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Reducing Fractions. By: Greg Stark EC&I 831. What is meant by reducing fractions?. To reduce a fraction means that we find an equivalent fraction that has no common factors in the numerator and the denominator - PowerPoint PPT Presentation
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Reducing Fractions
By: Greg StarkEC&I 831
What is meant by reducing fractions?
• To reduce a fraction means that we find an equivalent fraction that has no common factors in the numerator and the denominator
• To find this equivalent fraction, we divide both the numerator and the denominator by their GCF
Numerator--------------------Denominator Represents the number of parts into
which the whole has been divided
Represents the number of partsof a whole we have.
For example:
1
2
4
8
2
4
8
16
16
32= ===
X 2----X 2
X 2---X 2
X 2---X 2
X 2---X 2
16
32
1
2=
How do we find the GCF?
16
32
16
32 32
16: 1, 2, 4, 8,
:
We list the factors of the numerator and the denominator:
16,1, 2, 4, 8,
The greatest common factor is 16
Divide both the numerator and the denominator by the GCF
16
32
÷ 16----
÷ 16=
1
2
½ is the equivalent fraction in lowest terms to 16/32
Factoring by primes
12
27
12
27
3: 2 X 2 X
:
List the prime factors for the numerator and the denominator:
33 X 3 XThe GCF is 3
12
27
÷ 3----
÷ 3=
4
9
in lowest terms is1227
49
Factoring by primes
8
12
8
12
2: 2 X 2 X
:
List the prime factors for the numerator and the denominator:
32 X 2 XThe GCF is 2 X 2 = 4
8
12
÷ 4----
÷ 4=
2
3
in lowest terms is812
23
Review: To reduce a fraction to lowest terms
1. Find the GCF of both the numerator and the denominator by either:
1. listing the factors of each 2. prime factorization of each
2. Divide both the numerator and the denominator by the GCF