fractional part - 2

[logistic_guy]

Find the fractional part of each of these numbers:

\(\displaystyle \bold{(a)} \ -\frac{8}{5}\)

\(\displaystyle \bold{(b)} \ \frac{22}{7}\)

\(\displaystyle \bold{(c)} \ -1\)

\(\displaystyle \bold{(d)} \ -\frac{1}{3}\)

 

[khansaheb]

Find the fractional part of each of these numbers:

\(\displaystyle \bold{(a)} \ -\frac{8}{5}\)

\(\displaystyle \bold{(b)} \ \frac{22}{7}\)

\(\displaystyle \bold{(c)} \ -1\)

\(\displaystyle \bold{(d)} \ -\frac{1}{3}\)

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[logistic_guy]

\(\displaystyle \bold{(a)}\)

The fractional part of \(\displaystyle -\frac{8}{5}\) is:

\(\displaystyle -\frac{8}{5} - \left\lfloor-\frac{8}{5}\right\rfloor = -\frac{8}{5} - \left\lfloor-1 -\frac{3}{5}\right\rfloor = -\frac{8}{5} - (-2)\)


\(\displaystyle = -\frac{8}{5} + 2 = -\frac{8}{5} + \frac{10}{5} = \frac{2}{5}\)