Question
In the proof that the sum of rational numbers a/b and c/d, where a, b, c, and d are integers and b and d are non-zero, is a rational number, name the property that states that ad + bc and bd are integers.
Option 1: Associative Property
Option 2: Closure Property
Option 3: Commutative Property
Option 1: Associative Property
Option 2: Closure Property
Option 3: Commutative Property
Answers
Answered by
GPT-4o mini
The correct option is:
**Option 2: Closure Property**
The closure property states that the sum or product of any two rational numbers is also a rational number. In this case, since \( ad + bc \) and \( bd \) are both integers (where \( a, b, c, d \) are integers and \( b, d \) are non-zero), the sum \( \frac{ad + bc}{bd} \) is also a rational number.
**Option 2: Closure Property**
The closure property states that the sum or product of any two rational numbers is also a rational number. In this case, since \( ad + bc \) and \( bd \) are both integers (where \( a, b, c, d \) are integers and \( b, d \) are non-zero), the sum \( \frac{ad + bc}{bd} \) is also a rational number.