The document is a summary of a Khan Academy math lesson on ordering fractions, prime factorization, and working with fractions. It includes warm-up problems on ordering fractions, adding and subtracting fractions with different denominators, and multiplying and dividing mixed numbers. It defines key vocabulary terms like fundamental theorem of arithmetic, prime number, prime factorization, and greatest common factor. It provides examples of using prime factorization to simplify fractions by finding their greatest common factor. It also includes practice problems identifying numbers as prime or composite, writing their prime factorizations, and finding the prime factorizations of given numbers.

1. November 13, 2012 Today:
Khan Academy Extension
Warm-Up
Ordering Fractions
Vocabulary
Prime Factorization
Greatest Common Factor
Class Work

2. Warm-Up:
1.

3. Warm-Up:
2.
3. 18 = 3
x x-5

4. Warm-Up:
Ordering Mixed Numbers & Improper Fractions
Order From Least to Greatest
4.
5.

5. Warm-Up:
Adding & Subtracting Fractions with Different
Denominators
6. - 6/3 - 3/8 7. 9/6 + 1/8 8. 9/2 - 4/7
Multiplying & Dividing Mixed Numbers
9. 1 4/5 • 4 1/5 10. 3 3/5 ÷ 2 4/5
LCD: Lowest Common Denominator is used when adding &
subtracting fractions the old way. But since we don't need to
find a common denominator when adding & subtracting, we
have no need for the LCD. But what about simplifying
fractions? How do we know if 39/72 is simplified or not? For
that we must find the Greatest Common Factor by using Prime
Factorization.

6. Vocabulary:
Fundamental Theorem of Arithmetic: All integers
(whole numbers) greater than 1 are either prime
numbers, or can be written as a product of prime
numbers.
Prime Number: A number divisible only by 1 and
itself.
Prime Factorization: Writing a number as a product of
prime numbers.
Greatest Common Factor (GCF): Used to simplify
fractions by dividing numerator and denominator by
the product of their COMMON factors.
Prime Numbers from 2 - 100: 2 3 5 7 11 13 17 19 23
29 31 37 41 43 47 53 59 61 67 71 73 79 83 89 97

7. Practice Problems:
So what about our fraction 39/72? How do we use
Prime Factorization to simplify?
We take each number and break it up into the
product of its primes. What factor or
72 factors do these
39 numbers have in
2 36 common?
3 13
2 18
Dividing top & bottom by 3,
the fraction is reduced to
2 9
13/24. It cannot be simplified
any further. 3 3

8. Practice Problems:
Tell whether the number is prime or composite (a non-
prime number other than zero). If it is composite, first
write all its factors. Then, write its prime factorization
using exponents.
Number : 24
1. 24
Factors : 1, 2, 3, 4, 6, 8, 12, 24
24
Composite; It has positive
4 6 factors other then 1 and itself.
2 . 2 .2 . 3
So, 24 = 2 x 2 x 2 x 3 = 23 x 3

9. Practice Problems:
Find the prime factorization for the following
numbers. Use exponents when possible.
140
22 x 5x 7
27
33
354
2 x 3 x 59

10. Tomorrow:
Decimals: Adding, Subtracting Multiplying &
Dividing

11. Class Work: