Sums and products of rational number quick check
1. According to the Closure Property, which of these sums results in a rational number?(1 point)
Responses
36−−√+221−−−√
Start Root 36 End Root plus Start Root 221 End Root
0.643892553…+34
0.643892553 dot dot dot plus Start Fraction 3 over 4 End Fraction
0.6¯¯¯¯+910
0 point Modifying above 6 with bar plus Start Fraction 9 over 10 End Fraction
π+4–√
pi plus Start Root 4 End Root
2.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)
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, ad+bc and bd are both integers, and so ad+bcbd is a quotient of two integers.
By the Closure Property, ad+bcbd reduces to a whole number, which is a subset of rational number
3.The sum of two rational numbers is always(1 point)
Responses
radical.
zero.
irrational.
rational.
4. The Closure Property implies that the product of 4/5 and 15 is what type of number?(1 point)
irrational
rational
an integer
zero
5. Malanna says that when she multiplies two rational numbers, her product will be irrational. Jolene says that the product in this case will be rational. Who is correct?(1 point)
Responses
Neither of them, it depends on the number.
Malanna
Both options are possible depending on the numbers.
Jolene
How can you rewrite 812 using a root?(1 point)
Responses
1. 12−−√8
root index 8 Start Root Start Fraction 1 over 2 End Fraction End Root
2. 8–√1
root index 1 Start Root 8 End Root
3. 8–√12
root index Start Fraction 1 over 2 End Fraction Start Root 8 End Root
4. 8–√
Start Root 8 End Root
Neither of them, it depends on the numbers.
can i ask you another question
Of course! Feel free to ask another question.
According to the Closure Property, which of these sums results in a rational number?(1 point)
Responses
36−−√+221−−−√
Start Root 36 End Root plus Start Root 221 End Root
0.643892553…+34
0.643892553 dot dot dot plus Start Fraction 3 over 4 End Fraction
0.6¯¯¯¯+910
0 point Modifying above 6 with bar plus Start Fraction 9 over 10 End Fraction
π+4–√
According to the Closure Property, the sum that results in a rational number is:
0.643892553…+34
0.643892553 dot dot dot plus Start Fraction 3 over 4 End Fraction
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.
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.
By the Closure Property, ad+bc and bd are both integers, and so ad+bcbd is a quotient of two integers.
The sum of two rational numbers is always(1 point)
Responses
radical.
zero.
irrational.
rational.