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Math Problems
Algebra 1
Properties of operations on rational and irrational numbers
The number
d
d
d
is irrational. Which statement about
6
−
d
6 - d
6
−
d
is true?
\newline
Choices:
\newline
(A)
6
−
d
6 - d
6
−
d
is rational.
\newline
(B)
6
−
d
6 - d
6
−
d
is irrational.
\newline
(C)
6
−
d
6 - d
6
−
d
can be rational or irrational, depending on the value of
d
d
d
.
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The number
b
b
b
is irrational. Which statement about
9
+
b
9 + b
9
+
b
is true?
\newline
Choices:
\newline
(A)
9
+
b
9 + b
9
+
b
is rational.
\newline
(B)
9
+
b
9 + b
9
+
b
is irrational.
\newline
(C)
9
+
b
9 + b
9
+
b
can be rational or irrational, depending on the value of
b
b
b
.
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The number
v
v
v
is rational. Which statement about
9
+
v
9 + v
9
+
v
is true?
\newline
Choices:
\newline
(A)
9
+
v
9 + v
9
+
v
is rational.
\newline
(B)
9
+
v
9 + v
9
+
v
is irrational.
\newline
(C)
9
+
v
9 + v
9
+
v
can be rational or irrational, depending on the value of
v
v
v
.
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The number
x
x
x
is rational. Which statement about
x
−
5
x - 5
x
−
5
is true?
\newline
Choices:
\newline
(A)
x
−
5
x - 5
x
−
5
is rational.
\newline
(B)
x
−
5
x - 5
x
−
5
is irrational.
\newline
(C)
x
−
5
x - 5
x
−
5
can be rational or irrational, depending on the value of
x
x
x
.
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The number
b
b
b
is rational. Which statement about
b
−
10
b - 10
b
−
10
is true?
\newline
Choices:
\newline
(A)
b
−
10
b - 10
b
−
10
is rational.
\newline
(B)
b
−
10
b - 10
b
−
10
is irrational.
\newline
(C)
b
−
10
b - 10
b
−
10
can be rational or irrational, depending on the value of
b
b
b
.
Get tutor help
The number
x
x
x
is rational. Which statement about
10
−
x
10 - x
10
−
x
is true?
\newline
Choices:
\newline
(A)
10
−
x
10 - x
10
−
x
is rational.
\newline
(B)
10
−
x
10 - x
10
−
x
is irrational.
\newline
(C)
10
−
x
10 - x
10
−
x
can be rational or irrational, depending on the value of
x
x
x
.
Get tutor help
The number
y
y
y
is irrational. Which statement about
y
−
6
y - 6
y
−
6
is true?
\newline
Choices:
\newline
(A)
y
−
6
y - 6
y
−
6
is rational.
\newline
(B)
y
−
6
y - 6
y
−
6
is irrational.
\newline
(C)
y
−
6
y - 6
y
−
6
can be rational or irrational, depending on the value of
y
y
y
.
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The number
z
z
z
is irrational. Which statement about
3
+
z
\sqrt{3} + z
3
+
z
is true?
\newline
Choices:
\newline
(A)
3
+
z
\sqrt{3} + z
3
+
z
is rational.
\newline
(B)
3
+
z
\sqrt{3} + z
3
+
z
is irrational.
\newline
(C)
3
+
z
\sqrt{3} + z
3
+
z
can be rational or irrational, depending on the value of
z
z
z
.
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The number
p
p
p
is rational. Which statement about
p
+
2
p + 2
p
+
2
is true?
\newline
Choices:
\newline
(A)
p
+
2
p + 2
p
+
2
is rational.
\newline
(B)
p
+
2
p + 2
p
+
2
is irrational.
\newline
(C)
p
+
2
p + 2
p
+
2
can be rational or irrational, depending on the value of
p
p
p
.
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The number
r
r
r
is irrational. Which statement about
7
−
r
7 - r
7
−
r
is true?
\newline
Choices:
\newline
(A)
7
−
r
7 - r
7
−
r
is rational.
\newline
(B)
7
−
r
7 - r
7
−
r
is irrational.
\newline
(C)
7
−
r
7 - r
7
−
r
can be rational or irrational, depending on the value of
r
r
r
.
Get tutor help
The number
b
b
b
is rational. Which statement about
b
+
10
b + 10
b
+
10
is true?
\newline
Choices:
\newline
(A)
b
+
10
b + 10
b
+
10
is rational.
\newline
(B)
b
+
10
b + 10
b
+
10
is irrational.
\newline
(C)
b
+
10
b + 10
b
+
10
can be rational or irrational, depending on the value of
b
b
b
.
Get tutor help
The number
q
q
q
is irrational. Which statement about
6
−
q
6 - q
6
−
q
is true?
\newline
Choices:
\newline
(A)
6
−
q
6 - q
6
−
q
is rational.
\newline
(B)
6
−
q
6 - q
6
−
q
is irrational.
\newline
(C)
6
−
q
6 - q
6
−
q
can be rational or irrational, depending on the value of
q
q
q
.
Get tutor help
The number
c
c
c
is rational. Which statement about
6
+
c
6 + c
6
+
c
is true?
\newline
Choices:
\newline
(A)
6
+
c
6 + c
6
+
c
is rational.
\newline
(B)
6
+
c
6 + c
6
+
c
is irrational.
\newline
(C)
6
+
c
6 + c
6
+
c
can be rational or irrational, depending on the value of
c
c
c
.
Get tutor help
The number
b
b
b
is rational. Which statement about
b
+
7
b + 7
b
+
7
is true?
\newline
Choices:
\newline
(A)
b
+
7
b + 7
b
+
7
is rational.
\newline
(B)
b
+
7
b + 7
b
+
7
is irrational.
\newline
(C)
b
+
7
b + 7
b
+
7
can be rational or irrational, depending on the value of
b
b
b
.
Get tutor help
The number
b
b
b
is rational. Which statement about
b
−
28
b - \sqrt{28}
b
−
28
is true?
\newline
Choices:
\newline
(A)
b
−
28
b - \sqrt{28}
b
−
28
is rational.
\newline
(B)
b
−
28
b - \sqrt{28}
b
−
28
is irrational.
\newline
(C)
b
−
28
b - \sqrt{28}
b
−
28
can be rational or irrational, depending on the value of
b
b
b
.
Get tutor help
The number
x
x
x
is irrational. Which statement about
x
+
11
x + \sqrt{11}
x
+
11
is true?
\newline
Choices:
\newline
(A)
x
+
11
x + \sqrt{11}
x
+
11
is rational.
\newline
(B)
x
+
11
x + \sqrt{11}
x
+
11
is irrational.
\newline
(C)
x
+
11
x + \sqrt{11}
x
+
11
can be rational or irrational, depending on the value of
x
x
x
.
Get tutor help
The number
x
x
x
is irrational. Which statement about
5
+
x
5 + x
5
+
x
is true?
\newline
Choices:
\newline
(A)
5
+
x
5 + x
5
+
x
is rational.
\newline
(B)
5
+
x
5 + x
5
+
x
is irrational.
\newline
(C)
5
+
x
5 + x
5
+
x
can be rational or irrational, depending on the value of
x
x
x
.
Get tutor help
The number
y
y
y
is irrational. Which statement about
3
+
y
3 + y
3
+
y
is true?
\newline
Choices:
\newline
(A)
3
+
y
3 + y
3
+
y
is rational.
\newline
(B)
3
+
y
3 + y
3
+
y
is irrational.
\newline
(C)
3
+
y
3 + y
3
+
y
can be rational or irrational, depending on the value of
y
y
y
.
Get tutor help
The number
y
y
y
is rational. Which statement about
y
−
2
y - 2
y
−
2
is true?
\newline
Choices:
\newline
(A)
y
−
2
y - 2
y
−
2
is rational.
\newline
(B)
y
−
2
y - 2
y
−
2
is irrational.
\newline
(C)
y
−
2
y - 2
y
−
2
can be rational or irrational, depending on the value of
y
y
y
.
Get tutor help
The number
y
y
y
is rational. Which statement about
21
+
y
\sqrt{21} + y
21
+
y
is true?
\newline
Choices:
\newline
(A)
21
+
y
\sqrt{21} + y
21
+
y
is rational.
\newline
(B)
21
+
y
\sqrt{21} + y
21
+
y
is irrational.
\newline
(C)
21
+
y
\sqrt{21} + y
21
+
y
can be rational or irrational, depending on the value of
y
y
y
.
Get tutor help
The number
u
u
u
is irrational. Which statement about
u
+
4
u + 4
u
+
4
is true?
\newline
Choices:
\newline
(A)
u
+
4
u + 4
u
+
4
is rational.
\newline
(B)
u
+
4
u + 4
u
+
4
is irrational.
\newline
(C)
u
+
4
u + 4
u
+
4
can be rational or irrational, depending on the value of
u
u
u
.
Get tutor help
The number
c
c
c
is irrational. Which statement about
c
−
10
c - 10
c
−
10
is true?
\newline
Choices:
\newline
(A)
c
−
10
c - 10
c
−
10
is rational.
\newline
(B)
c
−
10
c - 10
c
−
10
is irrational.
\newline
(C)
c
−
10
c - 10
c
−
10
can be rational or irrational, depending on the value of
c
c
c
.
Get tutor help
The number
w
w
w
is irrational. Which statement about
4
+
w
4 + w
4
+
w
is true?
\newline
Choices:
\newline
(A)
4
+
w
4 + w
4
+
w
is rational.
\newline
(B)
4
+
w
4 + w
4
+
w
is irrational.
\newline
(C)
4
+
w
4 + w
4
+
w
can be rational or irrational, depending on the value of
w
w
w
.
Get tutor help
The number
y
y
y
is irrational. Which statement about
28
−
y
\sqrt{28} - y
28
−
y
is true?
\newline
Choices:
\newline
(A)
28
−
y
\sqrt{28} - y
28
−
y
is rational.
\newline
(B)
28
−
y
\sqrt{28} - y
28
−
y
is irrational.
\newline
(C)
28
−
y
\sqrt{28} - y
28
−
y
can be rational or irrational, depending on the value of
y
y
y
.
Get tutor help
The number
s
s
s
is irrational. Which statement about
28
+
s
\sqrt{28} + s
28
+
s
is true?
\newline
Choices:
\newline
(A)
28
+
s
\sqrt{28} + s
28
+
s
is rational.
\newline
(B)
28
+
s
\sqrt{28} + s
28
+
s
is irrational.
\newline
(C)
28
+
s
\sqrt{28} + s
28
+
s
can be rational or irrational, depending on the value of
s
s
s
.
Get tutor help
Which of the following is a correct interpretation of the expression
−
4
−
(
−
7
)
?
-4-(-7) ?
−
4
−
(
−
7
)?
\newline
Choose
1
1
1
answer:
\newline
(A) The number that is
4
4
4
to the left of
−
7
-7
−
7
on the number line
\newline
(B) The number that is
4
4
4
to the right of
−
7
-7
−
7
on the number line
\newline
(C) The number that is
7
7
7
to the left of
−
4
-4
−
4
on the number line
\newline
(D) The number that is
7
7
7
to the right of
−
4
-4
−
4
on the number line
Get tutor help
Which of the following is a correct interpretation of the expression
1
+
6
?
1+6 ?
1
+
6
?
\newline
Choose
1
1
1
answer:
\newline
(A) The number that is
6
6
6
to the left of
1
1
1
on the number line
\newline
(B) The number that is
6
6
6
to the right of
1
1
1
on the number line
\newline
(C) The number that is
1
1
1
to the left of
−
6
-6
−
6
on the number line
\newline
(D) The number that is
1
1
1
to the right of
−
6
-6
−
6
on the number line
Get tutor help
Which of the following is a correct interpretation of the expression
−
2
+
(
−
7
)
?
-2+(-7) ?
−
2
+
(
−
7
)?
\newline
Choose
1
1
1
answer:
\newline
(A) The number that is
2
2
2
to the left of
7
7
7
on the number line
\newline
(B) The number that is
2
2
2
to the right of
7
7
7
on the number line
\newline
(C) The number that is
7
7
7
to the left of
−
2
-2
−
2
on the number line
\newline
(D) The number that is
7
7
7
to the right of
−
2
-2
−
2
on the number line
Get tutor help
Which of the following is a correct interpretation of the expression
9
+
(
−
7
)
?
9+(-7) ?
9
+
(
−
7
)?
\newline
Choose
1
1
1
answer:
\newline
(A) The number that is
7
7
7
to the left of
9
9
9
on the number line
\newline
(B) The number that is
7
7
7
to the right of
9
9
9
on the number line
\newline
(C) The number that is
9
9
9
to the left of
7
7
7
on the number line
\newline
(D) The number that is
9
9
9
to the right of
7
7
7
on the number line
Get tutor help
Which of the following is a correct interpretation of the expression
2
+
7
2+7
2
+
7
?
\newline
Choose
1
1
1
answer:
\newline
(A) The number that is
2
2
2
to the left of
−
7
-7
−
7
on the number line
\newline
(B) The number that is
2
2
2
to the right of
−
7
-7
−
7
on the number line
\newline
(C) The number that is
7
7
7
to the left of
2
2
2
on the number line
\newline
(D) The number that is
7
7
7
to the right of
2
2
2
on the number line
Get tutor help
Which of the following is a correct interpretation of the expression
−
6
−
(
−
5
)
?
-6-(-5) ?
−
6
−
(
−
5
)?
\newline
Choose
1
1
1
answer:
\newline
(A) A The number that is
6
6
6
to the left of
−
5
-5
−
5
on the number line
\newline
(B) The number that is
6
6
6
to the right of
−
5
-5
−
5
on the number line
\newline
(C) The number that is
5
5
5
to the left of
−
6
-6
−
6
on the number line
\newline
(D) The number that is
5
5
5
to the right of
−
6
-6
−
6
on the number line
Get tutor help
Let
a
a
a
be a non-zero rational number and
b
b
b
be an irrational number. Is
a
b
\frac{a}{b}
b
a
rational or irrational? Choose
1
1
1
answer:
\newline
(A) Rational
\newline
(B) Irrational
\newline
(C) It can be either rational or irrational
Get tutor help
Let
a
a
a
and
b
b
b
be rational numbers, and let
b
b
b
be non-zero. Is
a
b
\frac{a}{b}
b
a
rational or irrational?
\newline
Choose
1
1
1
answer:
\newline
(A) Rational
\newline
(B) Irrational
\newline
(C) It can be either rational or irrational
Get tutor help
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