Chapter SH, Problem 2OWF

Solution

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

  $\frac{7}{6}$

Given:

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

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 denominator of 2 and 3 is 6. So, make both denominator equal to the LCM and combine the numerators directly over the common denominator as shown below

  $\begin{array}{c}\frac{1}{2}+\frac{2}{3}=\frac{1}{2}\cdot \frac{3}{3}+\frac{2}{3}\cdot \frac{2}{2}\\ =\frac{3}{6}+\frac{4}{6}\\ =\frac{3+4}{6}\\ =\frac{7}{6}\end{array}$

Thus, the simplified expression is $\frac{7}{6}$ .