Chapter 0.4, Problem 21E

To determine

To calculate: The simplified form of $\frac{1}{2}-\frac{1}{3}$ .

Answer to Problem 21E

The simplified form of $\frac{1}{2}-\frac{1}{3}$ is $\frac{1}{6}$ .

Explanation of Solution

Given information:

The statement “ $\frac{1}{2}-\frac{1}{3}$ .”

Formula used:

When two fractions with different denominators are subtracted then the two unlike fractions are converted into like fractions by multiplying the denominators with a common factor of their lowest common multiple(LCM).

Consider the provided statement “ $\frac{1}{2}-\frac{1}{3}$ .”

Recall that when two fractions with different denominators are subtracted then the two unlike fractions are converted into like fractions by multiplying the denominators with a common factor of their lowest common multiple(LCM).

LCM of 2 and 3 is 6.

So, multiply $\frac{1}{2}$ by 3 and $\frac{1}{3}$ by 2 in both numerator and denominator,

Thus, the given expression can be simplified as,

  $\begin{array}{c}\frac{1}{2}-\frac{1}{3}=\frac{1\times 3}{2\times 3}-\frac{1\times 2}{3\times 2}\\ \frac{1}{2}-\frac{1}{3}=\frac{3}{6}-\frac{2}{6}\\ \frac{1}{2}-\frac{1}{3}=\frac{3-2}{6}\\ \frac{1}{2}-\frac{1}{3}=\frac{1}{6}\end{array}$

Since, $\frac{1}{6}$ cannot be simplified further,

Hence, the simplified form of $\frac{1}{2}-\frac{1}{3}$ is $\frac{1}{6}$ .