Chapter 5.7, Problem 53E

To determine

Towrite:The simplest form ofexpression $\frac{5t}{2}-\frac{t}{6}$ .

Answer to Problem 53E

The simplest form of expression $\frac{5t}{2}-\frac{t}{6}$ is $\frac{7t}{3}$ .

Explanation of Solution

Given information: Considerthe expression $\frac{5t}{2}-\frac{t}{6}$ provided in the question.

Calculation:

To simplify the provided term $\frac{5t}{2}-\frac{t}{6}$ ,it is needed to calculate Least common multiple of $2\text{and}6$ is $6$ ,which is the Least common denominator of fraction $\frac{5t}{2}\text{and}\frac{t}{6}$ .

Make the denominator of both fractions as $6$ and operate the numerator

Therefore,

  $\begin{array}{l}\Rightarrow \frac{5t}{2}-\frac{t}{6}=\frac{5t\times 3}{2\times 3}-\frac{t}{6}\\ \Rightarrow \frac{5t}{2}-\frac{t}{6}=\frac{15t}{6}-\frac{t}{6}\\ \Rightarrow \frac{5t}{2}-\frac{t}{6}=\frac{15t-t}{6}\\ \Rightarrow \frac{5t}{2}-\frac{t}{6}=\frac{14t}{6}=\frac{7t}{3}\end{array}$

Hence,

The simplest form of expression $\frac{5t}{2}-\frac{t}{6}$ is $\frac{7t}{3}$ .