Equivalent Fractions: Simplifying And Building With Answers Page 9
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16Example 5
Use prime numbers to simplify each fraction.
21
a.
112
90
!
b.
198
168
!
c.
224
2
3
5x
y
d.
4
4x
y
Solution
a.
First find the prime factorizations of 21 and 112:
21 = 3 • 7
(
)
(
)
112 = 4 • 28 = 2 • 2
= 2 • 2 • 2 • 2 • 7
• 2 • 2 • 7
Now rewrite the fraction using prime numbers, and simplify:
21
3 • 7
=
prime factorizations
112
2 • 2 • 2 • 2 • 7
3 • / 7
=
cancelling common factors
2 • 2 • 2 • 2 • / 7
3
=
writing the remaining factors
2 • 2 • 2 • 2
3
=
multiplying
16
b.
First find the prime factorizations of 90 and 198:
(
)
(
)
90 = 9 • 10 = 3 • 3
= 2 • 3 • 3 • 5
• 2 • 5
(
)
198 = 2 • 99 = 2 • 9 • 11
= 2 • 3 • 3 • 11
Now rewrite the fraction using prime numbers, and simplify:
90
2 • 3 • 3 • 5
!
= !
prime factorizations
198
2 • 3 • 3 • 11
/ 2 • / 3 • / 3 • 5
= !
cancelling common factors
/ 2 • / 3 • / 3 • 11
5
= !
writing the remaining factors
11
153
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