Chapter 0.5, Problem 24E

To determine

To find: The simplified value of the expression $\frac{2}{7}\cdot 4\frac{2}{3}$ .

Answer to Problem 24E

The simplified value of the expression $\frac{2}{7}\cdot 4\frac{2}{3}$ is $\frac{4}{3}$ .

Explanation of Solution

Given information:

The expression $\frac{2}{7}\cdot 4\frac{2}{3}$ .

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 $\frac{2}{7}\cdot 4\frac{2}{3}$ .

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, $4\frac{2}{3}$ will be converted as,

  $\begin{array}{c}4\frac{2}{3}=\frac{\left(4\times 3\right)+2}{3}\\ =\frac{14}{3}\end{array}$

14 can be written as the product of 7 and 2.

So, $\frac{2}{7}\cdot 4\frac{2}{3}$ can be simplified as,

  $\begin{array}{c}\frac{2}{7}\cdot 4\frac{2}{3}=\frac{2}{7}\cdot \frac{14}{3}\\ =\frac{2\cdot 2\cdot 7}{7\cdot 3}\end{array}$

Striking off the common terms, we get,

  $\frac{2}{7}\cdot 4\frac{2}{3}=\frac{2\cdot 2}{3}$

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,

  $\frac{2}{7}\cdot 4\frac{2}{3}=\frac{4}{3}$

Thus, the simplified value of the expression $\frac{2}{7}\cdot 4\frac{2}{3}$ is $\frac{4}{3}$ .