To get the distance between
[tex]6[/tex] and [tex]4\frac{1}{4}[/tex], we subtract [tex]4\frac{1}{4}[/tex] from [tex]6[/tex]
That is,
[tex]d=6-4\frac{1}{4}[/tex]
We change the mixed number to improper fraction now to get,
[tex]d=6-\frac{17}{4}[/tex]
This is the same as,
[tex]d=\frac{6}{1}-\frac{17}{4}[/tex]
We collect LCM to be 4
[tex]=\frac{4\times6-17}{4}[/tex]
This gives us,
[tex]=\frac{24-17}{4}[/tex]
[tex]=\frac{7}{4}[/tex]
Convert back to mixed number to get,
[tex]=1\frac{3}{4}[/tex]
Therefore the distance between the two numbers is [tex]=1\frac{3}{4}[/tex]
Note that the other way round will result in negative value. That is subtracting 6 from [tex]4\frac{1}{4}[/tex] will give [tex]-1\frac{3}{4}[/tex]
But since this is distance we find the absolute value and get the same result.
[tex]d=|-1\frac{3}{4}|=1\frac{3}{4}[/tex]
