Question

Find each quantity. \(\frac{1}{2}\) of \(\frac{1}{2}\)

Short answer

\frac{1}{4}\

Step-by-step solution

Understand the Problem

We need to find \(\frac{1}{2}\) of \( \frac{1}{2} \). This means we need to multiply the two fractions together.

Multiply the Numerators

Multiply the numerators (the top numbers) of the fractions: \(1 \times 1 = 1\).

Multiply the Denominators

Multiply the denominators (the bottom numbers) of the fractions: \(2 \times 2 = 4\).

Write the Result

Combine the results from Steps 2 and 3 to get the final answer: \( \frac{1}{4} \).

Key concepts

numerator

Fractions are made up of two parts: the numerator and the denominator. The numerator is the top number in a fraction. It represents how many parts of the whole are being considered.

In our example, we have \(\frac{1}{2}\). Here, 1 is the numerator. When we multiply fractions, we multiply their numerators together. For instance, in the exercise, we multiplied \(\frac{1}{2}\) by \(\frac{1}{2}\). We first multiplied their numerators:

• Step 2: Multiplying numerators 1 and 1 gives 1. \[1 \times 1 = 1\ \]

Understanding the role of the numerator is crucial to mastering fraction multiplication.

denominator

Moving onto the denominator, which is the bottom number in a fraction. It tells us into how many equal parts the whole is divided. For our fraction \(\frac{1}{2}\), the denominator is 2, meaning the whole is divided into 2 equal parts.

When multiplying fractions, we also multiply their denominators. In the exercise, the denominators were part of the calculation:

• Step 3: Multiplying denominators 2 and 2 gives 4. \[2 \times 2 = 4\ \]

Combining the new numerator and denominator, we get our final fraction.

Understanding the concept of denominators helps you see how fractions represent parts of a whole.

step-by-step solution

Let's put everything together with a step-by-step solution to multiply fractions. This method helps break down the process and makes it easier to understand.

• Step 1: Understand the problem. We need to find what \(\frac{1}{2}\) of \(\frac{1}{2}\) is, which means multiplying the fractions.


• Step 2: Multiply the numerators. Take the numerators (1 and 1) and multiply them: \[1 \times 1 = 1\ \]


• Step 3: Multiply the denominators. Take the denominators (both 2) and multiply them: \[2 \times 2 = 4\ \]


• Step 4: Write the result. Combine the results from Step 2 and Step 3 to get the fraction: \(\frac{1}{4}\).

Following these steps helps demystify fraction multiplication and can be applied to solve similar problems with different fractions.