{x} represents the fractional part of a function.
It is defined as {x} = x - [x], where [x] is the greatest integer of x. This definition is useful when calculating the fractional part of negative numbers.
If x is a positive integer, to find the fractional part, we drop the number on the left of decimal point.
e.g. {6.7} = 0.7
But {-6.7} ≠ 0.7
{x} gives its distance between x and [x]
[-6.7]= -7
⇒ {x} = x - [x] = -6.7 - (-7)
= 0.3
Similarly, {0.23} = 0.23
{-0.23} = -0.23 - (-1)
= 0.77
{-1} = -1- (-1)
= 0
{0} = 0 - 0
= 0
{2.4} = 0.4
{-2.4} = -2.4 - (-3)
= 0.6
⇒ sum= 0.23 + 0.77 + 0 + 0 + 0.4 + 0.6
= 2