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June 19th

June 19th

# Simplifying Fractions

Prime Factorization
Method 1. Dividing by Primes

Begin with the smallest prime that divides the given number.

1) If the number is even, divide by 2 and continue to divide by 2
until an odd number results.

2) Next ,try 3,then 5,then 7,and so forth.

3) Stop when the when the result is a prime number.

Finding Prime Factorization

Example 6: Find the prime factorization of 54.

Because 54 is even, divide by 2:

 Stop when the number is prime. The prime factors are the divisors.

Write the prime factorization

Prime Factorization
Method 2. Using a Factor Tree

To prime factor a number with a factor tree,

1) Begin with any pair of factors of the given number.

2)Factor each branch.

3)Factor each succeeding branch, until each branch ends with
a prime number.

Example 6:Find the prime factorization of 150.

Factor Tree

 Factors of 150 Prime factors of 150

Practice Exercise 2

Find the prime factorization of 60.

Solution − Practice Exercise 2

Find the prime factorization of 60.

Practice Exercise 3

Find the prime factorization of 180.

Solution − Practice Exercise 3

Find the prime factorization of 180.

Simplifying Fractions with Variables

Because a variable re presents some "number," we can cancel variable
factors.

Example 7: Simplify

To simplify the fraction , factor the numerator and denominator .
Then cancel the common factors of 7 and y:

Practice Exercise 4

Simplify:

C. Can't be simplified

Solution − Practice Exercise 5

Simplify:

C. Can't be simplified