, 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, 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, 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+bcbd
reduces to a whole number, which is a subset of rational numbers.
By the Closure Property, the fraction with numerator A d plus b c and denominator b d reduces to a whole number, which is a subset of rational numbers.
1 answer
The correct response would be:
"By the Closure Property, ad + bc and bd are both integers, and so ad + bc/bd is a quotient of two integers."
This answer effectively explains that since \( ad + bc \) and \( bd \) are both integers (because \( a, b, c, d \) are all integers and \( b \) and \( d \) are non-zero), the result \( \frac{ad + bc}{bd} \) is a rational number, as rational numbers are defined as the quotient of two integers where the denominator is not zero.
