1. REVIEW CONFIDENTIAL 1 Review

2. REVIEW CONFIDENTIAL 2 GREATEST COMMON FACTOR Numbers often have common factors. The greatest of the common factors of two or more numbers is the GREATEST COMMON FACTOR (GCF) of the numbers.

3. REVIEW CONFIDENTIAL 3 Methods to find the GCF 1. By Listing factors 2. Using Prime Factorization

4. REVIEW CONFIDENTIAL 4 Finding GCF by Listing Factors We can find this with the help of an example: Find the GCF of 35 and 60 factors of 35 = 1, 5, 7, 35 Factors of 60 = 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60 The common factors = 1, 5 The greatest among them is 5. therefore, the GCF = 5

5. REVIEW CONFIDENTIAL 5 Finding GCF by Prime Factorization Find the GCF of 32 and 48 232 48 216 24 28 12 24 6 2 3 GCF = 2 x 2 x 2 x 2 = 16

6. REVIEW CONFIDENTIAL 6 Practice Problems Find the GCF of the following by listing the factors 30 and 72 37 and 81 45, 60 and 90 9, 18 and 42

7. REVIEW CONFIDENTIAL 7 GCF OF 30 AND 72 Factors of 30 = 1, 2, 3, 5, 6, 10, 15, 30 Factors of 72 = 1, 2, 3, 4, 6, 8, 9, 12, 24, 36, 72 common factors = 1, 2, 3, 6 GCF = 6

8. REVIEW CONFIDENTIAL 8 GCF OF 37 AND 81 Factors of 37 = 1, 37 Factors of 81 = 1, 3, 9, 27, 81 Common factors = 1 GCF = 1

9. REVIEW CONFIDENTIAL 9 GCF of 45, 60 & 90 Factors of 45 = 1, 3, 5, 9, 15, 45 Factors of 60 = 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60 factors of 90 = 1, 2, 3, 5, 6, 9,10, 15, 18, 30, 45, 90 common factors = 1, 3, 5, 15 GCF = 15

10. REVIEW CONFIDENTIAL 10 GCF of 9, 18 & 42 Factors of 9 = 1, 3, 9 Factors of 18 = 1, 2, 3, 6, 9, 18 Factors of 42 = 1, 2, 3, 6, 7, 14, 21, 42 Common factors = 1, 3 GCF = 3

11. REVIEW CONFIDENTIAL 11 Find the GCF by Prime Factorization 15 and 18 28 and 70 26, 52 and 65

12. REVIEW CONFIDENTIAL 12 GCF of 15 and 18 315 18 5 6 GCF = 3

13. REVIEW CONFIDENTIAL 13 GCF OF 28 & 70 2 28 70 714 35 2 5 GCF = 2 X 7 = 14

14. REVIEW CONFIDENTIAL 14 GCF OF 26, 52 AND 78 1326 52 65 2 4 5

15. REVIEW CONFIDENTIAL 15

16. REVIEW CONFIDENTIAL 16 EQUIVALENT FRACTIONS Fractions that name the same number. To find equivalent fractions, we can multiply or divide the numerator and denominator by the same non-zero number.

17. REVIEW CONFIDENTIAL 17 Simplifying Fractions A fraction is in simplest form when the GCF of the numerator and denominator is 1 To write a fraction in simplest form, we can either: Divide the numerator and denominator by common factors until the only common factor is 1, or Divide the numerator and denominator by the GCF.

18. REVIEW CONFIDENTIAL 18 Example Replace each * with a number so that the fractions are equivalent. 2 = * 3 24 Here, 3 x 8 = 24. So, 2 x 8 = 16 That is 2 = 16 3 24

19. REVIEW CONFIDENTIAL 19 PRACTICE PROBLEMS Replace each * with a number so that the fractions are equivalent 1. 5 = 35 5 x 7 = 35. So, 8 x 7 = 56 8 * * = 56 2. * = 12 24÷ 4 = 6. So 12 ÷ 4 = 3 6 24 * = 3 3.7 = 63 63 ÷ 9 = 7. So 81 ÷9 = 9 * 81* = 9

20. REVIEW CONFIDENTIAL 20 Fraction in simplest form Write each fraction in the simplest form. 1. 21 = 7 24 8 2.15 = 3 80 16 3.14 in the simplest form. 23

21. REVIEW CONFIDENTIAL 21 Mixed Numbers & Improper Fractions A mixed number indicates the sum of a whole number and a fraction. If the numerator of a fraction is greater than the denominator, then it is a said to be an improper fraction. A mixed number can also be represented as an improper fraction.

22. REVIEW CONFIDENTIAL 22 Mixed Numbers as Improper Fractions Example: Write 3 ¼ as an improper fraction. 3 ¼ = (3 x 4) + 1 = 13 4 4

23. REVIEW CONFIDENTIAL 23 Exercises Write each mixed number as an improper fraction. 1.5 3 = 43 8 8 2. 2 5 = 17 6 6 3. 7 2 = 65 9 9 4 4 ½ = 9 2

24. REVIEW CONFIDENTIAL 24 Improper Fractions as Mixed Numbers Write 23 as mixed fractions 4 423 -20 3 5. 23 = 5 ¾.. 4

25. REVIEW CONFIDENTIAL 25 Exercise Write each improper fraction as mixed fraction. 1. 48 = 5 1 9 3 2. 38 =5 3 7 7 3. 49=24 ½ 2

26. REVIEW CONFIDENTIAL 26 LEAST COMMON MULTIPLE(LCM) The smallest number other than 0 that is a multiple of 2 or more whole numbers is the Least Common Multiple (LCM) of the numbers.

27. REVIEW CONFIDENTIAL 27 Finding LCM by making a list Example Find the LCM of 10 and 25 Multiple of 10 =10, 20, 30, 40, 50, 60, 70, Multiples of 25 =25, 50, 75, 100 The LCM of 10 and 25 = 50

28. REVIEW CONFIDENTIAL 28 Exercises 1.Find the LCM of 18 and 27 multiples of 18 = 18, 36, 54, 72, 90 multiples of 27 = 27, 54, 81, 108, LCM = 54 2.Find the LCM of 8 and 10 multiples of 8 = 8,16,24,32,40,48,56,64 multiples of 10 =10, 20, 30, 40, 50, 60 LCM = 40

29. REVIEW CONFIDENTIAL 29 Find LCM by Prime Factorization Find the LCM of 12 and 16 12 43 223 16 44 2222 LCM = 2 x 2x 3 x 2x 2 = 48

30. REVIEW CONFIDENTIAL 30 Exercises Find the LCM of the following: a.20 and 30=60 b.8 and 9= 72 c.8, 12 and 16= 48

31. REVIEW CONFIDENTIAL 31 LET’S SOLVE THIS http://www.thekidzpage.com/onlinejigs awpuzzles/kids-jigsaw-puzzles/12- piece-jigsaw/xmas2007-jigsaw-001.html http://www.thekidzpage.com/onlinejigs awpuzzles/kids-jigsaw-puzzles/12- piece-jigsaw/xmas2007-jigsaw-001.html

32. REVIEW CONFIDENTIAL 32 Comparing and Ordering Fractions To compare two fractions, we can write them as fractions with the same denominator. The method used for comparing fractions can be used for ordering fractions.

33. REVIEW CONFIDENTIAL 33 Steps to compare two fractions To compare two fractions, Find the least common denominator (LCD) of the fractions. That is, find the least common multiple of the denominators. Rewrite each fraction as an equivalent fractions using the LCD. Compare the numerators.

34. REVIEW CONFIDENTIAL 34 Comparing Fractions Which one is smaller 2 or 4 5 9 LCM of 5 and 9 = 45 2 x 9 = 4 x 5 that is, 18 = 20 5 x 9 9 x 5 45 45 Compare numerator- 18 < 20 2 < 4 5 9

35. REVIEW CONFIDENTIAL 35 Exercises 1 12 = 4 Insert >, <, or = 15 5 2½ < ¾ 37 > 5 12 9

36. REVIEW CONFIDENTIAL 36 Order Fractions Order 2, 4, 8, 3 from least to greatest 3 5 15 5 LCM of 3, 5, 15 = 15 That is., 2 x 5 = 10 ; 4 x 3 = 12 ; 3 x 3 = 9 3 x 5 15 5 x 3 15 5 x 3 15 Comparing numerators 8 < 9 < 10 < 12 therefore, 8, 3, 2, 4 15 5 3 5

37. REVIEW CONFIDENTIAL 37 Practice Problems Order the fractions from least to greatest. 2, ¾, ½, 5 =½, 5/9, 2/3, ¾ 3 9 7, 5, 5, ¾ = 7/12, 5/8, ¾, 5/6 12 8 6

38. REVIEW CONFIDENTIAL 38 Changing Decimals to Fractions The following are the steps for changing decimals to fractions Identify the place value of the last decimal place. Write the decimal as a fraction using the place value as the denominator. If necessary, simplify the fraction.

39. REVIEW CONFIDENTIAL 39 Example Write 0.9 as a fraction 0.9 means nine tenths That means 0.9 = 9 10 Write 2.64 as a mixed fraction 2. 64 = 2 + 64 16 100 25 2.64 = 2 16 25

40. REVIEW CONFIDENTIAL 40 Problems Write each decimal as a fraction 0.006 = 3 500 2.9.315 = 9 63 200 3. 3.005 = 3 1 200

41. REVIEW CONFIDENTIAL 41 Changing Fractions to Decimals Fractions with denominators of 10, 100, 1000 can be written as a decimal using place value. Any fraction can be written as a decimal using division There are 2 types of decimals: a)Decimals line 0.25, 0.75 etc are called terminating decimals because the division ends or terminates, when the remainder is zero. b) A decimal like 0.222222…is called a repeating decimal, because the digits repeat

42. REVIEW CONFIDENTIAL 42 Writing fractions as Terminating Decimal Write 9 as decimal 15 15 9.0000 - 9 0 0 0.6 Therefore, 9 = 0.6 15

43. REVIEW CONFIDENTIAL 43 Writing Fractions as Repeating Decimal Write 5 as 12 repeating decimal 12 5.0000 - 48 20 -12 80 -72 80 -72 8 0.41 6 6… So, 5 = 0.41666 = 0.416 12

44. REVIEW CONFIDENTIAL 44 Practice Problems Write each fraction or mixed number as decimal. a. 3 = 0.6 5 b. 9 = 0.5625 16 c. 8 2 = 8.6666…. 3 d. 4 = 0.4 9 e. 10 1 = 10.333… 3

45. REVIEW CONFIDENTIAL 45 Review Numbers often have common factors. The greatest of the common factors of two or more numbers is the GREATEST COMMON FACTOR (GCF) of the numbers Fractions that name the same number. To find equivalent fractions, we can multiply or divide the numerator and denominator by the same non-zero number. The smallest number other than 0 that is a multiple of 2 or more whole numbers is the Least Common Multiple (LCM) of the numbers.

46. REVIEW CONFIDENTIAL 46 THAT ‘S THE END OF THIS CHAPER