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Math Problems
Grade 7
Identify equivalent linear expressions I
Grant and Tim made
8
8
8
.
2
2
2
gallons of chili. About how many liters of chili did they make?
\newline
(
1
1
1
gallon
≈
3.785
\approx 3.785
≈
3.785
liters)
\newline
Choose
1
1
1
answer:
\newline
(A)
31
31
31
\newline
(B)
12
12
12
\newline
(C)
4
4
4
.
4
4
4
\newline
(D)
3
3
3
.
8
8
8
Get tutor help
In a recent survey of
1
1
1
,
000
000
000
randomly selected registered voters in the town of Armstrong,
803
803
803
are in favor of installing bicycle safety signs. Based on the survey results, approximately how many of Armstrong's
16
16
16
,
092
092
092
registered voters are in favor of installing bicycle safety signs?
\newline
Choose
1
1
1
answer:
\newline
(A)
803
803
803
\newline
(B)
3
3
3
,
170
170
170
\newline
(C)
12
12
12
,
922
922
922
\newline
(D)
15
15
15
,
092
092
092
Get tutor help
Which of the following expressions is equivalent to
−
2
(
−
x
2
−
3
)
-2\left(-x^{2}-3\right)
−
2
(
−
x
2
−
3
)
?
\newline
Choose
1
1
1
answer:
\newline
(A)
2
x
2
−
6
2 x^{2}-6
2
x
2
−
6
\newline
(B)
2
x
2
−
3
2 x^{2}-3
2
x
2
−
3
\newline
(C)
2
x
2
+
3
2 x^{2}+3
2
x
2
+
3
\newline
(D)
2
x
2
+
6
2 x^{2}+6
2
x
2
+
6
Get tutor help
Which of the following expressions is equivalent to
−
3
(
x
2
−
4
y
2
)
-3\left(x^{2}-4 y^{2}\right)
−
3
(
x
2
−
4
y
2
)
?
\newline
Choose
1
1
1
answer:
\newline
(A)
−
3
x
2
−
12
y
2
-3 x^{2}-12 y^{2}
−
3
x
2
−
12
y
2
\newline
(B)
−
3
x
2
−
4
y
2
-3 x^{2}-4 y^{2}
−
3
x
2
−
4
y
2
\newline
(C)
−
3
x
2
+
12
y
2
-3 x^{2}+12 y^{2}
−
3
x
2
+
12
y
2
\newline
(D)
−
7
x
2
y
2
-7 x^{2} y^{2}
−
7
x
2
y
2
Get tutor help
Which of the following is equivalent to
(
x
2
+
1
)
+
(
2
x
−
1
)
\left(x^{2}+1\right)+(2 x-1)
(
x
2
+
1
)
+
(
2
x
−
1
)
?
\newline
Choose
1
1
1
answer:
\newline
(A)
x
2
−
2
x
+
2
x^{2}-2 x+2
x
2
−
2
x
+
2
\newline
(B)
x
2
+
2
x
x^{2}+2 x
x
2
+
2
x
\newline
(C)
x
2
+
2
x
+
1
x^{2}+2 x+1
x
2
+
2
x
+
1
\newline
(D)
3
x
2
3 x^{2}
3
x
2
Get tutor help
Which of the following is an equivalent form of
(
2
x
+
3
)
−
(
7
x
−
6
)
?
(2 x+3)-(7 x-6) ?
(
2
x
+
3
)
−
(
7
x
−
6
)?
\newline
Choose
1
1
1
answer:
\newline
(A)
−
5
x
−
3
-5 x-3
−
5
x
−
3
\newline
(B)
−
5
x
+
9
-5 x+9
−
5
x
+
9
\newline
(C)
4
x
4 x
4
x
\newline
(D)
9
x
−
3
9 x-3
9
x
−
3
Get tutor help
8
v
28
w
+
21
−
3
v
+
10
4
w
+
3
\frac{8 v}{28 w+21}-\frac{3 v+10}{4 w+3}
28
w
+
21
8
v
−
4
w
+
3
3
v
+
10
\newline
Which expression is equivalent to the difference?
\newline
Choose
1
1
1
answer:
\newline
(A)
8
v
2
−
21
v
+
10
24
w
+
18
\frac{8 v^{2}-21 v+10}{24 w+18}
24
w
+
18
8
v
2
−
21
v
+
10
\newline
(B)
−
13
v
+
10
24
w
+
18
\frac{-13 v+10}{24 w+18}
24
w
+
18
−
13
v
+
10
\newline
(C)
53
v
+
10
28
w
+
21
\frac{53 v+10}{28 w+21}
28
w
+
21
53
v
+
10
\newline
(D)
−
13
v
−
70
28
w
+
21
\frac{-13 v-70}{28 w+21}
28
w
+
21
−
13
v
−
70
Get tutor help
Which of the following is equivalent to
(
3
x
y
)
(
2
x
7
)
\frac{\left(\frac{3 x}{y}\right)}{\left(\frac{2 x}{7}\right)}
(
7
2
x
)
(
y
3
x
)
?
\newline
Choose
1
1
1
answer:
\newline
(A)
21
2
y
\frac{21}{2 y}
2
y
21
\newline
(B)
42
y
42 y
42
y
\newline
(C)
2
y
21
\frac{2 y}{21}
21
2
y
\newline
(D)
6
x
2
7
y
\frac{6 x^{2}}{7 y}
7
y
6
x
2
Get tutor help
Which of the following is equivalent to
(
3
x
2
)
(
3
x
+
2
)
\frac{\left(\frac{3 x}{2}\right)}{\left(\frac{3}{x}+2\right)}
(
x
3
+
2
)
(
2
3
x
)
?
\newline
Choose
1
1
1
answer:
\newline
(A)
9
4
\frac{9}{4}
4
9
\newline
(B)
3
x
+
2
9
\frac{3 x+2}{9}
9
3
x
+
2
\newline
(C)
9
x
2
4
\frac{9 x^{2}}{4}
4
9
x
2
\newline
(D)
3
x
2
6
+
4
x
\frac{3 x^{2}}{6+4 x}
6
+
4
x
3
x
2
Get tutor help
Which of the following is equivalent to
(
a
+
6
c
)
(
2
a
+
6
2
c
)
\frac{\left(\frac{a+6}{c}\right)}{\left(\frac{2 a+6}{2 c}\right)}
(
2
c
2
a
+
6
)
(
c
a
+
6
)
?
\newline
Choose
1
1
1
answer:
\newline
(A)
c
2
\frac{c}{2}
2
c
\newline
(B)
a
+
6
a
+
3
\frac{a+6}{a+3}
a
+
3
a
+
6
\newline
(C)
a
+
6
2
(
a
+
3
)
\frac{a+6}{2(a+3)}
2
(
a
+
3
)
a
+
6
\newline
(D)
1
1
1
Get tutor help
Which of the following expressions is equivalent to
−
55
r
+
77
−
88
r
−
44
\frac{-55 r+77}{-88 r-44}
−
88
r
−
44
−
55
r
+
77
?
\newline
Choose
1
1
1
answer:
\newline
(A)
−
5
r
−
7
−
8
r
−
4
\frac{-5 r-7}{-8 r-4}
−
8
r
−
4
−
5
r
−
7
\newline
(B)
−
5
r
+
77
−
8
r
−
44
\frac{-5 r+77}{-8 r-44}
−
8
r
−
44
−
5
r
+
77
\newline
(C)
−
5
r
+
7
−
8
r
−
4
\frac{-5 r+7}{-8 r-4}
−
8
r
−
4
−
5
r
+
7
\newline
(D)
−
5
r
+
7
8
r
+
4
\frac{-5 r+7}{8 r+4}
8
r
+
4
−
5
r
+
7
Get tutor help
For
t
≠
0
t \neq 0
t
=
0
, which of the following expressions is equivalent to
−
12
t
2
−
18
t
8
t
2
+
18
t
\frac{-12 t^{2}-18 t}{8 t^{2}+18 t}
8
t
2
+
18
t
−
12
t
2
−
18
t
?
\newline
Choose
1
1
1
answer:
\newline
(A)
6
t
+
9
4
t
+
9
\frac{6 t+9}{4 t+9}
4
t
+
9
6
t
+
9
\newline
(B)
−
6
t
+
9
4
t
+
9
\frac{-6 t+9}{4 t+9}
4
t
+
9
−
6
t
+
9
\newline
(C)
−
6
t
−
1
4
t
+
1
\frac{-6 t-1}{4 t+1}
4
t
+
1
−
6
t
−
1
\newline
(D)
−
6
t
−
9
4
t
+
9
\frac{-6 t-9}{4 t+9}
4
t
+
9
−
6
t
−
9
Get tutor help
Which of the following expressions is equivalent to
−
2
p
+
8
2
p
+
2
\frac{-2 p+8}{2 p+2}
2
p
+
2
−
2
p
+
8
?
\newline
Choose
1
1
1
answer:
\newline
(A)
−
p
+
8
p
+
2
\frac{-p+8}{p+2}
p
+
2
−
p
+
8
\newline
(B)
−
p
+
4
2
p
+
2
\frac{-p+4}{2 p+2}
2
p
+
2
−
p
+
4
\newline
(C)
−
p
+
4
p
+
1
\frac{-p+4}{p+1}
p
+
1
−
p
+
4
\newline
(D)
p
+
4
p
+
1
\frac{p+4}{p+1}
p
+
1
p
+
4
Get tutor help
Which of the following expressions is equivalent to
72
n
+
8
40
n
+
72
\frac{72 n+8}{40 n+72}
40
n
+
72
72
n
+
8
?
\newline
Choose
1
1
1
answer:
\newline
(A)
9
n
+
8
5
n
+
9
\frac{9 n+8}{5 n+9}
5
n
+
9
9
n
+
8
\newline
(B)
9
n
+
1
5
n
+
72
\frac{9 n+1}{5 n+72}
5
n
+
72
9
n
+
1
\newline
(C)
9
n
+
1
40
n
+
72
\frac{9 n+1}{40 n+72}
40
n
+
72
9
n
+
1
\newline
(D)
9
n
+
1
5
n
+
9
\frac{9 n+1}{5 n+9}
5
n
+
9
9
n
+
1
Get tutor help
Which of the following expressions is equivalent to
9
n
45
n
+
9
\frac{9 n}{45 n+9}
45
n
+
9
9
n
?
\newline
Choose
1
1
1
answer:
\newline
(A)
1
6
\frac{1}{6}
6
1
\newline
(B)
n
5
n
+
1
\frac{n}{5 n+1}
5
n
+
1
n
\newline
(C)
n
5
n
+
9
\frac{n}{5 n+9}
5
n
+
9
n
\newline
(D)
n
45
n
+
1
\frac{n}{45 n+1}
45
n
+
1
n
Get tutor help
Which of the following expressions is equivalent to
9
x
−
12
−
12
x
−
3
\frac{9 x-12}{-12 x-3}
−
12
x
−
3
9
x
−
12
?
\newline
Choose
1
1
1
answer:
\newline
(A)
3
x
−
4
4
x
+
1
\frac{3 x-4}{4 x+1}
4
x
+
1
3
x
−
4
\newline
(B)
3
x
+
4
−
4
x
+
1
\frac{3 x+4}{-4 x+1}
−
4
x
+
1
3
x
+
4
\newline
(C)
3
x
−
4
−
4
x
−
1
\frac{3 x-4}{-4 x-1}
−
4
x
−
1
3
x
−
4
\newline
(D)
−
3
x
−
4
4
x
+
1
\frac{-3 x-4}{4 x+1}
4
x
+
1
−
3
x
−
4
Get tutor help
Which of the following expressions is equivalent to
24
−
12
k
+
84
\frac{24}{-12 k+84}
−
12
k
+
84
24
?
\newline
Choose
1
1
1
answer:
\newline
(A)
2
k
+
7
\frac{2}{k+7}
k
+
7
2
\newline
(B)
2
−
k
+
7
\frac{2}{-k+7}
−
k
+
7
2
\newline
(C)
2
−
k
+
84
\frac{2}{-k+84}
−
k
+
84
2
\newline
(D)
2
−
12
k
+
7
\frac{2}{-12 k+7}
−
12
k
+
7
2
Get tutor help
Which of the following expressions is equivalent to
54
k
−
12
−
48
k
+
42
\frac{54 k-12}{-48 k+42}
−
48
k
+
42
54
k
−
12
?
\newline
Choose
1
1
1
answer:
\newline
(A)
9
k
−
2
−
8
k
+
7
\frac{9 k-2}{-8 k+7}
−
8
k
+
7
9
k
−
2
\newline
(B)
9
k
−
2
8
k
+
7
\frac{9 k-2}{8 k+7}
8
k
+
7
9
k
−
2
\newline
(C)
9
k
−
2
−
8
k
−
7
\frac{9 k-2}{-8 k-7}
−
8
k
−
7
9
k
−
2
\newline
(D)
9
k
−
12
−
8
k
+
7
\frac{9 k-12}{-8 k+7}
−
8
k
+
7
9
k
−
12
Get tutor help
Which of the following expressions is equivalent to
8
p
+
8
−
32
p
+
4
\frac{8 p+8}{-32 p+4}
−
32
p
+
4
8
p
+
8
?
\newline
Choose
1
1
1
answer:
\newline
(A)
p
+
2
−
4
p
+
1
\frac{p+2}{-4 p+1}
−
4
p
+
1
p
+
2
\newline
(B)
2
p
+
2
−
8
p
+
1
\frac{2 p+2}{-8 p+1}
−
8
p
+
1
2
p
+
2
\newline
(C)
2
p
+
2
8
p
+
1
\frac{2 p+2}{8 p+1}
8
p
+
1
2
p
+
2
\newline
(D)
p
+
1
−
8
p
+
1
\frac{p+1}{-8 p+1}
−
8
p
+
1
p
+
1
Get tutor help
Which of the following expressions is equivalent to
49
r
+
14
42
r
+
42
\frac{49 r+14}{42 r+42}
42
r
+
42
49
r
+
14
?
\newline
Choose
1
1
1
answer:
\newline
(A)
7
r
+
1
6
r
+
3
\frac{7 r+1}{6 r+3}
6
r
+
3
7
r
+
1
\newline
(B)
7
r
+
2
r
+
1
\frac{7 r+2}{r+1}
r
+
1
7
r
+
2
\newline
(C)
49
r
+
2
42
r
+
6
\frac{49 r+2}{42 r+6}
42
r
+
6
49
r
+
2
\newline
(D)
7
r
+
2
6
r
+
6
\frac{7 r+2}{6 r+6}
6
r
+
6
7
r
+
2
Get tutor help
Which of the following expressions is equivalent to
−
5
k
−
10
40
k
+
45
\frac{-5 k-10}{40 k+45}
40
k
+
45
−
5
k
−
10
?
\newline
Choose
1
1
1
answer:
\newline
(A)
k
+
2
8
k
+
9
\frac{k+2}{8 k+9}
8
k
+
9
k
+
2
\newline
(B)
−
k
−
2
8
k
−
9
\frac{-k-2}{8 k-9}
8
k
−
9
−
k
−
2
\newline
(C)
−
k
−
2
8
k
+
9
\frac{-k-2}{8 k+9}
8
k
+
9
−
k
−
2
\newline
(D)
−
k
+
2
8
k
+
9
\frac{-k+2}{8 k+9}
8
k
+
9
−
k
+
2
Get tutor help
Which of the following is equivalent to
(
2
x
−
6
y
)
(
x
−
3
y
+
1
)
\frac{\left(\frac{2 x-6}{y}\right)}{\left(\frac{x-3}{y+1}\right)}
(
y
+
1
x
−
3
)
(
y
2
x
−
6
)
?
\newline
Choose
1
1
1
answer:
\newline
(A)
2
2
2
\newline
(B)
2
x
−
6
x
−
3
\frac{2 x-6}{x-3}
x
−
3
2
x
−
6
\newline
(C)
y
+
1
2
y
\frac{y+1}{2 y}
2
y
y
+
1
\newline
(D)
2
(
y
+
1
)
y
\frac{2(y+1)}{y}
y
2
(
y
+
1
)
Get tutor help
Which of the following is equivalent to
−
8
x
2
−
8
x
y
+
12
y
2
-8 x^{2}-8 x y+12 y^{2}
−
8
x
2
−
8
x
y
+
12
y
2
?
\newline
Choose
1
1
1
answer:
\newline
(A)
−
4
(
2
x
2
−
2
x
y
−
3
y
2
)
-4\left(2 x^{2}-2 x y-3 y^{2}\right)
−
4
(
2
x
2
−
2
x
y
−
3
y
2
)
\newline
(B)
−
4
(
2
x
2
−
2
x
y
+
3
y
2
)
-4\left(2 x^{2}-2 x y+3 y^{2}\right)
−
4
(
2
x
2
−
2
x
y
+
3
y
2
)
\newline
(C)
−
4
(
2
x
2
+
2
x
y
−
3
y
2
)
-4\left(2 x^{2}+2 x y-3 y^{2}\right)
−
4
(
2
x
2
+
2
x
y
−
3
y
2
)
\newline
(D)
−
4
(
2
x
2
+
2
x
y
+
3
y
2
)
-4\left(2 x^{2}+2 x y+3 y^{2}\right)
−
4
(
2
x
2
+
2
x
y
+
3
y
2
)
Get tutor help
Dalia is installing a tile floor in a rectangular room. Dalia has
152
152
152
tiles available to tile the room. If each row requires
9
9
9
.
5
5
5
tiles, and
19
19
19
tiles broke while Dalia is laying the floor, how many full rows of unbroken tile can she install before running out of tiles?
\newline
Choose
1
1
1
answer:
\newline
(A)
12
12
12
\newline
(B)
14
14
14
\newline
(C)
16
\mathbf{1 6}
16
\newline
(D)
18
\mathbf{1 8}
18
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Devin is a landscaper who needs to prepare different types of grass seed for his customers' yards. Bluegrass seed costs
$
2.00
\$ 2.00
$2.00
per pound while drought-resistant seed costs
$
3.00
\$ 3.00
$3.00
per pound. If for a particular day the two types of grass seed totaled
$
68.00
\$ 68.00
$68.00
and together weighed
25
25
25
pounds, how many pounds of bluegrass seed did Devin prepare?
\newline
Choose
1
1
1
answer:
\newline
(A)
4
4
4
\newline
(B)
7
7
7
\newline
(C)
18
18
18
\newline
(D)
21
21
21
Get tutor help
Factor
99
−
45
f
+
36
b
99-45 f+36 b
99
−
45
f
+
36
b
to identify the equivalent expressions.
\newline
Choose
2
2
2
answers:
\newline
A
9
(
11
−
5
f
+
4
b
)
9(11-5 f+4 b)
9
(
11
−
5
f
+
4
b
)
\newline
B
3
(
33
−
15
+
12
)
3(33-15+12)
3
(
33
−
15
+
12
)
\newline
c
11
(
9
−
4
f
+
3
b
)
11(9-4 f+3 b)
11
(
9
−
4
f
+
3
b
)
\newline
D
3
(
33
−
15
f
+
12
b
)
3(33-15 f+12 b)
3
(
33
−
15
f
+
12
b
)
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Factor
48
m
+
42
n
48 m+42 n
48
m
+
42
n
to identify the equivalent expressions.
\newline
Choose
2
2
2
answers:
\newline
A
6
(
8
m
+
7
n
)
6(8 m+7 n)
6
(
8
m
+
7
n
)
\newline
B
3
(
16
m
+
14
n
)
3(16 m+14 n)
3
(
16
m
+
14
n
)
\newline
C
2
(
12
m
+
21
n
)
2(12 m+21 n)
2
(
12
m
+
21
n
)
\newline
D
7
(
7
m
+
6
n
)
7(7 m+6 n)
7
(
7
m
+
6
n
)
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Factor
140
c
+
28
−
14
a
140 c+28-14 a
140
c
+
28
−
14
a
to identify the equivalent expressions.
\newline
Choose
2
2
2
answers:
\newline
A
7
(
20
c
+
4
−
2
a
)
7(20 c+4-2 a)
7
(
20
c
+
4
−
2
a
)
\newline
B
2
(
70
c
+
28
−
14
a
)
2(70 c+28-14 a)
2
(
70
c
+
28
−
14
a
)
\newline
c
14
(
10
c
+
2
−
a
)
14(10 c+2-a)
14
(
10
c
+
2
−
a
)
\newline
D
2
(
70
a
+
14
−
7
c
)
2(70 a+14-7 c)
2
(
70
a
+
14
−
7
c
)
Get tutor help
Which of the following expressions is equivalent to
\newline
5.9
×
8.7
5.9 \times 8.7
5.9
×
8.7
?
\newline
Choose
1
1
1
answer:
\newline
(A)
59
×
87
×
1
100
59 \times 87 \times \frac{1}{100}
59
×
87
×
100
1
\newline
(B)
59
×
87
×
1
1
,
000
59 \times 87 \times \frac{1}{1,000}
59
×
87
×
1
,
000
1
\newline
(C)
59
×
87
×
1
10
,
000
59 \times 87 \times \frac{1}{10,000}
59
×
87
×
10
,
000
1
\newline
(D)
59
×
87
×
1
100
,
000
59 \times 87 \times \frac{1}{100,000}
59
×
87
×
100
,
000
1
Get tutor help
Which of the following expressions is equivalent to
\newline
4.11
×
0.055
4.11 \times 0.055
4.11
×
0.055
?
\newline
Choose
1
1
1
answer:
\newline
(A)
411
×
55
×
1
100
411 \times 55 \times \frac{1}{100}
411
×
55
×
100
1
\newline
(B)
411
×
55
×
1
1
,
000
411 \times 55 \times \frac{1}{1,000}
411
×
55
×
1
,
000
1
\newline
(C)
411
×
55
×
1
10
,
000
411 \times 55 \times \frac{1}{10,000}
411
×
55
×
10
,
000
1
\newline
(D)
411
×
55
×
1
100
,
000
411 \times 55 \times \frac{1}{100,000}
411
×
55
×
100
,
000
1
Get tutor help
Which of the following expressions is equivalent to
\newline
0.8
×
12.4
0.8 \times 12.4
0.8
×
12.4
?
\newline
Choose
1
1
1
answer:
\newline
(A)
8
×
124
÷
100
8\times124\div100
8
×
124
÷
100
\newline
(B)
8
×
124
÷
1
,
000
8\times124\div1,000
8
×
124
÷
1
,
000
\newline
(C)
8
×
124
÷
10
,
000
8\times124\div10,000
8
×
124
÷
10
,
000
\newline
(D)
8
×
124
÷
100
,
000
8\times124\div100,000
8
×
124
÷
100
,
000
Get tutor help
Which of the following expressions is equivalent to
\newline
4.56
×
0.031
4.56 \times 0.031
4.56
×
0.031
?
\newline
Choose
1
1
1
answer:
\newline
(A)
456
×
31
÷
100
456 \times 31 \div 100
456
×
31
÷
100
\newline
(B)
456
×
31
÷
1
,
000
456 \times 31 \div 1,000
456
×
31
÷
1
,
000
\newline
(C)
456
×
31
÷
10
,
000
456 \times 31 \div 10,000
456
×
31
÷
10
,
000
\newline
(D)
456
×
31
÷
100
,
000
456 \times 31 \div 100,000
456
×
31
÷
100
,
000
Get tutor help
Which of the following expressions is equivalent to
\newline
0.034
×
4.8
0.034 \times 4.8
0.034
×
4.8
?
\newline
Choose
1
1
1
answer:
\newline
(A)
34
×
48
×
1
10
34 \times 48 \times \frac{1}{10}
34
×
48
×
10
1
\newline
(B)
34
×
48
×
1
100
34 \times 48 \times \frac{1}{100}
34
×
48
×
100
1
\newline
(C)
34
×
48
×
1
1
,
000
34 \times 48 \times \frac{1}{1,000}
34
×
48
×
1
,
000
1
\newline
(D)
34
×
48
×
1
10
,
000
34 \times 48 \times \frac{1}{10,000}
34
×
48
×
10
,
000
1
Get tutor help
Which of the following expressions is equivalent to
\newline
2.3
×
5.01
2.3 \times 5.01
2.3
×
5.01
?
\newline
Choose
1
1
1
answer:
\newline
(A)
23
×
501
×
1
10
23 \times 501 \times \frac{1}{10}
23
×
501
×
10
1
\newline
(B)
23
×
501
×
1
100
23 \times 501 \times \frac{1}{100}
23
×
501
×
100
1
\newline
(C)
23
×
501
×
1
1
,
000
23 \times 501 \times \frac{1}{1,000}
23
×
501
×
1
,
000
1
\newline
(D)
23
×
501
×
1
10
,
000
23 \times 501 \times \frac{1}{10,000}
23
×
501
×
10
,
000
1
Get tutor help
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