Q15. - Algebra 1

Question

The simplified value of the expression $3\frac{1}{2}.1\frac{1}{2}$.

Step-by-Step Solution

Answer

The simplified value of the expression $3\frac{1}{2}.1\frac{1}{2}$ is $\frac{21}{4}$.

Step 1. Given

The expression $3\frac{1}{2}·1\frac{1}{2}$.

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 $\left(\right),\times \mathrm{or}·$.

Step 3. Calculation.

Consider the expression $3\frac{1}{2}·1\frac{1}{2}$.

 

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, $3\frac{1}{2}$ will be converted as,

$$\begin{gathered} 3\frac{1}{2}=\frac{\left(3\times 2\right)+1}{2} \\ =\frac{7}{2} \end{gathered}$$ 

 

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

$$\begin{gathered} 1\frac{1}{2}=\frac{\left(1\times 2\right)+1}{2} \\ =\frac{3}{2} \end{gathered}$$        

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,

$\begin{array}{c}3\frac{1}{2}·1\frac{1}{2}=\frac{7}{2}·\frac{3}{2}\\ =\frac{7·3}{2·2}\\ =\frac{21}{4}\end{array}$

Thus, the simplified value of the expression $3\frac{1}{2}·1\frac{1}{2}$ is $\frac{21}{4}$.