1. What is the least common denominator of
4 3
3 2
5 7
and
x x
?
B.
3
35x
B.
5
35x
C.
4
35x
D.
2
35x
2. What is the equivalent fraction of the rational expression
3 2
3 5
9 7
x
and
y y
?
A.
2
3 3
21 45
63 63
x y and
y y
B.
21 45
63 63
xy and
y y
C.
2 2
21 45
63 63
xy y and
y y
D.
2 2
21 45
63 63
xy and
y y
3. What is the equivalent fraction of the rational expression
2
5 3
8 2
x x and
y y
?
A.
2 2
5 12
8 8
x xy and
y y
B.
2 2
5 12
8 8
xy x and
y y
C.
2 2
5 12
8 8
x xy and
y y
D.
5 12
8 8
xy x and
y y
4. If we have
2
1 2
,
x x − + 1 3
, what is their Least Common Denominator?
A.
( 1)( 1)( 3) xxx +++ C.
( 1)( 1)( 3) x x x + − +
B.
( 1)( 3) x x + + D.
( 1)( 3) x x − +
5. If we have
2
1 2
,
x x x + + + 5 4 3
, what is their Least Common Denominator?
A.
( 1)( 4)( 3) x x x + + +
C.
( 1)( 4)( 3) x x x − − +
B.
( 1)( 4)( 3) x x x − + +
D.
( 1)( 4)( 3) x x x + − +
6. What is the sum of
5
4x
and
2
6x
?
A.
21
6x
B.
13
8x
C.
32
48x
D.
19
12x
7. What is the sum of the rational algebraic expression
3 1 2
2 2
x x and
x x
+
+ +
?
A.
2
3 1
( 2)
x
x
+
+
B.
5 1
2
x
x
+
+
C.
2
2 3
( 2)
x
x
+
+
D.
2
1 2
( 2)
x
x
+
+
8. What is the difference of
4 6
3
m n
m
−
and
2
1
6m
?
A.
2
2
8 12 1
6
m mn
m
− −
B.
8 12 1
6
m n
m
− +
C.
8 12 2
6
m n
m
+ +
D.
8 12 1
6
m n
m
+ +
33
9. What rational expression should be subtracted from
7x
5
to get
1
7x
?
A.
4
7x
B.
3x
1
C.
3x
2
D.
3x
4
10.What is the simplified form of the difference between
2
2
4 4 2
4 2
x x and
x x
− +
− −
?
A.
2 ( 6)
( 2)( 2)
x x
x x
−
+ −
B.
( 6)
( 2)( 2)
x
x x
−
+ −
C.
2( 6)
( 2)( 2)
x
x x
−
+ −
D.
( 6)
( 2)( 2)
x x
x x
−
+ −
11.What is the product of
2
12x
x
and
4
2
6
x
x
?
A.
12
6
x
x
B.
6x
C.
2x D.
2
12
6
x
x
12.What is the quotient of the rational algebraic expression
3 4
4 12
3 8
n m and
m n
?
A.
3
28n
B.
5
4
8
9
n
m
C.
4
8
n
m
D.
5
5
18n
13.What is the quotient of
2
4
v
v
+
+
and
2
2
v
v
+
−
?
A.
1
v − 4
B.
2
4
v
v
+
+
C.
2
4
v
v
−
−
D.
2
4
v
v
−
+
14.What rational expression should be multiplied to
7x
5
to get
2
3
15
28
y
x
?
A.
2
2
3
4
y
x
B.
3
3
y
x
C.
3
4
y
x
D.
3x
4
15.What is the simplified answer of the product of
2
4 20 6
6 2
x x x and
x
+
?
A.
2
6
x
x
B.
6
2
x
C.
2
5
6
x x
x
+
D.
2 ( 5) x x +
16.What is the equivalent mathematical sentence for “four decreased by a
number x divided by five more than thrice a number x”?
A.
4
3 5
x
x
−
+
B.
4
5 3
x
x
−
+
C.
4
5
x
x
−
+
D.
4
5 3
x
x
+
+
34

17.What is the equivalent mathematical sentence for “the difference of
fifteen and twice a number y divided by the sum of twenty and thrice a
number x ”?
A.
20 3
15 2
y
x
−
+
B.
15 2
20 3
y
x
+
−
C.
20 3
15 2
y
x
+
−
D.
15 2
20 3
y
x
−
+
18.What is the equivalent mathematical sentence “One-fourth of a
number y multiplied by three fifth of the number x”?
A.
1 3
4 5
y x • B.
1 3
4 5 x y
• C.
1 3
4 5
• xy D.
1 3
4 5
xy •
19.Kirsten can clean the house in 3 times as fast as Sophia, it takes them
4 hours to finish the work? How long would it take if Sophia will clean the
house alone?
A.
2
3
B.
2
4
3
C.
1
3
D.
1
5
3
20.Kirby can paint a wall in 6 hours, but Conrad needs 4 hours to paint
the same wall. How does it take them to paint the wall if they work
together?
A.
2
5
hours B.
2
3
5
hours C.
2
1
5
hours D.
2
2
5
hours