Chapter SR4, Problem 65P

Solution

To simplify the expression $\frac{15}{16}-\frac{7}{10}+\frac{1}{2}$ .

  $\frac{59}{80}$

Given:

The expression, $\frac{15}{16}-\frac{7}{10}+\frac{1}{2}$.

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 16, 10, and 2 is 80. So, make all denominators equal to the LCM and combine the numerators over the common LCM to simplify further as shown below

  $\begin{array}{c}\frac{15}{16}-\frac{7}{10}+\frac{1}{2}=\frac{15}{16}\cdot \frac{5}{5}-\frac{7}{10}\cdot \frac{8}{8}+\frac{1}{2}\cdot \frac{40}{40}\\ =\frac{75}{80}-\frac{56}{80}+\frac{40}{80}\\ =\frac{75-56+40}{80}\\ =\frac{59}{80}\end{array}$

Thus, the simplified expression is $\frac{59}{80}$ .