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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
• 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
88
2 x 2 x 2 x 3 x 32 x 2 x 2 x 3 x 3
Simplifying Fractions using common factors
Simplifying Fractions using common factors
You can simplify fractions by dividing the numerator and denominator by common factors.
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 PRIMERELATIVELY PRIME
How do you know when your fraction is in SIMPLEST FORM? - When your numerator and denominator become RELATIVELY PRIMERELATIVELY PRIME
The only factor in common is 1The only factor in common is 1
Try theseTry these
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
Let’s see how this works on the next slide
Common Factors vs GCF
Common FactorsCommon Factors
Greatest Common FactorGreatest Common Factor
Simplify using the GCF
Using Prime Factorization to Simplify
Step 1: Find the prime factorization of the numerator and denominatorStep 1: Find the prime factorization of the numerator and denominator
Step 2: If the numerator and denominator have a prime factor in common, cross them out.
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.
Step 3: Look at what is remaining in your numerator then multiply together. Then do the same for your denominator.
But why are we crossing out the common prime
factors?
Let’s look at it again.
11 11 11 11
11 11 11 11
Use Prime Factorization to Simplify