Chapter 0.5, Problem 21E

To determine

To find: The simplified value of the expression $-\frac{30}{11}\cdot \left(-\frac{1}{3}\right)$ .

Answer to Problem 21E

The simplified value of the expression $-\frac{30}{11}\cdot \left(-\frac{1}{3}\right)$ is $\frac{10}{11}$ .

Explanation of Solution

Given information:

The expression $-\frac{30}{11}\cdot \left(-\frac{1}{3}\right)$ .

Formula used:

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 two negative real numbers is always positive.

Calculation:

Consider the expression $-\frac{30}{11}\cdot \left(-\frac{1}{3}\right)$ .

  $30$ can be written as the product of 3 and 10.

So, it can be simplified as,

  $-\frac{30}{11}\cdot \left(-\frac{1}{3}\right)=+\frac{10\cdot 3\cdot 1}{11\cdot 3}$

Striking off the common terms, we get,

  $-\frac{30}{11}\cdot \left(-\frac{1}{3}\right)=\frac{10\cdot 1}{11}$

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,

  $-\frac{30}{11}\cdot \left(-\frac{1}{3}\right)=\frac{10}{11}$

Thus, the simplified value of the expression $-\frac{30}{11}\cdot \left(-\frac{1}{3}\right)$ is $\frac{10}{11}$ .