Chapter SR4, Problem 56P

Solution

To simplify the expression $\frac{2}{3}-\frac{1}{6}$ .

  $\frac{1}{2}$

Given:

The expression, $\frac{2}{3}-\frac{1}{6}$.

Concept Used:

To add or subtract fractions with unlike denominators, follow the below steps:

Step 1: Find the least common multiple (LCM) for the denominators.

Step 2: Multiply the numerator and denominator to get like denominators.

Step 3: Turn the other fractions into equivalent fractions.

Step 4: Add the numerators over the common denominator.

Step 5: Simplify and reduce the answer if necessary.

Calculation:

In order to simplify the given expression, note that the least common multiple of 3 and 6 is 6. So, make both denominators equal to the LCM and combine the numerators of the common LCM to simplify further as shown below

  $\begin{array}{c}\frac{2}{3}-\frac{1}{6}=\frac{2}{3}\cdot \frac{2}{2}-\frac{1}{6}\\ =\frac{4}{6}-\frac{1}{6}\\ =\frac{4-1}{6}\\ =\frac{3}{6}\\ =\frac{1}{2}\end{array}$

Thus, the simplified expression is $\frac{1}{2}$ .