1. Chapter 2

2.   prime number  composite number  prime factorization  factor tree  common factor  equivalent fractions  simplest form  multiple  least common multiple  least common denominator  improper fraction  mixed number Words To Know

3.  2.1 Prime Factorization 2.2 Greatest Common Factor 2.3 Fundamental Fraction Concepts 2.4 Fractions in Simplest Form 2.5 Least Common Multiple 2.6 Comparing and Ordering Fractions 2.7 Mixed Numbers and Improper Fractions Overview

4. 2.1

5.  A nonzero whole number that divides another nonzero whole number evenly Or A number that divides another without remainders What is a factor? 1)What would the factors of 14 be?

6.  A number whose only whole number factors are 1 and itself Or A number whose factors are only 1 and itself Define: Prime Number 1)What would the factors of 3 be? 2)What would the factors of 2 be?

7.  A number that has factors other than 1 and itself Define: Composite Number 1)What would the factors of 10 be? 2)What would the factors of 20 be?

8.  What is 1? It is neither a prime nor a composite number Something to Ponder

9.  1)12 2)8 3)15 4)21 5)35 Practice What are the factors of?

10.  This means writing the number as a product of prime numbers Prime Factorization Write the prime factorization of … 1)6 2)15 3)12

11.  Find the prime factorization of each Practice 18 64 75 98 140 150 99 345 222

12. 2.2

13.  The largest number that is a factor of two or more nonzero whole numbers. (GCF) [also can be called greatest common divisor (GCD) ] Greatest Common Factor This will be helpful to know how to do when simplifying fractions.

14.  Find the Greatest Common Factor by listing all the factors of the numbers. 1.14, 21 2.72, 84 3.18, 27, 45 4.12, 35 5.66, 96 Practice

15. 2.3

16.  = Part of a Whole Fractions 3434 = Numerator = Denominator Top Number? Bottom Number?

17.  Numerator = number of objects that are being looked at Denominator = number of total equal parts that make up the Whole What do they mean? Note: the fraction bar means to divide the numerator by the denominator

18.  N umerator = N orth Easy Way To Remember! 3434 D enominator = D own What you have Whole Amount Divided by

19.  = one part of the whole Or a fraction where the numerator is one What is a Unit Fraction?

20.  = a comparison of two quantities What is a Ratio? Examples: Miles per gallon Girls to Boys Write it like a fraction Know the denominator does not have to = the Whole

21. 2.4

22.  Different fractions that name the same value What are Equivalent Fractions? Examples: 1212 2424 3636 4848 5 10 6 12 === = = The numbers are different but the value is the same!

23.  Multiply the numerator AND denominator by the same non zero whole number Creating Equivalent Fractions 1212 18 x= 36 Example: They look different but they have the same value

24.  Three methods  Simplify all fractions  Cross Multiply  Get a common denominator Are they Equivalent?

25.  Simplify all Fractions 6 15 10 50 = = 2 x 3 5 x 3 = 2525 2 x 5 10 x 5 = 1515 2 x 1 2 x 5 = Reduced to different numbers Not Equivalent

26.  Cross Multiply 15 36 30 70 1050 1080 = Not Equivalent

27.  Common Denominators 6 25 15 50 4444 2222 x x= = 24 100 30 100 Not Equivalent

28.  How do you know if … A fraction is in its simplest form? The numerator and denominator have a greatest common factor of 1.

29.   Can it be reduced by 2?  Can it be reduced by 3?  Can it be reduced by 5?  Can it be reduced by 7, 11 etc.? Simplifying Fractions

30.  Reducing by 2 Are both numbers even? 46 98 85 175 Yes No

31.  Reducing by 2 Divide both top and bottom by 2 46 98 2222 ÷ = 23 49 If answer comes out even repeat this step

32.  Reducing by 3 2 + 3 4 + 9 Do both the numbers add up to a number divisible by 3? 23 49 No = = = 5 13 No Can’t be reduced by 3

33.  Reducing by 3 Do both the numbers add up to a number divisible by 3? 8 + 5 1 + 7 + 5 85 175 No = = = 13 Can’t be reduced by 3 13 No

34.  Reducing by 5 Do both numbers end in either 5 or 0? 23 49 85 175 Yes No

35.  Reducing by 5 5555 Divide both top and bottom by 5 85 175 ÷ = 17 35 If answer comes out with a 5 in the top and bottom repeat this step

36.  Reducing by 7… etc. Divide the top and bottom by 7 23 49 7777 ÷ = 3.3 7 Can’t be reduced by 7

37.  Reducing by 7… etc. Divide the top and bottom by 7 7777 17 35 ÷ = 2.4 5 Can’t be reduced by 7

38.  Reducing 23 49 17 35 Simplified

39.  79 19 Simplifying Improper Fractions Divide the numerator by the denominator 7919 = x 76 4 - 3

40.  79 19 Simplifying Improper Fractions The remainder becomes the new numerator 7919 = x 4 76 - 3

41.  3 19 Simplifying Improper Fractions The mixed number is 4

42.  3 19 Check your Answer! Multiply the Whole number by the denominator 4 = x 76 + =79 19 Add the answer to the numerator

43.  Give 2 equivalent fractions for each: Practice 12 20 8989 1515 9 10

44.  Is the fraction in it’s simplest form? Practice 72 81 27 100 28 56 24 27

45. 2.5

46.   Define:  Multiple = the product of a number and any nonzero whole number  Common Multiple = a multiple shared by two or more numbers  Least Common Multiple (LCM) = the smallest of all the common multiples of two or more numbers Least Common Multiple

47.   Two ways to find them: 1.List the first several multiples of each number and then compare the lists for the common multiples and choose the lowest one. 2.Compare their prime factorization How to find LCM

48.  Find the LCM of LCM Listing 1.8, 10 8 = 16, 24, 32, 40, 48, 56, 64, 72, 80 10 = 20, 30, 40, 50, 60, 70, 80 Answer: 40

49.  Find the LCM of Practice Listing 1.7, 11 2.4, 6 3.6, 8 4.9, 11 5.15, 25

50.  LCM Prime Factorization Find the LCM of 1.12, 16 12 = 2 x 2 x 3 16 = 2 x 2 x 2 x 2 Circle the factors the two have in common Write out the factors of both, writing out the ones they have in common only once 2 x 2 x 3 x 2 x 2 = 48 Answer: 48

51.  Practice Prime Factorization Find the LCM of 1.10, 14 2.16, 20 3.9, 33 4.13, 39 5.5, 9, 15

52. 2.6

53.  1 10 Sequence 3 10 7 10 9 10 Fractions that have the same denominator? The numerator with the highest number is the greatest fraction

54.  1 10 Sequence 3 10 7 10 9 10 So… Is the proper order

55.  5 24 Sequence 3838 7 15 9 25 Fractions with unlike denominators (and unlike numerators)? Convert them to equivalent fractions with common denominators in order to compare them

56.  5 24 Sequence 3838 7 15 9 25 To find the least common denominator (LCD) you have to find the least common multiple of the denominators.

57.  24 Denominators 8 15 25x x x x 40 75 25 24 = = = = 600

58.  5 Numerators 3 7 9x x x x 40 75 25 24 = = = = 280 225 125 216

59.  125 600 Sequence 225 600 280 600 216 600 Compare: Set in order

60.  125 600 Sequence 225 600 280 600 216 600

61.  1818 Sequence 1919 1616 1515 Fractions with all the same numerator As the denominator gets bigger the fraction gets smaller.

62.  1818 Sequence 1919 1616 1515 Fractions with all the same numerator As the denominator gets bigger the fraction gets smaller.

63.  Cheat Sheet!

64.  Compare Fractions: Practice 2323 5656 1313 5 12 7 30 5 18 4949 3838

65. 2.7

66.  A fraction in which the numerator is less than the denominator. What is a Proper Fraction? 3434 Example:

67.  A fraction in which the numerator is greater than or equal to the denominator. What is an Improper Fraction? 4444 Examples: 7474

68.  A whole-number and a fraction What is a Mixed Number? 3434 16 Examples:

69.  Cheat Sheet!

70.  Write as a proper fraction: Practice 7575 7272 23 7 16 3 11 6 27 4

71. 2.8

72.  Convert Fractions to Decimals 3 10 0.3 = 323 1000 = 0.323 17 100 0.17 = 9 1000 =0.009

73.  Convert Fractions to Decimals If you can turn the denominator into 10, 100, 1,000 (any power of 10) then it’s simple: 1515 3 25 5858 = = = x x x 2222 4444 125 625 1000 12 100 2 10 = = = 0.2 0.12 0.625

74.  Convert Fractions to Decimals 3434 3 50 3 2 x 2 = x 25 = 75 100 =.75 3 2 x 5 x 5 = x 2222 = 6 100 =.06

75.  Convert Fractions to Decimals What about this? That 3 makes it so you can’t use this method, but there is another way… 7 75 = 7 3 x 5 x 5

76.  Terminating Decimals Decimals that stop! Notice that these denominators are easily turned into powers of 10 3 100 1818 1 25 = = = 0.03 0.125 0.04

77.  Repeating Decimals Decimals that do not stop! The dot dot dot means it goes on forever 7.3333333333… 6.4545454545… 2.0188888888… 9.1234234234… = = = = 7.3 6.45 2.018 9.1234

78.   https://www.khanacademy.org/math/algebr a/solving-linear-equations-and- inequalities/conv_rep_decimals/v/coverting -repeating-decimals-to-fractions-1 https://www.khanacademy.org/math/algebr a/solving-linear-equations-and- inequalities/conv_rep_decimals/v/coverting -repeating-decimals-to-fractions-1

79.  Writing a Fraction as a Decimal To write a fraction as a decimal, divide the numerator by the denominator

80.  Convert Fractions to Decimals So let’s address these kinds of fractions 7 75 7 3 x 5 x 5 = 7 75 = 0.0933… = 0.093 75 7.0

81.  Convert Fractions to Decimals 2 11 2 2.00 11 =.1818… =.18

82.  Convert Decimals to Fractions Remember to Simplify! 5 10 5555 1212.5 = ÷ =

83.  Convert Decimals to Fractions 26 100 2222 13 50.26 =÷=

84.  Convert Decimals to Fractions You can check your answer by… 325 1000 25 13 40.325 =÷ = 13 ÷ 40=.325

85.  Practice 5858 7 12 29 2 23 20

86.  Practice 17 9 8585 6 13 11 14 6767

87.  Practice 0.23 4.8 0.8 2.75

88.  Practice 3.02 0.27 2.6 0.48