Chapter 0.5, Problem 15E

To determine

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

Answer to Problem 15E

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

Explanation of Solution

Given information:

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

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 $\left(\right),\times \text{ or }\cdot$ .

Calculation:

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

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,

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

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

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

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,

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

Thus, the simplified value of the expression

  $3\frac{1}{2}\cdot 1\frac{1}{2}$ is $\frac{21}{4}$ .