Chapter SR4, Problem 61P

Solution

To simplify the expression $\frac{7}{8}+\frac{3}{16}-\frac{1}{4}$ .

  $\frac{13}{16}$

Given:

The expression, $\frac{7}{8}+\frac{3}{16}-\frac{1}{4}$.

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 8, 16, and 4 is 16. So, make all denominators equal to the LCM and combine the numerators over the common LCM to simplify further as shown below

  $\begin{array}{c}\frac{7}{8}+\frac{3}{16}-\frac{1}{4}=\frac{7}{8}\cdot \frac{2}{2}+\frac{3}{16}-\frac{1}{4}\cdot \frac{4}{4}\\ =\frac{14}{16}+\frac{3}{16}-\frac{4}{16}\\ =\frac{14+3-4}{16}\\ =\frac{13}{16}\end{array}$

Thus, the simplified expression is $\frac{13}{16}$ .