Chapter SR4, Problem 51P

Solution

To simplify the expression $\frac{4}{5}+\frac{1}{8}$ .

  $\frac{37}{40}$

Given:

The expression, $\frac{4}{5}+\frac{1}{8}$.

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 5 and 8 is 40. So, make both denominators equal to the LCM and combine the numerators of the common LCM to simplify further as shown below

  $\begin{array}{c}\frac{4}{5}+\frac{1}{8}=\frac{4}{5}\cdot \frac{8}{8}+\frac{1}{8}\cdot \frac{5}{5}\\ =\frac{32}{40}+\frac{5}{40}\\ =\frac{32+5}{40}\\ =\frac{37}{40}\end{array}$

Thus, the simplified expression is $\frac{37}{40}$ .