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.