Equivalent Fractions: Simplifying And Building With Answers Page 12
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16Solution
a.
Finding the prime factorization of 85:
85 = 5 • 17
Since the denominator has a prime factor other than 2 or 5 (17), the decimal
form is a repeating decimal.
b.
Finding the prime factorization of 400:
400 = 4 • 100
(
)
(
)
= 2 • 2
• 10 • 10
(
)
(
)
= 2 • 2
• 2 • 5 • 2 • 5
= 2 • 2 • 2 • 2 • 5 • 5
Since the denominator has only 2 and 5 prime factors, the decimal form is a
terminating decimal.
c.
Finding the prime factorization of 320:
320 = 10 • 32
(
)
(
)
= 2 • 5
• 4 • 8
(
)
(
)
= 2 • 5
• 2 • 2 • 2 • 2 • 2
= 2 • 2 • 2 • 2 • 2 • 2 • 5
Since the denominator has only 2 and 5 prime factors, the decimal form is a
terminating decimal.
d.
Finding the prime factorization of 440:
440 = 10 • 44
(
)
(
)
= 2 • 5
• 4 • 11
(
)
(
)
= 2 • 5
• 2 • 2 • 11
= 2 • 2 • 2 • 5 • 11
Since the denominator has a prime factor other than 2 or 5 (11), the decimal
form is a repeating decimal.
Terminology
equivalent fractions
Fundamental Property of Fractions
common factor
building fractions
simplifying (or reducing) fractions
greatest common factor (GCF)
156
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