Chapter P, Problem 1PST

Find the most simplified answer for the given problems involving fractions:

$\frac{5}{2}-6=$

To determine

To find:

The most simplified answer for the problem “$\frac{5}{2}-6=$” involving fractions.

Answer to Problem 1PST

Solution:

The simplified answer is $-\frac{7}{2}$.

Explanation of Solution

Definition:

For all expressions P, Q, R, with $Q\ne 0$, $\frac{P}{Q}+\frac{R}{Q}=\frac{P+R}{Q}$ and $\frac{P}{Q}-\frac{R}{Q}=\frac{P-R}{Q}$.

If the fractions have different denominators, find the common denominator and then proceed as indicated above.

Calculation:

The given expression is $\frac{5}{2}-6$.

The number 6 can be written in fraction as $\frac{6}{1}$.

Rewriting the given expression, $\frac{5}{2}-\frac{6}{1}$.

Here 2 is the common denominator, because it has each of 2, 1 as factors.

$\begin{array}{rll}\frac{5}{2}-6& =& \frac{5}{2}-\frac{6}{1}\\ & =& \frac{5}{2}-\frac{6\left(2\right)}{1\left(2\right)}\\ & =& \frac{5}{2}-\frac{12}{2}\\ & =& \frac{5-12}{2}\\ & =& \frac{-7}{2}\\ \frac{5}{2}-6& =& -\frac{7}{2}\end{array}$

Hence, the simplified answer for the given problem is $-\frac{7}{2}$.