Equivalent Fractions: Simplifying And Building With Answers Page 8
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1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
1612
c.
The GCF of 48 and 132 is 12, so the form of 1 to use is
. Therefore:
12
48
4 • 12
4
!
= !
= !
132
11 • 12
11
5x
d.
The GCF of 5xy and 10x is 5x , so the form of 1 to use is
. Therefore:
5x
5xy
y • 5x
y
=
=
10x
2 • 5x
2
This illustrates how we can simplify fractions with symbols also.
Thus far, we have found the GCF by guessing at it, but recall our alternate approach using
primes, which works particularly well for larger numbers. For example, to reduce the fraction
168
, it would be difficult to guess at the GCF of 168 and 180. We first factor each number into
180
primes:
(
)
(
)
(
)
(
)
168 = 8 • 21 = 2 • 4
= 2 • 2 • 2
= 2 • 2 • 2 • 3 • 7
• 3 • 7
• 3 • 7
(
)
(
)
(
)
(
)
180 = 10 • 18 = 2 • 5
= 2 • 5
= 2 • 2 • 3 • 3 • 5
• 3 • 6
• 3 • 2 • 3
Instead of finding the GCF, we will use the primes in our fraction, remembering that common
factors of the numerator and denominator will cancel:
168
2 • 2 • 2 • 3 • 7
=
prime factorizations
180
2 • 2 • 3 • 3 • 5
/ 2 • / 2 • 2 • / 3 • 7
=
cancelling common factors
/ 2 • / 2 • / 3 • 3 • 5
2 • 7
=
writing the remaining factors
3 • 5
14
=
multiplying
15
For fractions with larger numbers, this is usually the most efficient, and more importantly the
most accurate, approach.
152
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