Verified Answer :

  • Identify the least common denominator for the fractions \(\frac{1}{4}\) and \(\frac{1}{2}\), which is 4.
  • Convert \(\frac{1}{2}\) to the equivalent fraction \(\frac{2}{4}\).
  • Add the numerators of the two fractions over the common denominator: \(\frac{1}{4} + \frac{2}{4} = \frac{3}{4}\).
  • The simplest form of the sum is \(\boxed{\frac{3}{4}}\).

Explanation

  1. Analyzing the Fractions

To add the fractions \(\frac{1}{4}\) and \(\frac{1}{2}\), we must first ensure they have a common denominator. The denominators are 4 and 2. The least common multiple (LCM) of 4 and 2 is 4.

  1. Finding a Common Denominator

We convert \(\frac{1}{2}\) to an equivalent fraction with a denominator of 4. We do this by multiplying both the numerator and the denominator by 2:
\[\frac{1 \times 2}{2 \times 2} = \frac{2}{4}.\]

  1. Performing the Addition

Now that both fractions have the same denominator, we can add them by summing their numerators while keeping the denominator the same:
\[\frac{1}{4} + \frac{2}{4} = \frac{1+2}{4} = \frac{3}{4}.\]

  1. Finalizing the Result

The resulting fraction is \(\frac{3}{4}\). Since the greatest common divisor of 3 and 4 is 1, the fraction is already in its simplest form. Thus, the final answer is \(\boxed{\frac{3}{4}}\).

Examples

Adding fractions is a fundamental skill used in many everyday situations, such as cooking or DIY projects. For instance, if a recipe calls for \(\frac{1}{4}\) cup of sugar for one part of a cake and \(\frac{1}{2}\) cup for another, you need to add these amounts together to know how much sugar you need in total. Calculating \(\frac{1}{4} + \frac{1}{2} = \frac{3}{4}\) ensures that your recipe measurements are accurate, leading to perfectly baked goods.

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