1. Bell Work: Find the perimeter and area of a rectangle with a length of 12cm and a width of 9cm.

2. Answer: Perimeter = 42cm Area = 108cm 2

3. Lesson 9: Prime Numbers

4. Prime Numbers*: a counting number greater than 1 whose only two factors are the number 1 and itself.

5. 7 is a Prime Number. Its only factors are 1 and 7. 10 is not a Prime Number. Its factors are 1, 2, 5, and 10.

6. This grid shows 6 x 1. We can also arrange the grid like this. This grid shows 3 x 2. These two rectangles illustrate the two counting number factor pairs of 6.

7. The grid 7 x 1 however can only form 1 rectangle meaning that it has only 1 factor pair. A prime number can only form a “n x 1” rectangle.

8. Composite Numbers*: a counting number greater than 1 that can be expressed as a product of prime numbers. Every composite number has 3 or more factors.

9. 9 is divisible by 1, 3 and 9. It is composite. 11 is divisible by 1 and 11. It is not composite.

10. Prime Factorization*: The expression of a composite number as a product of its prime factors. Prime factorization of 60 is 2 x 2 x 3 x 5

11. Example: What is the prime factorization of 36 and 45?

12. Answer: 36 = 2 x 2 x 3 x 3 45 = 3 x 3 x 5

13. Divisible*: Ability to be divided by a counting number without a remainder.

14. One way to test if a counting number is prime or composite is to determine if it divisible by a counting number other than 1 and itself.

15. Divisible Tests ConditionNumber is Divisible by Example using 3420 The number is even (ends in 0, 2, 4, 6, 8)23420 The sum of the digits is divisible by 33 3 + 4 + 2 + 0 = 9 9 is divisible by 3 The number ends in 0 or 553420

16. We can combine these tests to build divisibility tests for other numbers. Here are some examples. A number is divisible by 2 and 5 is divisible by 10 (2 x 5). Thus 3420 is divisible of 10. A number is divisible by 2 and 5 is divisible by 10 (2 x 5). Thus 3420 is divisible of 10.

17. A number divisible by 2 and 3 is divisible by 6 (2 x 3). Thus 3420 is divisible by 6. A number divisible by 2 and 3 is divisible by 6 (2 x 3). Thus 3420 is divisible by 6. A number is divisible by 9 if the sum of its digits is divisible by 9 (3 x 3). Thus 3420 is divisible by 9 because the sum of its digits = 9. A number is divisible by 9 if the sum of its digits is divisible by 9 (3 x 3). Thus 3420 is divisible by 9 because the sum of its digits = 9.

18. A number is divisible by 4 if its last two digits are divisible by 4. thus 3420 is divisible by 4 since its last two digits (20) are divisible by 4. A number is divisible by 4 if its last two digits are divisible by 4. thus 3420 is divisible by 4 since its last two digits (20) are divisible by 4.

19. Example: Determine whether the following numbers are prime or composite and state how you know. 1,237,526520,611

20. Answer: 1,237,526 is composite because because it is even and thus divisible by 2. 520,611 is composite because the sum of its digits is divisible by 3. (5 + 2 + 0 + 6 + 1 + 1 = 15) (5 + 2 + 0 + 6 + 1 + 1 = 15)

21. HW: Lesson 9 #1-30 Due Tomorrow