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