In the proof that ab+cd
, where a, b, c, and d are integers and b and d are non-zero, explain why ad+bcbd
is a rational number.(1 point)
Responses
By the Closure Property, a quotient of imaginary numbers is a rational number.
By the Closure Property, a quotient of imaginary numbers is a rational number.
By the Closure Property, ad+bc
and bd
are both quotients of integers, and so ad+bcbd
is a quotient of two integers.
By the Closure Property, A d plus b c and b d are both quotients of integers, and so the fraction with numerator A d plus b c and denominator b d is a quotient of two integers.
By the Closure Property, ad+bc
and bd
are both integers, and so ad+bcbd
is a quotient of two integers.
By the Closure Property, A d plus b c and b d are both integers, and so the fraction with numerator A d plus b c and denominator b d is a quotient of two integers.
By the Closure Property, ad+bcbd
reduces to a whole number, which is a subset of rational numbers.
1. C 0.6 + 9/10
2. C By the closure property, ad + bc and bd are both integers
3. A rational
4. D rational
5. B jolene
By the Closure Property, ad+bcbd reduces to a whole number, which is a subset of rational numbers.
I'm sorry, but I don't understand what you are asking. Can you please provide more context or clarify your question?
The correct response is:
By the Closure Property, ad+bc and bd are both integers, and so ad+bcbd is a quotient of two integers.
I'm sorry, but neither of the responses provided would be correct explanations for why ad+bcbd is a rational number.
To explain why ad+bcbd is a rational number, we can use the definition of rational numbers.
A rational number is defined as any number that can be expressed as the quotient or fraction of two integers, where the denominator is not equal to zero.
In the expression ad+bcbd, we have a sum of two terms: ad and bcbd.
Here's how we can show that ad+bcbd is a rational number:
1. ad is a product of two integers (a and d), and we know that the product of two integers is always an integer.
2. bcbd is also a product of two integers (bc and bd), and again, the product of two integers is always an integer.
3. Since ad and bcbd are both integers, their sum, ad+bcbd, will also be an integer.
4. Therefore, ad+bcbd can be expressed as the quotient or fraction of two integers (the numerator being ad+bcbd and the denominator being 1).
5. Since the denominator is not equal to zero, ad+bcbd satisfies the definition of a rational number.
So, ad+bcbd is indeed a rational number.