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**Fractions VI Simplifying Fractions**

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**Factor A number that divides evenly into another.**

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

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What are the factors of 9? Factors of 9 are 1, 3 and 9.

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What are the factors of 10? Factors of 10 are 1, 2, 5 and 10.

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What are the factors of 7? Factors of 7 are 1 and 7.

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

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Name THE GCF of 9 and 27? 9 – 1,3,9 27 – 1,3,9, 27 GCF - 9

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NaME THE GCF of 4 and 8? 4 – 1,2,4 8 – 1,2,4,8 GCF - 4

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Name the GCF of 15 and 30? 15 – 1,3,5, 15 30 – 1,2,3,5,6, 10, 15, 30 GCF - 15

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Name the GCF of 9 and 21? 9 – 1,3,9 21 – 1,3,7, 21 GCF = 3

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Name the GCF of 10 and 25? 10 – 1,2,5,10 25 – 1,5, 25 GCF = 5

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Name the GCF of 3 and 4? 3 – 1,3 4 – 1,4 GCF IS 1!

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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

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**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

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**What is the Greatest Common Factor?**

8 = 1, 2, 4, 8 12 = 1, 2, 3, 4, 6, 12

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**What is the Greatest Common Factor?**

8 = 1, 2, 4, 8 14 = 1, 2, 7,14

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**What is the Greatest Common Factor?**

6 = 1, 2, 3, 6 18 = 1, 2, 3, 6, 9, 15

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**What is the Greatest Common Factor?**

6 = 1, 2, 3, 6 12 = 1, 2, 3, 4, 6, 12

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**What is the Greatest Common Factor?**

8 = 1, 2, 4, 8 16 = 1, 2, 4, 8, 16

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**What is the Greatest Common Factor?**

8 = 1, 2, 4, 8 10 = 1, 2, 5, 10

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**What is the Greatest Common Factor?**

3 = 1, 3 6 = 1, 2, 3, 6

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**What is the Greatest Common Factor?**

4 = 1, 2, 4 6 = 1, 2, 3, 6

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**What is the Greatest Common Factor?**

7 = 1, 7, 21 = 1, 3, 7, 21

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**What is the Greatest Common Factor?**

15 = 1, 3, 5, 15 24 = 1, 2, 3, 8, 12, 24

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**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

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**Simplify or Reduce This Fraction**

12 6 2 ÷ = 18 6 3

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**Simplify or Reduce This Fraction**

9 3 3 ÷ = 21 3 7

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**Simplify or Reduce This Fraction**

12 4 3 ÷ = 20 4 5

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**Simplify or Reduce This Fraction**

10 5 2 ÷ = 15 5 3

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**Simplify or Reduce This Fraction**

10 2 5 ÷ = 16 2 8

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**Simplify or Reduce This Fraction**

12 4 3 ÷ = 16 4 4

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**Simplify or Reduce This Fraction**

3 3 1 ÷ = 12 3 4

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**Simplify or Reduce This Fraction**

2 2 1 ÷ = 8 2 4

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**Simplify or Reduce This Fraction**

2 2 1 ÷ = 4 2 2

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**Simplify or Reduce This Fraction**

6 3 2 ÷ = 9 3 3

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**Simplify or Reduce This Fraction**

6 2 3 ÷ = 8 2 4

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