# Writing Fractions with a Denominator of 2 in Decimal Form

On the next web exercise (finding the average of two signed numbers), you will need to report your answers in decimal form.

All your answers will *initially*
be fractions with a denominator of
$\,2\,$,
and you should be able to convert them to a decimal
*without* having
to pull out your calculator!

To convert (say)
$\,\frac{15}{2}\,$ to decimal form,
go through this thought process:
How many times does
$\,2\,$ go into
$\,15\,$?

Answer:
It goes in
$\,7\,$ times, with
$\,1\,$ left over.
The answer is
$\,7.5\,$.

Here are the details: $$ \begin{align} \cssId{s12}{\frac{15}2} &\cssId{s13}{\ =\ \frac{14+1}2 } \cssId{s14}{\ =\ \frac{14}2 + \frac12}\\ &\cssId{s15}{\ =\ 7 + \frac 12 } \cssId{s16}{\ =\ 7 + 0.5}\\ &\cssId{s17}{\ =\ 7.5} \end{align} $$

To convert a negative fraction (say,
$\,-\frac{19}{2}$) to decimal form,
go through this thought process:
Firstly, the answer will be negative.
How many times does
$\,2\,$ go into
$\,19\,$?

Answer:
It goes in $\,9\,$ times,
with $\,1\,$ left over.
The answer is
$\,-9.5\,$.

Of course, if $\,2\,$ goes in evenly, then you don't need a decimal at all to report your answer. For example, $\,-\frac{16}2 = -8\,$.