1. Do Now 1/4/10 Copy HW in your planner. Copy HW in your planner. –Text p. 214, #1-17 all (you need your text) –Chapter 4 Test Wednesday Be ready to review sections 4.1 – 4.4. Be ready to review sections 4.1 – 4.4. Be ready to copy POTW #6. Be ready to copy POTW #6.

2. Objective SWBAT review prime factorization, greatest common factor, equivalent fractions, and least common multiple SWBAT review prime factorization, greatest common factor, equivalent fractions, and least common multiple

3. Section 4.1 “Factors and Prime Factorization” Natural numbers are classified according to how many factors they have: (1) Prime numbers: -a whole number that is greater than 1 and has exactly TWO factors, itself and 1. (2) Composite numbers: -a whole number that is greater than 1 and has -a whole number that is greater than 1 and has more than two factors. more than two factors. (3) The number 1: 1 is neither prime nor composite. 1 is neither prime nor composite.

4. Factoring Natural Numbers You can use TREE DIAGRAMS to factor a number until all factors are primes. You can use TREE DIAGRAMS to factor a number until all factors are primes. 30 103 325 ∙ ∙∙ 30 152 235 ∙ ∙∙ 30 65 523 ∙ ∙∙ Prime Factorization **HINT Write your factors in increasing order. -writing a number as a product of prime factors.

5. Monomial a number, x 3x³yz² or the product of a number and one or more variables with whole number exponents or the product of a number and one or more variables with whole number exponents a variable, a variable, 7 To FACTOR a monomial, write the monomial as a product of prime numbers and variables with exponents of 1. To FACTOR a monomial, write the monomial as a product of prime numbers and variables with exponents of 1. 3a³ = 3 · a · a · a

6. Greatest Common Factor The common factor of two numbers. LARGEST 8: 1, 2, 4, 8 12: 1, 2, 3, 4, 6, 12 List the factors of the two numbers and then compare. Find the GCF of 8 and 12. From the list you can see that 1, 2, and 4 are common factors. Of these 4 is the greatest common factor. Section 4.2 “Greatest Common Factor”

7. Greatest Common Factors Find the GCF of 39 and 50. When the numbers are too large to list the factors of the two numbers, find the prime factorization of each and then compare. 39: 3 · 13 50: 2 · 5 · 5 From the list you can see that there are NO common prime factors. However, two numbers always have 1 as a common factor. So the GCF is 1 and the two numbers are relatively prime. Relatively Prime: Two numbers are relatively prime if their greatest common factor is 1.

8. GCF of Variable Expressions Find the GCF of 18xy² and 28x²y³. Write the prime factorization of each and then compare. 18xy²: 2 · 3 · 3 · x · y · y 28x²y³: 2 · 2 · 7 · x · x · y · y · y From the list you can see that 2, x, y, and y are common prime factors. The greatest common factor of is the product of 2 · x · y · y, which is 2xy².

9. EQUIVALENT FRACTIONS- two fractions are equivalent if they represent the same quantity. = = A fraction is in SIMPLEST FORM if its numerator and denominator have a greatest common factor of 1. Section 4.3 “Equivalent Fractions”

10. Simplifying Fractions = When simplifying fractions, look for the greatest common factor in the numerator and denominator. Then divide. = = =

11. Simplify Variable Expressions To simplify a variable expression, you can factor the numerator and denominator and then divide out any common factors. To simplify a variable expression, you can factor the numerator and denominator and then divide out any common factors. A variable expression is in SIMPLEST FORM if the numerator and denominator have no factors in common other than 1. A variable expression is in SIMPLEST FORM if the numerator and denominator have no factors in common other than 1.

12. Section 4.4 “Least Common Multiple” Least Common Multiple Of all the common multiples of two numbers, the smallest is the least common multiple. Of all the common multiples of two numbers, the smallest is the least common multiple. A multiple of a number is the product of the number and any other number greater than zero. A multiple of a number is the product of the number and any other number greater than zero. What are the multiples of 5? Think of counting by fives… 5: 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55 …

13. Find the LCM of 64 and 72. When the numbers are too large to list the multiples of the two numbers, find the prime factorization of each number. The LCM is the product of the common prime factors and the factors that are not common. 64: 2 · 2 · 2 · 2 · 2 · 2 72: 2 · 2 · 2 · 3 · 3 From the list you can see that 2, 2, and 2 are common prime factors, and the factors that are not common are 2, 2, 2, 3, and 3. The LCM is then 2 · 2 · 2 · 2 · 2 · 2· 3 · 3 which is 576. The LCM is then 2 · 2 · 2 · 2 · 2 · 2 · 3 · 3 which is 576. Least Common Multiple CommonFactors Not Common Factors 2 · 2 · 2 2 · 2 · 2 2 · 2 · 2 3 · 3 3 · 3

14. Find the LCM of 2a³b and 3ab. Find the LCM of 2a³b and 3ab. The LCM is the product of the common prime factors and the factors that are not common. 2a³b : 2 · a · a · a · b 3ab : 3 · a · b · b · b · b · b From the list you can see that a and b are common prime factors, and the factors that are not common are 2, 3, a, a, b, b, b, and b. The LCM is then a · b · 2 · a· a · 3· b · b· b · b b, b, and b. The LCM is then a · b · 2 · a · a · 3 · b · b · b · b which is 6a³b. Least Common Multiple Common Factors Not Common Factors a · b 2 · a · a 3 · b · b · b · b 3 · b · b · b · b 5 5 5

15. B-I-N-G-O Complete numbers #6, 8, 10, 12 – 32 all on page 806. Complete numbers #6, 8, 10, 12 – 32 all on page 806. Using your correct answers we will play BINGO.

16. BINGO Review Text p. 806, #6, 8, 10, 12-32 all 6) prime 6) prime 8) 8) 10) 1; yes 10) 1; yes 12) 8; no 12) 8; no 13) 4y 13) 4y 14) 4p 14) 4p 15) 2s 15) 2s 16) 3x 16) 3x 17) 3/16 17) 3/16 18) 2/21 18) 2/21 19) 7/11 19) 7/11 20) 2/5 20) 2/5 21) 21) 22) 22) 23) 23) 24) 24) 25) 30 25) 30 26) 84 26) 84 27) 480 27) 480 28) 90 28) 90 29) 29) 30) 30) 31) 31) 32) 32)

17. Homework Text p. 214, #1-17 all