november 13
TRANSCRIPT
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: