Part II: The Answers
128
Answers
1–100
3.
11
Write each factor as a fraction and then multiply across the numerator and denominator (cancel common factors as well!):
2
3
21 11
14
2
3
21
1
11
14
2 21 11
3 1 14
2 2
( ) ( ) ( )
= ( )( )( )
=
=
( )( )( )
( )( )( )
( )( 1 1 11
3 1 14
11
1
11
)( )
( )( )( )
=
=
4.
11
9
Recall that to divide by a fraction, you multiply by its reciprocal:
a b
c d
a
b
d
c
ad
bc
= ( )( ) = . After rewriting the fraction, cancel common factors before
multiplying:
5 6
15 22
5
6
22
15
1
3
11
3
11
9
= ( )( ) = ( )( ) =
5.
5
7
10
3
2
x
y
x
x y
+
+
To add the fractions, you need a common denominator. The least common multiple of
the denominators is x
2
y, so multiply each fraction accordingly to get this denominator
for each term. Then write the answer as a single fraction:
5
7 10
5
7
10
5
7
2
2
2
2
2
2
yx x
x
y
x
yx x
y
x y
x x
y x
x
x y
y
x y
+
+
=
+
+
( )
( )
=
+
+
( )
( )
( )
( )
1 10
5
7 10
3
2
3
2
x
x y
x
y
x
x y
=
+ +