﻿ Writing Fractions With a Denominator of 2 in Decimal Form

# 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, $\,-\frac{16}2 = -8\,$.