Multiplying Fractions: A Comprehensive Guide

What is Fraction Multiplication?

Fraction multiplication is the process of finding the product of two or more fractions. This operation is fundamental in mathematics and has numerous real-world applications.

Formula and Its Components

The general formula for multiplying two fractions is:

\[\frac{a}{b} \times \frac{c}{d} = \frac{ac}{bd}\]

Where:

• \(\frac{a}{b}\) is the first fraction
• \(\frac{c}{d}\) is the second fraction
• \(a\) and \(c\) are numerators
• \(b\) and \(d\) are denominators

Calculation Steps

1. Multiply the numerators: \(a \times c\)
2. Multiply the denominators: \(b \times d\)
3. Write the result as a new fraction: \(\frac{ac}{bd}\)
4. Simplify the resulting fraction if possible

Example with Calculation

Let's multiply \(\frac{2}{3}\) and \(\frac{3}{4}\):

\[\frac{2}{3} \times \frac{3}{4} = \frac{2 \times 3}{3 \times 4} = \frac{6}{12} = \frac{1}{2}\]

Visual Representation

This visual representation shows how multiplying \(\frac{2}{3}\) and \(\frac{3}{4}\) results in \(\frac{1}{2}\) of the total area.