Chapter SR4, Problem 49P

Solution

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

  $\frac{5}{6}$

Given:

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

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 2 and 3 is 6. So, make both denominators equal to the LCM and combine the numerators of the common LCM to simplify further as shown below

  $\begin{array}{c}\frac{1}{2}+\frac{1}{3}=\frac{1}{2}\cdot \frac{3}{3}+\frac{1}{3}\cdot \frac{2}{2}\\ =\frac{3}{6}+\frac{2}{6}\\ =\frac{3+2}{6}\\ =\frac{5}{6}\end{array}$

Thus, the simplified expression is $\frac{5}{6}$ .