Chapter SH, Problem 6OWF

Solution

To simplify the expression $5\frac{1}{2}-3\frac{2}{5}$ .

  $\frac{21}{10}\text{ or }2\frac{1}{10}$

Given:

The expression, $5\frac{1}{2}-3\frac{2}{5}$.

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, rewrite the mixed fraction as improper fractions as shown below

  $5\frac{1}{2}-3\frac{2}{5}=\frac{11}{2}-\frac{17}{5}$

Now, to simplify the fractions, note that the least common denominator of 2 and 5 is 10. So, make both denominator equal to the LCM and combine the numerators directly over the common denominator as shown below

  $\begin{array}{c}5\frac{1}{2}-3\frac{2}{5}=\frac{11}{2}-\frac{17}{5}\\ =\frac{11}{2}\cdot \frac{5}{5}-\frac{17}{5}\cdot \frac{2}{2}\\ =\frac{55}{10}-\frac{34}{10}\\ =\frac{55-34}{10}\\ =\frac{21}{10}\\ =2\frac{1}{10}\end{array}$

Thus, the simplified expression is $\frac{21}{10}\text{ or }2\frac{1}{10}$ .