Question

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

Answer 1

Without solving, will the sum of 4.2+36−−√
be rational or irrational? Enter 1 for rational. Enter 2 for irrational. (1 point)

Answer 2

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

Answer 3

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 :

Answer 4

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 :

Answer 5

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.

Answer 6

Option 2: Closure Property

Answer 7

2. irrational

Answer 8

Option 1: ab is rational

Answer 9

1. Rational

Answer 10

1. Rational

Answer 11

Option 2: They are both integers.