In the proof that the product of a/b

Question

and c/d
, where a, b, c, and d are integers and b and d are non-zero, what does the Closure Property tell you about the products a⋅c
and b⋅d
? Enter 1 for option 1 and 2 for option 2.

Option 1: They are both imaginary numbers.

Option 2: They are both integers.

Answer 1

In the context of the proof that the product of \( \frac{a}{b} \) and \( \frac{c}{d} \) leads to a valid fraction, the Closure Property tells us about the behavior of integers under multiplication. Specifically, the products \( a \cdot c \) and \( b \cdot d \) are both integers since they result from multiplying integers \( a \) and \( c \), as well as \( b \) and \( d \).

Therefore, the correct answer is:

2 for option 2: They are both integers.