# August 15, M1 1.4 Common Factors_Multiples Compacted.notebook. Warm Up MI 36. Jun 20 10:53 AM

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1 Warm Up MI Jun 20 10:53 AM 1

2 Assignment Jun 20 12:36 PM 2

3 Practice 7 13 A = bh 7 x A = ½bh ½(7 x 7) ½(49) 24.5 Jun 20 12:36 PM 3

4 Practice A=½bh 4 6x8 24 A=bh 4x A=bh 12x A=½h(b1 + b2) ½(4)(8 + 5) ½(4)(13) (2)(13) = Jun 20 12:36 PM 4

5 Practice 24 6 A=bh 24 x 6 Jun 20 12:36 PM 5

6 Practice A=bh 44x10 Jun 20 12:36 PM 6

7 Stretch Whole Kite A= bh 12 x Whole White = White Kite A= bh 12 x Jun 20 12:36 PM 7

8 Stretch Rhombus A=bh 5 x Triangle A=½bh ½(5 x 4) = Triangle A=½bh ½(5 x 4) 10 Jun 20 12:36 PM 8

9 Review A=½h(b1 + b2) ½(8)(15 + 6) ½(8)(21) (4)(21) Jun 20 12:36 PM 9

10 Review A=½bh ½(4.5x4) ½(18) A=bh (4.5x20) Jun 20 12:36 PM 10

11 A=bh 14x14 14 Review 14 5( ) = 5 x x 20 Jun 20 12:36 PM 11

12 Jun 21 2:28 PM 12

13 learning goals Jun 20 10:53 AM 13

14 / / # M1: 1.4 Common Factors and Multiples Essential Question: How can you use shapes to see relationships between numbers? Examples: 18 Rainbow Notes: Factor Pairs: two natural numbers other than zero that are multiplied together to produce another number. Distinct Factors: factors that appear only once in a list. T- Chart Aug 13 12:24 PM 14

15 MI 40 Jun 21 2:38 PM 15

16 / / # M1: 1.4 Common Factors and Multiples Essential Question: How can you use shapes to see relationships between numbers? Examples: Notes: Common Factor: a factor of 2 or more numbers. numbers that share the same factors. Greatest Common Factor (GCF): The greatest of 2 or more numbers in common. The greatest amount of ways to divide something equally. 3 Ways: 1. T-chart- list factors 2. Tree 3. Ladder Aug 13 12:24 PM 16

17 MI 40 Circle the common factors & find the GCF Common Factors: 1, 3 GCF: 3 Common Factors: 1, 2, 4 GCF: 4 Jun 21 2:38 PM 17

18 / / # M1: 1.4 Common Factors and Multiples Essential Question: How can you use shapes to see relationships between numbers? Examples: 3 = 1 x 3 8 = 1 x 8 8 = 2 x 4 Notes: Prime: 2 factors, 1 and itself. Composite: more than 3 factors Aug 13 12:24 PM 18

19 Jun 21 2:52 PM 19

20 Sieves of Eratosthenes Jun 21 2:52 PM 20

21 / / # M1: 1.4 Common Factors and Multiples Essential Question: How can you use shapes to see relationships between numbers? Examples: Factor Tree Notes: Prime Factorization: long string of ONLY prime factors Written as the product of primes. Divide number until all prime numbers are revealed. DO NOT DIVIDE BY 1 Answer written in exponents Ladder > 2 2 x 5 20 Only divide by prime numbers , 3, 5, 7, 11 Until you get to 1 The numbers on the side of the ladder are the prime factors. Write them in exponent form. > 2 2 x 5 Aug 13 12:24 PM 21

22 Find the prime factorization of using a tree x 3 x 5 Find the prime factorization of using a ladder x 7 2 x 3 x 7 Aug 14 10:07 PM 22

23 MI List the common factors comparing 2 numbers. 1, 3 12 & 15 = 1, 2, 4 12 & 16 = 1, 2, 4 12 & 20 = 1 15 & 16 = 1, 5 15 & 20 = 1, 2, 4 16 & 20 = Jun 21 2:38 PM 23

24 MI 40 Jun 21 3:12 PM 24

25 Jun 21 2:53 PM 25

26 Find the prime factorization of 54 and 84 using a tree /ladder. Aug 14 10:26 PM 26

27 / / # M1: 1.4 Common Factors and Multiples Essential Question: How can you use shapes to see relationships between numbers? Examples: 20 and Common Factors: 1 & 5 GCF = 5 Notes: Greatest Common Factor (GCF): The largest factor two or more numbers have in common. The greatest amount of ways to divide something equally. Relatively Prime: Two numbers that do not have any common factors other than 1. GCF & the distributive property 5 is the GCF of 20 and 35. 5( ) = 5 x x 7 Aug 13 12:24 PM 27

28 Jun 21 2:51 PM 28

29 Cycles Jun 21 3:06 PM 29

30 / / # M1: 1.4 Common Factors and Multiples Essential Question: How can you use shapes to see relationships between numbers? Examples: 2: 2, 4, 6, 8, 10, 12 4: 4, 8, 12, 16, 20 LCM = 4 a b = b a 2 4 = 4 2 Notes: Multiple: shared products of numbers Common Multiple: A number that is a multiple of 2 or more numbers. Least Common Multiple (LCM): Smallest product (other than zero) that two or more numbers have in common. Commutative Property of Multiplication: States that for any numbers a and b, the product a b is equal to the product b a. Aug 13 12:24 PM 30

31 Jun 21 3:07 PM 31

32 Jun 21 2:44 PM 32

33 / / # M1: 1.4 Common Factors and Multiples Essential Question: How can you use shapes to see relationships between numbers? Examples: Ladder/ Hockey Sticks Notes: LCM using the ladder. 1. Divide by prime numbers. 2. Go until the 2 numbers don't have any more common factors. 3. Multiply all the numbers on the outside of the ladder together. Aug 13 12:24 PM 33

34 Find the LCM of 24 & 16 using the ladder. Aug 14 10:37 PM 34

35 18 56 Jun 21 2:44 PM 35

36 Jun 21 2:44 PM 36

37 Jun 21 2:44 PM 37

38 Jun 21 2:44 PM 38

39 Remember!! Jun 20 12:36 PM 39

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Page 1 of 14 Review of Rational Epressions and Equations A rational epression is an epression containing fractions where the numerator and/or denominator may contain algebraic terms 1 Simplify 6 14 Identification/Analysis

### Foundations of Mathematics

Foundations of Mathematics 978-1-63545-087-3 To learn more about all our offerings Visit Knewton.com Source Author(s) (Text or Video) Title(s) Link (where applicable) OpenStax Lynn Marecek, Santa Ana College

### Evaluate and simplify.

Math 52 Midterm Practice Exam The following exercises are taken from the book s end-of-chapter Practice Tests. The exercise numbers here correspond to the numbers in those tests. The answers to these exercises