In the proof that the sum of rational numbers ab
and cd
, 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. Enter 1 for option 1, 2 for option 2, and 3 for option 3.
Option 1: Associative Property
Option 2: Closure Property
Option 3: Commutative Property
Option 2: Closure Property
Without solving, will the sum of 4.2+36−−√
be rational or irrational? Enter 1 for rational. Enter 2 for irrational. (1 point)
What must be true about ab
if cd
and ad+bcbd
are both rational numbers? Enter 1 for option 1 and 2 for option 2.
Option 1: ab
is rational
Option 2: ab
is irrational
Option 1: ab is rational
Without solving, will the product of 49−−√
and 13
be rational or irrational? Enter 1 for rational. Enter 2 for irrational.(1 point)
Remaining Attempts :
1. Rational
Without solving, will the product of √49
and 1/3
be rational or irrational? Enter 1 for rational. Enter 2 for irrational.(1 point)
Remaining Attempts :
1. Rational
In the proof that the product of ab
and cd
, 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.