Simplifying Fractions

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

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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
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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
4
Try these
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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

Lets see how this works on the next slide
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Common Factors vs GCF
Common Factors
Greatest Common Factor
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Simplify using the GCF
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Using Prime Factorization to Simplify
3
42 56
2 x 3 x 7


4
2 x 2 x 2 x 7
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.
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Lets look at it again.
1
1
1
1
2 x 2 x 2 x 3
1


3
2 x 2 x 2 x 3 x 3
1
1
1
1
10
Use Prime Factorization to Simplify
2 x 2 x 2 x 7


2x2x2x2x2x2
2x2x2x3x3


2x2x3x3x3