To determine which property of equality [tex]\( \frac{c}{b} = \frac{d}{b} \)[/tex] represents given that [tex]\( c = d \)[/tex] and [tex]\( b \neq 0 \)[/tex], let's break down the problem step by step.
1. Starting with the given equality:
We know that [tex]\( c = d \)[/tex].
2. Understanding the property applied:
To go from [tex]\( c = d \)[/tex] to [tex]\( \frac{c}{b} = \frac{d}{b} \)[/tex], we are dividing both sides of the equation [tex]\( c = d \)[/tex] by the same nonzero number [tex]\( b \)[/tex].
3. Identifying the property:
The property that states that dividing both sides of an equation by the same nonzero number maintains the equality is known as the Division Property of Equality. This property ensures that the equality holds true after division.
Therefore, the equation [tex]\( \frac{c}{b} = \frac{d}{b} \)[/tex] demonstrates the Division Property of Equality.
So, the answer is B) division.
