Chapter SR4, Problem 60P

Solution

To simplify the expression $\frac{9}{10}-\frac{1}{5}-\frac{1}{2}$ .

  $\frac{3}{10}$

Given:

The expression, $\frac{9}{10}-\frac{1}{5}-\frac{1}{2}$.

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 10, 5, and 2 is 10. So, make all denominators equal to the LCM and combine the numerators over the common LCM to simplify further as shown below

  $\begin{array}{c}\frac{9}{10}-\frac{1}{5}-\frac{1}{2}=\frac{9}{10}-\frac{1}{5}\cdot \frac{2}{2}-\frac{1}{2}\cdot \frac{5}{5}\\ =\frac{9}{10}-\frac{2}{10}-\frac{5}{10}\\ =\frac{9-2-5}{10}\\ =\frac{3}{10}\end{array}$

Thus, the simplified expression is $\frac{3}{10}$ .