Simplifying Fractions

1
Simplifying Fractions
2
Factor

• A number that divides evenly into
  another.

• Factors of 24 are 1,2, 3, 4, 6, 8, 12 and 24.

3
What are the factors of 9?

• Factors of 9 are 1, 3 and 9.

4
What are the factors of 10?

• Factors of 10 are 1, 5 and 10.

5
What are the factors of 7?

• Factors of 7 are 1 and 7.

6
What are the factors of 56?

• Factors of 56 are 1, 2, 4, 7, 8, 14, 28, and 56.

7
Common Factor

• When two numbers have the same factor it is
  called a common factor.
• A common factor of 12 and 6 is 3.

8
Name a Common Factor of 9 and 27?
1, 3, 9
9
Name a Common Factor of 4 and 8?
1, 2, 4
10
Name a Common Factor of 4 and 8?
1, 2, 4
11
Name a Common Factor of 15 and 30?
1, 3, 5, 15
12
Name a Common Factor of 12 and 48?
1, 2, 3, 4, 6, 12
13
Name a Common Factor of 9 and 21?
1, 3, 9,
14
Name a Common Factor of 10 and 25?
1, 5, 10
15
Name a Common Factor of 3 and 4?
1
16
Simplest Form

• When the only common factor of the numerator
  and denominator is 1, the fraction is in simplest
  form.

3
3
1


4
4
1
17
Highest Common Factor

• The highest common factor is the largest factor
  between two numbers.

12 1, 2, 3, 4, 6, 12
18 1, 2, 3, 6, 9, 18
18
What is the Highest Common Factor?
8 1, 2, 4, 8
12 1, 2, 3, 4, 6, 12
19
What is the Highest Common Factor?
8 1, 2, 4, 8
14 1, 2, 7,14
20
What is the Highest Common Factor?
6 1, 2, 3, 6
18 1, 2, 3, 6, 9, 15
21
What is the Highest Common Factor?
6 1, 2, 3, 6
12 1, 2, 3, 4, 6, 12
22
What is the Highest Common Factor?
8 1, 2, 4, 8
16 1, 2, 4, 8, 16
23
What is the Highest Common Factor?
8 1, 2, 4, 8
10 1, 2, 5, 10
24
What is the Highest Common Factor?
3 1, 3
6 1, 2, 3, 6
25
What is the Highest Common Factor?
4 1, 2, 4
6 1, 2, 3, 6
26
What is the Highest Common Factor?
7 1, 7,
21 1, 3, 7, 21
27
What is the Highest Common Factor?
15 1, 3, 5, 15
24 1, 2, 3, 8, 12, 24
28
How to Find the Simplest Form of a Fraction

• Find the highest common factor of the numerator
  and the denominator and divide both the numerator
  and the denominator by that number.

12
2
6


18
3
6
29
Simplify or Reduce This Fraction
12
2
6


18
3
6
30
Simplify or Reduce This Fraction
9
3
3


21
7
3
31
Simplify or Reduce This Fraction
12
3
4


20
5
4
32
Simplify or Reduce This Fraction
10
2
5


15
3
5
33
Simplify or Reduce This Fraction
10
5
2


16
8
2
34
Simplify or Reduce This Fraction
12
3
4


16
4
4
35
Simplify or Reduce This Fraction
3
1
3


12
4
3
36
Simplify or Reduce This Fraction
2
1
2


8
4
2
37
Simplify or Reduce This Fraction
2
1
2


4
2
2
38
Simplify or Reduce This Fraction
6
2
3


9
3
3
39
Simplify or Reduce This Fraction
6
3
2


8
4
2