Question

property
\\(\frac{a cdot cancel{c}}{b cdot cancel{c}} = \frac{a}{b}\\)

Explanation:

To determine the property shown by the equation \(\boldsymbol{\frac{a \cdot c}{b \cdot c} = \frac{a}{b}}\) (assuming \(c
eq 0\)):

Step 1: Recall Fraction Properties

A fundamental property of fractions states that multiplying (or dividing) both the numerator and denominator of a fraction by the same non - zero number does not change the value of the fraction. This is known as the Simplification (or Cancellation) Property of Fractions (also related to the concept of equivalent fractions).

Step 2: Analyze the Given Equation

In the equation \(\frac{a \cdot c}{b \cdot c}=\frac{a}{b}\), we are taking the fraction \(\frac{a\cdot c}{b\cdot c}\) and removing the common factor \(c\) from both the numerator (\(a\cdot c\)) and the denominator (\(b\cdot c\)). As long as \(c
eq0\) (because division by zero is undefined), we can cancel out the non - zero common factor \(c\) from the numerator and the denominator, and the value of the fraction remains the same.

This property is also related to the Fundamental Law of Fractions or the concept of reducing a fraction to its simplest form by canceling common factors.

Answer:

This equation represents the Simplification (Cancellation) Property of Fractions (or the Fundamental Law of Fractions), where a non - zero common factor (\(c\)) is canceled from the numerator and denominator of a fraction, leaving an equivalent fraction.