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Math Problems
Algebra 2
Multiply and divide rational expressions
Which of the following is a whole number?
\newline
Choices:
\newline
(A)
11
3
\frac{11}{3}
3
11
\newline
(B)
−
5
-5
−
5
\newline
(C)
8
8
8
\newline
(D)
3
6
\frac{3}{6}
6
3
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What is the value of
q
2
−
p
2
q^{2}-p^{2}
q
2
−
p
2
for
q
=
4
q=4
q
=
4
and
p
=
2
p=2
p
=
2
?
\newline
A.
2
2
2
\newline
B.
4
4
4
\newline
C.
8
8
8
\newline
D.
12
12
12
\newline
E.
14
14
14
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Select all the expressions that are equivalent to
(
2
8
)
0
(2^8)^0
(
2
8
)
0
.
\newline
Multi-select Choices:
\newline
(A)
1
2
8
\frac{1}{2^8}
2
8
1
\newline
(B)
2
8
2^8
2
8
\newline
(C)
1
2
0
\frac{1}{2^0}
2
0
1
\newline
(D)
2
2
2
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Select all of the true statements.
\newline
Multi-select Choices:
\newline
(A)
4
×
1
0
−
6
4 \times 10^{-6}
4
×
1
0
−
6
is
0.02
0.02
0.02
times as much as
2
×
1
0
−
4
2 \times 10^{-4}
2
×
1
0
−
4
.
\newline
(B)
6
×
1
0
−
3
6 \times 10^{-3}
6
×
1
0
−
3
is
150
150
150
times as much as
4
×
1
0
−
5
4 \times 10^{-5}
4
×
1
0
−
5
.
\newline
(C)
4
×
1
0
5
4 \times 10^{5}
4
×
1
0
5
is
80
80
80
times as much as
5
×
1
0
4
5 \times 10^{4}
5
×
1
0
4
.
\newline
(D)
9
×
1
0
−
4
9 \times 10^{-4}
9
×
1
0
−
4
is
0.02
0.02
0.02
0
0
0
times as much as
0.02
0.02
0.02
1
1
1
.
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Subtract. Simplify your answer.
\newline
(
r
3
−
9
r
2
+
3
r
)
−
(
8
r
3
−
8
r
2
+
3
r
−
7
)
(r^{3}-9r^{2}+3r)-(8r^{3}-8r^{2}+3r-7)
(
r
3
−
9
r
2
+
3
r
)
−
(
8
r
3
−
8
r
2
+
3
r
−
7
)
\newline
◻
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Divide.
\newline
(
25
x
z
0
+
20
x
6
z
0
)
÷
(
−
4
x
3
z
5
)
(25 xz^{0}+20x^{6}z^{0})\div(-4x^{3}z^{5})
(
25
x
z
0
+
20
x
6
z
0
)
÷
(
−
4
x
3
z
5
)
\newline
Simplify your answer as much as possible.
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Divide.
\newline
Write your answer in simplest form.
\newline
−
5
4
÷
4
3
=
?
-\frac{5}{4} \div \frac{4}{3}=?
−
4
5
÷
3
4
=
?
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Divide.
\newline
Write your answer in simplest form.
\newline
2
3
÷
(
−
2
7
)
=
?
\frac{2}{3} \div\left(-\frac{2}{7}\right)=?
3
2
÷
(
−
7
2
)
=
?
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Divide.
\newline
Write your answer in simplest form.
\newline
1
7
÷
5
2
=
?
\frac{1}{7} \div \frac{5}{2}=?
7
1
÷
2
5
=
?
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Divide.
\newline
Write your answer in simplest form.
\newline
9
7
÷
(
−
9
5
)
=
?
\frac{9}{7} \div\left(-\frac{9}{5}\right)=?
7
9
÷
(
−
5
9
)
=
?
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Divide.
\newline
Write your answer in simplest form.
\newline
−
5
7
÷
1
5
=
?
-\frac{5}{7} \div \frac{1}{5}=?
−
7
5
÷
5
1
=
?
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Divide.
\newline
Write your answer in simplest form.
\newline
1
9
÷
5
4
=
?
\frac{1}{9} \div \frac{5}{4}=?
9
1
÷
4
5
=
?
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Divide.
\newline
Write your answer in simplest form.
\newline
−
4
3
÷
9
5
=
?
-\frac{4}{3} \div \frac{9}{5}=?
−
3
4
÷
5
9
=
?
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Divide.
\newline
Write your answer in simplest form.
\newline
1
7
÷
2
5
=
?
\frac{1}{7} \div \frac{2}{5}=?
7
1
÷
5
2
=
?
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Divide.
\newline
Write your answer in simplest form.
\newline
2
9
÷
(
−
6
5
)
=
?
\frac{2}{9} \div\left(-\frac{6}{5}\right)=?
9
2
÷
(
−
5
6
)
=
?
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Divide.
\newline
Write your answer in simplest form.
\newline
−
3
7
÷
3
8
=
?
-\frac{3}{7} \div \frac{3}{8}=?
−
7
3
÷
8
3
=
?
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Divide.
\newline
Write your answer in simplest form.
\newline
−
5
2
÷
5
7
=
?
-\frac{5}{2} \div \frac{5}{7}=?
−
2
5
÷
7
5
=
?
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Divide.
\newline
Write your answer in simplest form.
\newline
5
3
÷
(
−
6
7
)
=
?
\frac{5}{3} \div\left(-\frac{6}{7}\right)=\text { ? }
3
5
÷
(
−
7
6
)
=
?
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Divide.
\newline
Write your answer in simplest form.
\newline
−
8
3
÷
1
4
=
?
-\frac{8}{3} \div \frac{1}{4}=?
−
3
8
÷
4
1
=
?
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Divide.
\newline
Write your answer in simplest form.
\newline
1
2
÷
(
−
1
7
)
=
?
\frac{1}{2} \div\left(-\frac{1}{7}\right)=?
2
1
÷
(
−
7
1
)
=
?
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Divide.
\newline
Write your answer in simplest form.
\newline
4
5
÷
(
−
2
9
)
=
?
\frac{4}{5} \div\left(-\frac{2}{9}\right)=?
5
4
÷
(
−
9
2
)
=
?
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Divide.
\newline
Write your answer in simplest form.
\newline
2
5
÷
2
3
=
?
\frac{2}{5} \div \frac{2}{3}=?
5
2
÷
3
2
=
?
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Divide.
\newline
Write your answer in simplest form.
\newline
−
7
9
÷
9
8
=
?
-\frac{7}{9} \div \frac{9}{8}=?
−
9
7
÷
8
9
=
?
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Divide.
\newline
Write your answer in simplest form.
\newline
−
3
2
÷
7
4
=
?
-\frac{3}{2} \div \frac{7}{4}=?
−
2
3
÷
4
7
=
?
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Chad was asked whether the following equation is an identity:
\newline
(
3
x
+
2
y
)
2
=
(
3
x
+
2
y
)
(
3
x
−
2
y
)
+
2
(
2
y
)
2
(3 x+2 y)^{2}=(3 x+2 y)(3 x-2 y)+2(2 y)^{2}
(
3
x
+
2
y
)
2
=
(
3
x
+
2
y
)
(
3
x
−
2
y
)
+
2
(
2
y
)
2
\newline
He performed the following steps:
\newline
(
3
x
+
2
y
)
2
(3 x+2 y)^{2}
(
3
x
+
2
y
)
2
\newline
↪
Step
1
=
9
x
2
+
4
y
2
\stackrel{\text { Step } 1}{\hookrightarrow}=9 x^{2}+4 y^{2}
↪
Step
1
=
9
x
2
+
4
y
2
\newline
↪
Step
2
=
9
x
2
+
4
y
2
+
4
y
2
−
4
y
2
\stackrel{\text { Step } 2}{\hookrightarrow}=9 x^{2}+4 y^{2}+4 y^{2}-4 y^{2}
↪
Step
2
=
9
x
2
+
4
y
2
+
4
y
2
−
4
y
2
\newline
↪
Step
3
=
(
9
x
2
−
4
y
2
)
+
8
y
2
\stackrel{\text { Step } 3}{\hookrightarrow}=\left(9 x^{2}-4 y^{2}\right)+8 y^{2}
↪
Step
3
=
(
9
x
2
−
4
y
2
)
+
8
y
2
\newline
↪
Step
4
=
(
3
x
+
2
y
)
(
3
x
−
2
y
)
+
2
(
2
y
)
2
\stackrel{\text { Step } 4}{\hookrightarrow}=(3 x+2 y)(3 x-2 y)+2(2 y)^{2}
↪
Step
4
=
(
3
x
+
2
y
)
(
3
x
−
2
y
)
+
2
(
2
y
)
2
\newline
For this reason, Chad stated that the equation is a true identity.
\newline
Is Chad correct? If not, in which step did he make a mistake?
\newline
Choose
1
1
1
answer:
\newline
(A) Chad is correct.
\newline
(B) Chad is incorrect. He made a mistake in step
1
1
1
.
\newline
(C) Chad is incorrect. He made a mistake in step
2
2
2
.
\newline
(D) Chad is incorrect. He made a mistake in step
4
4
4
.
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Solve the following equation for
x
x
x
. Express your answer in the simplest form.
\newline
9
(
−
8
x
+
2
)
−
9
=
−
5
−
3
2
(
−
6
x
−
10
)
9(-8 x+2)-9=-5-\frac{3}{2}(-6 x-10)
9
(
−
8
x
+
2
)
−
9
=
−
5
−
2
3
(
−
6
x
−
10
)
\newline
Get tutor help
Question
\newline
Rewrite in simplest terms:
−
6
(
0.6
w
−
3
w
−
0.9
)
−
0.9
w
-6(0.6 w-3 w-0.9)-0.9 w
−
6
(
0.6
w
−
3
w
−
0.9
)
−
0.9
w
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Calculate
0.75
÷
3
/
4
−
0.75
÷
3
/
8
+
0.375
÷
3
/
8
−
0.0625
÷
1
/
8
0.75 \div 3 / 4-0.75 \div 3 / 8+0.375 \div 3 / 8-0.0625 \div 1 / 8
0.75
÷
3/4
−
0.75
÷
3/8
+
0.375
÷
3/8
−
0.0625
÷
1/8
.
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Solve. Graph each solution on a number line.
\newline
5
−
3
c
≤
c
+
17
5-3 c \leq c+17
5
−
3
c
≤
c
+
17
\newline
(A)
c
≥
−
3
c \geq-3
c
≥
−
3
\newline
(B)
c
>
−
3
c>-3
c
>
−
3
\newline
(C)
c
≥
3
c \geq 3
c
≥
3
\newline
(D)
c
≤
−
3
c \leq-3
c
≤
−
3
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Simplify. Write your answer using whole numbers and variables.
\newline
j
2
−
7
j
j
−
7
\frac{j^2 - 7j}{j - 7}
j
−
7
j
2
−
7
j
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Simplify. Write your answer using whole numbers and variables.
\newline
u
2
−
u
u
−
1
\frac{u^2 - u}{u - 1}
u
−
1
u
2
−
u
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Simplify. Write your answer using whole numbers and variables.
\newline
r
−
3
r
2
−
3
r
\frac{r - 3}{r^2 - 3r}
r
2
−
3
r
r
−
3
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Divide. Write your answer in simplest form.
\newline
5
h
+
4
3
÷
(
5
h
+
4
)
\frac{5h +4}{3}\div {(5h + 4)}
3
5
h
+
4
÷
(
5
h
+
4
)
Get tutor help
Divide. Write your answer in simplest form.
\newline
m
−
4
10
m
3
−
6
m
2
÷
7
5
\frac{m - 4}{10m^3 - 6m^2} \div \frac{7}{5}
10
m
3
−
6
m
2
m
−
4
÷
5
7
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Divide. Write your answer in simplest form.
\newline
2
k
−
5
k
+
4
÷
(
2
k
−
5
)
\frac{2k - 5}{k + 4} \div (2k - 5)
k
+
4
2
k
−
5
÷
(
2
k
−
5
)
Get tutor help
Divide. Write your answer in simplest form.
\newline
25
j
3
−
5
j
2
3
j
+
2
÷
5
j
2
\frac{25j^3 - 5j^2}{3j + 2} \div 5j^2
3
j
+
2
25
j
3
−
5
j
2
÷
5
j
2
Get tutor help
Multiply. Write your answer in simplest form.
\newline
3
p
2
−
4
p
5
p
+
4
×
5
p
+
4
p
\frac{3p^2 - 4p}{5p + 4} \times \frac{5p + 4}{p}
5
p
+
4
3
p
2
−
4
p
×
p
5
p
+
4
Get tutor help
Multiply. Write your answer in simplest form.
\newline
4
k
−
3
5
k
×
(
k
2
−
1
)
\frac{4k - 3}{5k} \times (k^2 - 1)
5
k
4
k
−
3
×
(
k
2
−
1
)
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Divide. Write your answer in simplest form.
\newline
9
r
2
−
1
r
+
3
÷
2
r
\frac{9r^2 - 1}{r + 3} \div 2r
r
+
3
9
r
2
−
1
÷
2
r
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Multiply. Simplify your answer.
\newline
15
y
2
z
15
z
×
19
y
2
z
16
z
\frac{15y^2z}{15z} \times \frac{19y^2z}{16z}
15
z
15
y
2
z
×
16
z
19
y
2
z
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Multiply. Write your answer in simplest form.
\newline
j
2
4
j
+
1
×
9
j
2
−
6
j
+
1
2
j
−
1
\frac{j^2}{4j + 1} \times \frac{9j^2 - 6j + 1}{2j - 1}
4
j
+
1
j
2
×
2
j
−
1
9
j
2
−
6
j
+
1
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Multiply. Write your answer in simplest form.
\newline
3
d
+
5
5
d
2
⋅
d
+
4
3
d
+
5
\frac{3d + 5}{5d^2} \cdot \frac{d + 4}{3d + 5}
5
d
2
3
d
+
5
⋅
3
d
+
5
d
+
4
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Multiply. Simplify your answer.
\newline
4
r
16
q
r
×
18
q
2
11
q
r
\frac{4r}{16qr} \times \frac{18q^2}{11qr}
16
q
r
4
r
×
11
q
r
18
q
2
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Divide. Write your answer in simplest form.
\newline
v
2
v
+
3
÷
5
v
−
1
v
2
−
4
\frac{v}{2v + 3} \div \frac{5v - 1}{v^2 - 4}
2
v
+
3
v
÷
v
2
−
4
5
v
−
1
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Divide. Write your answer in simplest form.
\newline
14
g
−
7
g
+
1
÷
3
g
+
5
3
g
\frac{14g - 7}{g + 1} \div \frac{3g + 5}{3g}
g
+
1
14
g
−
7
÷
3
g
3
g
+
5
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Divide. Write your answer in simplest form.
\newline
v
−
5
35
v
+
14
÷
v
−
5
7
\frac{v - 5}{35v + 14} \div \frac{v - 5}{7}
35
v
+
14
v
−
5
÷
7
v
−
5
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Divide. Write your answer in simplest form.
\newline
4
p
2
−
4
p
+
1
6
p
÷
p
−
4
p
+
5
\frac{4p^2 - 4p + 1}{6p} \div \frac{p - 4}{p + 5}
6
p
4
p
2
−
4
p
+
1
÷
p
+
5
p
−
4
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Divide. Write your answer in simplest form.
\newline
2
x
3
−
3
x
2
2
x
+
3
÷
x
2
2
x
+
3
\frac{2x^3 - 3x^2}{2x + 3} \div \frac{x^2}{2x + 3}
2
x
+
3
2
x
3
−
3
x
2
÷
2
x
+
3
x
2
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Multiply. Write your answer in simplest form.
\newline
g
+
4
g
−
4
×
g
2
+
7
g
+
6
2
g
\frac{g + 4}{g - 4} \times \frac{g^2 + 7g + 6}{2g}
g
−
4
g
+
4
×
2
g
g
2
+
7
g
+
6
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Divide. Write your answer in simplest form.
\newline
2
g
−
3
g
2
−
1
÷
g
2
2
g
+
3
\frac{2g - 3}{g^2 - 1} \div \frac{g^2}{2g + 3}
g
2
−
1
2
g
−
3
÷
2
g
+
3
g
2
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1
2
3
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