Transcript Simplifying Fractions

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: 1 2 3 4 6 12
– Factors of 16: 1 2 4 8 16
• What is the greatest common factor of 24 and
32?
8
• What is the prime factorization of 72?
2x2x2x3x3
Simplifying Fractions using 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 PRIME
The only factor in
common is 1
Try 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
Common Factors vs GCF
Common Factors
Greatest Common Factor
Simplify using the GCF
Using Prime Factorization to Simplify
Step 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 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.
1
1
1
1
1
1
1
1
Use Prime Factorization to Simplify