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Example 97. Reduce 168 to lowest terms by finding and cancelling the GCF.
252
Solution. The prime factorizations of the numerator and denominator are
3
168 = 2 · 3 · 7
2
2
252 = 2 · 3 · 7.
The smallest exponent on 2 is 2, and the smallest exponents on 3 and 7 are 1; it follows that the GCF
2
is 2 · 3 · 7 = 84. Cancelling the GCF yields lowest terms:
✟ ✟✯ 2
168 ✟ 168 2
= = (cancelling the GCF, 84).
252 ✟ ✟✯ 3 3
✟ 252
3.6.5 Exercises
Reduce each fraction to lowest terms by finding and cancelling the GCF of the numerator and denomi-
nator. Convert improper fractions to mixed numbers.
36
1.
72
48
2.
36
14
3.
48
36
4.
14
14
5.
15
72
6.
84
48
7.
180
96
8.
56
105
9.
147
300
10.
360
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