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Simplifying Fractions: Understanding GCF and Simplest Form Techniques

This guide explains how to simplify fractions using the Greatest Common Factor (GCF). A number that divides evenly into another is called a common factor, and the greatest common factor is the largest of these. For instance, the GCF of 12 and 18 is 6. When fractions are in simplest form, the only common factor of the numerator and denominator is 1. This resource includes step-by-step instructions and examples to simplify fractions effectively, ensuring clarity in the concepts of common factors and reducing fractions to their lowest terms.

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Simplifying Fractions: Understanding GCF and Simplest Form Techniques

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Presentation Transcript

  1. Simplifying Fractions using GCF

  2. Factor • A number that divides evenly into another number.

  3. Common Factor • When two numbers have the same factor.

  4. 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 GCF = 6

  5. What is the Greatest Common Factor? 8 = 1, 2, 4, 8 12 = 1, 2, 3, 4, 6, 12 GCF = 4

  6. What is the Greatest Common Factor? 6= 1, 2, 3, 6 18 = 1, 2, 3, 6, 9, 15 GCF = 6

  7. Simplest Form • When the only common factor of the numerator and denominator is 1, the fraction is in simplest form, or it is reduced to lowest terms. 3 1 3 ÷ = 4 1 4

  8. How to Simply a Fraction • Find the greatest common factor of the numerator and the denominator and divide both by that number.

  9. Simplifying a Fraction: 2 12 6 ÷ = 18 6 3

  10. Simplify: 9 3 3 ÷ = 21 3 7

  11. Simplify: 12 4 3 ÷ = 4 5 20

  12. Simplify: 10 5 2 ÷ = 15 5 3

  13. Simplify: 10 2 5 ÷ = 16 2 8

  14. Simplify: 12 4 3 ÷ = 16 4 4

  15. Simplify: 3 3 1 ÷ = 12 3 4

  16. Simplify: 2 2 1 ÷ = 4 2 2

  17. Simplify: 6 3 2 ÷ = 9 3 3

  18. Begin working on your Assignment!

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