1. 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

2. 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? 8
2 x 2 x 2 x 3 x 3

3. Simplifying Fractions using common factors2 = 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

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

5. 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

6. 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

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

8. Using Prime Factorization to Simplify42 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.

9. 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.

10. Use Prime Factorization to Simplify56 64 7 8
2 x 2 x 2 x 7 = =
2x2x2x2x2x2 72
108 2 3
2x2x2x3x3 = =
2x2x3x3x3