Chapter SR4, Problem 63P

Solution

To simplify the expression $\frac{1}{6}+\frac{4}{15}+\frac{1}{3}$ .

  $\frac{23}{30}$

Given:

The expression, $\frac{1}{6}+\frac{4}{15}+\frac{1}{3}$.

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 6, 15, and 3 is 30. So, make all denominators equal to the LCM and combine the numerators over the common LCM to simplify further as shown below

  $\begin{array}{c}\frac{1}{6}+\frac{4}{15}+\frac{1}{3}=\frac{1}{6}\cdot \frac{5}{5}+\frac{4}{15}\cdot \frac{2}{2}+\frac{1}{3}\cdot \frac{10}{10}\\ =\frac{5}{30}+\frac{8}{30}+\frac{10}{30}\\ =\frac{5+8+10}{30}\\ =\frac{23}{30}\end{array}$

Thus, the simplified expression is $\frac{23}{30}$ .