Today:November 13, 2012

Khan Academy ExtensionWarm-Up

Ordering FractionsVocabulary

Prime FactorizationGreatest Common Factor

Class Work

Warm-Up:

1.

Warm-Up:

2.

3. 18 = 3 x x - 5

Warm-Up:

Ordering Mixed Numbers & Improper FractionsOrder From Least to Greatest

4.

5.

Warm-Up:

Adding & Subtracting Fractions with Different Denominators

6. - 6/3 - 3/8

7. 9/6 + 1/8

8. 9/2 - 4/7Multiplying & 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.

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

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.

39

3 13

72

2 36

2 182 9

3 3

What factor or factors do these numbers have in common?

Dividing top & bottom by 3, the fraction is reduced to 13/24. It cannot be simplified any further.

Practice Problems:

1. 24

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.

So, 24 =

Number :24

1, 2, 3, 4, 6, 8, 12, 24

Composite; It has positive factors other then 1 and itself.

24

4 6

2 2 2 3.2 x 2 x 2 x 3 = 23 x 3

Factors :

..

Practice Problems:

Find the prime factorization for the following numbers. Use exponents when possible.

14022 x 5x 7

2733

3542 x 3 x 59

Tomorrow:

Decimals: Adding, Subtracting Multiplying & Dividing

Class Work: