Simplifying Fractions Standard: M6N1 Objective: Students will know how to reduce a fraction into simplest form using three methods Common Factors Greatest Common Factors Prime Factorization

Warm - ups What are the common factors of 12 and 16? Factors of 12: Factors of 16: What is the greatest common factor of 24 and 32? What is the prime factorization of 72? 1 2 3 4 6 12 1 2 4 8 16 8 2 x 2 x 2 x 3 x 3

Simplifying Fractions using common factors 2 = 2 = 2 = 32 40 16 20 8 10 4 5 You can simplify fractions by dividing the numerator and denominator by common factors. How do you know when your fraction is in SIMPLEST FORM? - When your numerator and denominator become RELATIVELY PRIME The only factor in common is 1

Try these = 4 2 6 8 24 32 3 4 = 2 10 22 20 44 5 11

Simplifying Fractions using GCF What is the difference between simplifying with common factors and the GCF? Common factors will take multiple steps GCF will only take one step Let’s see how this works on the next slide

2 = 2 = 3 = 48 60 24 30 12 15 4 5 48 60 12 = 4 5 Common Factors vs GCF Greatest Common Factor 48 60 12 = 4 5

Simplify using the GCF = 8 32 56 4 7 = 7 28 35 4 5

Using Prime Factorization to Simplify 42 56 3 2 x 3 x 7 = = 2 x 2 x 2 x 7 4 Step 1: Find the prime factorization of the numerator and denominator But why are we crossing out the common prime factors? Step 2: If the numerator and denominator have a prime factor in common, cross them out. Step 3: Look at what is remaining in your numerator then multiply together. Then do the same for your denominator.

24 72 2 x 2 x 2 x 3 1 = = 2 x 2 x 2 x 3 x 3 3 Let’s look at it again.

Use Prime Factorization to Simplify 56 64 7 8 2 x 2 x 2 x 7 = = 2x2x2x2x2x2 72 108 2 3 2x2x2x3x3 = = 2x2x3x3x3