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