Problem 36 - Introductory Algebra for College Students

Question

Perform the indicated subtraction. $$\frac{2}{5}-\left(-\frac{1}{10}\right)$$

Step-by-Step Solution

Answer

The result of the subtraction \(\frac{2}{5}-\left(-\frac{1}{10}\right)\) is \(\frac{1}{2}\).

Step 1: Simplify the Expression

Rewrite the given arithmetic operation taking into account that subtracting a negative number is equivalent to adding a positive number. So, the original expression \(\frac{2}{5}-\left(-\frac{1}{10}\right)\) simplifies to \(\frac{2}{5}+\frac{1}{10}\).

Step 2: Find Common Denominator

In order to add or subtract fractions, the fractions must have the same denominator. The common denominator for fractions \(\frac{2}{5}\) and \(\frac{1}{10}\) is 10 because 10 is the least common multiple of 10 and 5.

Step 3: Re-write Fractions Using Common Denominator

Now, re-write the fractions so that they both have the denominator of 10. This gives: \(\frac{4}{10}+\frac{1}{10}\), since we multiplied the numerator and denominator of \(\frac{2}{5}\) by 2 to achieve the equivalent fraction with denominator 10.

Step 4: Add the fractions

Now the fractions can be added: \(\frac{4}{10}+\frac{1}{10} = \frac{5}{10}\)

Step 5: Simplify the result

Reduce the fraction to its lowest term, yielding \(\frac{1}{2}\) as the final result, as 5 is a common factor for both the numerator and denominator in \(\frac{5}{10}\).