Q14. - Algebra 1

Question

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

Step-by-Step Solution

Answer

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

Step 1.

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

Step 2. Concept.

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

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

 

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

 

The product of a negative and a positive integer is always negative.

Step 3. Calculation.

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

 

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,

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

Step 4. Simplification.

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 $\left(\right),\times \mathrm{or}·$.

 

Simplify it,

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

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