Problem 38 - Introductory Algebra for College Students

Question

Perform the indicated subtraction. $$\frac{2}{5}-\frac{1}{10}$$

Step-by-Step Solution

Answer

The solution is \(\frac{3}{10}\).

Step 1: Identify common denominator

The first step is to find a common denominator for both fractions. In this case, the smallest number that both 5 and 10 can divide into is 10.

Step 2: Convert fractions to equivalent fractions

The second step is to convert the fractions to an equivalent form, with a denominator of 10. To do this, multiply the numerator and denominator of \(\frac{2}{5}\) by 2. This gives \(\frac{4}{10}\). The fraction \(\frac{1}{10}\) is already in this form, so no change is needed.

Step 3: Perform the subtraction

The final step is to perform the subtraction of the two fractions. Subtract the numerator of \(\frac{1}{10}\) from the numerator of \(\frac{4}{10}\) to get the final answer.