Transcript Fractions V Mixed Numbers

Fractions VI
Simplifying Fractions
By Monica Yuskaitis
Edited by LaDora Loggins
Factor

A number that divides evenly into another.
Factors of 24 are
1 24
2 12
38
46
What are the factors of 9?

Factors of 9 are
19
33
 Notice three is repeated
When we list the factors we list them in order, least
to greatest and do not write any number twice.
The factors of 9: 1, 3, 9
What are the factors of 10?

Factors of 10 are
1 10
25
You can write the factors in a series: 1,2,5,10 going from
least to greatest.
 Or as divisibility pairs: 1,10
2,5

What are the factors of 7?

Factors of 7 are 1 and 7.
Therefore 7 is a
prime
______________
number.

What are the factors of 56?

Factors of 56 are:
1 56
2 28
4 14
7 8
1, 2, 4, 7, 8, 14, 28, and 56.
Common Factor
When two numbers have the
same factor it is called a common
factor.

Factors of 12: 1, 2, 3, 4, 6, 12
Factors of 6: 1, 2, 3, 6
1, 2, 3, and 6 are the common factors of 12 and 6.
But 6 is the greatest common factor!
Greatest Common Factor

The greatest common
factor is the largest factor
between two numbers.
12 = 1, 2, 3, 4, 6, 12
18 = 1, 2, 3, 6, 9, 18
Name the Common Factors
of 9 and 27?
9:
27:
1, 3, 9
1, 3, 9, 27
What is the Greatest Common
Factor of 9 and 27?
9
Name a Common Factor of
15 and 30?
15: 1, 3, 5, 15
30: 1, 2, 3, 5, 6, 10, 15, 30
What is the Greatest Common
Factor of 15 and 30?
15
List the Factor of 12 and 48?
12: 1, 2, 3, 4, 6, 12
48: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48
What is the Greatest Common
Factor of 12 and 48?
12
Name a Common Factor of
3 and 4?
1
Simplest Form

When the only common
factor of the numerator and
denominator is 1, the
fraction is in simplest form.
3
1
3
÷
=
4
1
4
How to Find the Simplest Form
of a Fraction

Find the greatest common
factor of the numerator and the
denominator and divide both
the numerator and the
denominator by that number.
12
6
2
÷
=
18
6
3
Simplify or Reduce a Fraction
Method I
• First, find the greatest common factor
12: 1, 2, 3, 4, 6, 12
18: 1, 2, 3, 6, 9, 18
The GCF is 6
• Then, divide by the GCF of 12 and 18
12
6
2
÷ =
18
6
3
Simplify or Reduce a Fraction
Method II
• First, find the greatest common factor using the ladder method
(division).
2 12
3 6
1 2
2
18
9
3
3
These are the digits of the reduced fraction
because we have already divided by the
common prime factors!
The product of these factors is the GCF!
2 ∙ 3 ∙ 1= 6
Simplify or Reduce These Fractions
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