 - 2/13
1 - x = -3/12 - 2/13 = -1/4 - 2/13 = -13/(4*13) - (2*4)/(4*13) = -21/52
x = 1 + 21/52
