Chapter 0.5, Problem 14E

To determine

The simplified value of the expression $2\frac{1}{2}\cdot \left(-\frac{1}{4}\right)$ .

Answer to Problem 14E

The simplified value of the expression $2\frac{1}{2}\cdot \left(-\frac{1}{4}\right)$ is $-\frac{5}{8}$ .

Explanation of Solution

Given information:

The expression $2\frac{1}{2}\cdot \left(-\frac{1}{4}\right)$ .

Formula used:

Mixed fractions of the form $m\frac{p}{q}$ can be converted into proper fractions as,

  $m\frac{p}{q}=\frac{\left(m\times q\right)+p}{q}$

Product of two real numbers is obtained when they are multiplied together. That is two or more numbers are separated by multiplication signs $\left(\right),\times \text{ or }\cdot$ .

Product of a negative and a positive integer is always negative.

Calculation:

Consider the expression $2\frac{1}{2}\cdot \left(-\frac{1}{4}\right)$ .

Recall that mixed fractions of the form $m\frac{p}{q}$ can be converted into proper fractions as,

  $m\frac{p}{q}=\frac{\left(m\times q\right)+p}{q}$

So, $2\frac{1}{2}$ will be converted as,

  $\begin{array}{c}2\frac{1}{2}=\frac{\left(2\times 2\right)+1}{2}\\ =\frac{5}{2}\end{array}$

Recall that product of two real numbers is obtained when they are multiplied together. That is two or more numbers are separated by multiplication signs $\left(\right),\times \text{ or }\cdot$ .

Simplify it,

  $\begin{array}{c}\frac{5}{2}\cdot \left(-\frac{1}{4}\right)=-\frac{1\cdot 5}{2\cdot 4}\\ =-\frac{5}{8}\end{array}$

Thus, the simplified value of the expression $2\frac{1}{2}\cdot \left(-\frac{1}{4}\right)$ is $-\frac{5}{8}$ .