Problem 135 - Introductory Algebra for College Students

Question

What is the Fundamental Principle of Fractions?

Step-by-Step Solution

Answer

The Fundamental Principle of Fractions states that if the same nonzero number is multiplied or divided into both the numerator and the denominator of a fraction, the value of the fraction will not change. For example, \( \frac{3}{4} = \frac{6}{8} \) when both the numerator and the denominator are multiplied by 2.

Step 1: Introduction to the Fundamental Principle of Fractions

The 'Fundamental Principle of Fractions' (FPF), also known as the 'Fundamental Theorem of Fractions', is a foundational concept in maths that defines something key about fractions. It's important to understand this principle when working with fractions.

Step 2: Define the Fundamental Principle of Fractions

The Fundamental Principle of Fractions states that if the same nonzero number is multiplied or divided into both the numerator and the denominator of a fraction, the value of the fraction does not change.

Step 3: Illustrate with an example

For example, consider the fraction \( \frac{3}{4} \). Multiplying both the numerator and denominator by 2 results in \( \frac{6}{8} \). Despite the numbers being different, both these fractions have the same value or represent the same quantity. So, the Fundamental Principle of Fractions is maintained.