Problem 29 - Introductory Algebra for College Students

Question

Perform the indicated subtraction. $$\frac{1}{5}-\left(-\frac{3}{5}\right)$$

Step-by-Step Solution

Answer

\(\frac{4}{5}\)

Step 1: Identify the Problem

We want to subtract \(- \frac{3}{5}\) from \(\frac{1}{5}\). Since subtracting a negative number is equivalent to adding a positive number, the expression can be rewritten as \(\frac{1}{5} + \frac{3}{5}\).

Step 2: Add the Fractions

Since the fractions have the same denominator, we can simply add their numerators. Adding together 1 and 3 we get 4. Therefore, \(\frac{1}{5} + \frac{3}{5} = \frac{4}{5}\).

Step 3: Verification

To verify the result, one can substitute \(\frac{1}{5} + \frac{3}{5} = \frac{4}{5}\) into the original problem. The original problem states \(\frac{1}{5}-\left(-\frac{3}{5}\right)\). Rewriting this as \(\frac{1}{5} + \frac{3}{5}\), it can be verified that the solution is indeed \(\frac{4}{5}\).