Equivalent Fractions Calculator

Understanding Equivalent Fractions

What are Equivalent Fractions?

Equivalent fractions are fractions that represent the same value or portion of a whole, even though they may look different. In other words, equivalent fractions are different ways of expressing the same quantity. This concept is fundamental in mathematics and is widely used in various fields, including engineering, physics, and everyday calculations.

Formula for Equivalent Fractions

The basic formula for creating equivalent fractions is:

\[\frac{a}{b} = \frac{a \times n}{b \times n}\]

Where:

• \(a\) is the numerator of the original fraction
• \(b\) is the denominator of the original fraction
• \(n\) is any non-zero number (positive or negative)

Creating Equivalent Fractions

To create an equivalent fraction, follow these steps:

1. Choose a non-zero number to multiply by (let's call it n)
2. Multiply both the numerator and denominator by n
3. The resulting fraction is equivalent to the original fraction

Calculation Steps

Let's create an equivalent fraction for 2/3:

1. Choose a multiplier, say 4
2. Multiply numerator: 2 × 4 = 8
3. Multiply denominator: 3 × 4 = 12

Therefore, 2/3 = 8/12

Example with Visual Representation

Let's visualize the equivalence of 2/3 and 8/12:

This diagram shows that 2/3 and 8/12 represent the same portion of a whole, despite having different numerators and denominators.