Problem 35 - Introductory Algebra for College Students

Question

Perform the indicated subtraction. $$\frac{1}{2}-\left(-\frac{1}{4}\right)$$

Step-by-Step Solution

Answer

The result of the operation is \(\frac{3}{4}\).

Step 1 - Change of Subtraction of a Negative Fraction to Addition

In mathematics, subtracting a negative number is the same as adding a positive number. Thus, the operation \(\frac{1}{2}-\left(-\frac{1}{4}\right)\) becomes \(\frac{1}{2}+\frac{1}{4}\)

Step 2 - Addition of Fractions

When adding fractions, if the denominators are not the same, one needs to make them the same before proceeding. In this case, they're already different. A common denominator for 2 and 4 will be 4. So, this results in the sum becomes \(\frac{2}{4}+\frac{1}{4}\). Now, it's just a matter of adding the numerators which gives \(\frac{3}{4}\).