Elementary Number Theory and Its Application, 6th Edition by Kenneth H. Rosen Exercises 1.1.9

9. Find the fractional part of each of these numbers:
(a) 8/5
(b) 1/7
(c) -11/4
(d) 7

Solution:  The fractional part of a real number x, denoted by {x}, is the difference between x and the largest integer less than or equal to x, that is,[x]

In other words, {x}=x-[x]

(a) 8/5

The fractional part of 8/5 is
{8/5}=8/5-{8/5]
=8/5-1
=(8/5)/5
=3/5
Therefore,
{8/5}=3/5

(b) 1/7

The fractional part of 1/7 is
{1/7}=1/7-[1/7]
=1/7-0
=1/7
Therefore,
{1/7}=1/7

(c) -11/4

The fractional part of -11/4 is
{-11/4}=-11/4-[-11/4]
=-11/4-(-3)
=-11/4+3
=(-11+12)/4
Therefore,
{-11/4}=1/4

(d) 7

The fractional part of 7 is
{7}=7-[7]
=7-7
=0
Therefore,
{7}=0

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