1. Multiplying Fractions & Mixed Numbers

2. Essential Question: Why is the product of a fraction and mixed number larger than the product of two fractions? Common Core Obj./Student Friendly Terms: ( 6.NS.1) Students will be able to multiply fractions and mixed numbers with one and two digit like and unlike denominators with at least 80% accuracy.

3. Vocabulary Multiplying Fractions & Mixed Numbers Difference Numerator LCD Like Fraction Unlike Fraction Mixed Number LCM Denominator Quotient Sum Product

4. Real World: Carlos won 4 / 5 of the games for which he was the pitcher last season. If Carlos pitched in 30 games last season, how many of those games did he win? 4 / 5 of 30= 4 / 5 x 30= 4 / 5 x 30 / 1 Multiplying Fractions & Mixed Numbers

5. RULES for Multiplying Fractions & Mixed Numbers: (1) Change Mixed Numbers to Improper Fractions; (2) Multiply Numerators (Multiply Across); (3) Multiply Denominators (Multiply Across) (4) Simplify/Reduce Multiplying Fractions & Mixed Numbers

6. Example #1: Find 1 / 2 x 1 / 4 14 14 x 12 12 Multiplying Fractions & Mixed Numbers

7. Example #1: Find 1 / 2 x 1 / 4 14 14 x 12 12 x Multiplying Fractions & Mixed Numbers

8. Example #1: Find 1 / 2 x 1 / 4 14 14 x 1 x 1 2 x 4 12 12 = x = Multiplying Fractions & Mixed Numbers

9. Example #1: Find 1 / 2 x 1 / 4 14 14 x 1 x 1 2 x 4 12 12 = 18 18 = x = Multiplying Fractions & Mixed Numbers x xxx

10. Example #2: Find 2 / 3 x 3 / 4 3434 x 2323 Multiplying Fractions & Mixed Numbers

11. Example #2: Find 2 / 3 x 3 / 4 3434 x 2323 x Multiplying Fractions & Mixed Numbers

12. Example #2: Find 2 / 3 x 3 / 4 3434 x 2 x 3 3 x 4 2323 = x= Multiplying Fractions & Mixed Numbers

13. Example #2: Find 2 / 3 x 3 / 4 3434 x 2 x 3 3 x 4 2323 = x= 6 12 = Multiplying Fractions & Mixed Numbers

14. Example #2: Find 2 / 3 x 3 / 4 3434 x 2 x 3 3 x 4 2323 = 1212 = x= 6 12 = Multiplying Fractions & Mixed Numbers x x x xx

15. Example #3: Find 6 x 1 / 2 1212 x 6 Multiplying Fractions & Mixed Numbers

16. Example #3: Find 6 x 1 / 2 1212 x 6 x Multiplying Fractions & Mixed Numbers

17. Example #3: Find 6 x 1 / 2 1212 x 6 x Multiplying Fractions & Mixed Numbers 1212 x 6161 =

18. Example #3: Find 6 x 1 / 2 1212 x 6 x 1 1 x 2 6 = x Multiplying Fractions & Mixed Numbers 1212 x 6161 =

19. Example #3: Find 6 x 1 / 2 1212 x 6 x 1 1 x 2 6 = x = 6262 = Multiplying Fractions & Mixed Numbers 1212 x 6161 = xxxxxx

20. Example #3: Find 6 x 1 / 2 1212 x 6 x 1 1 x 2 6 = 3 = x = 6262 = Multiplying Fractions & Mixed Numbers 1212 x 6161 = xxxxxx =

21. Example #4: Find 3 / 8 x 1 1 / 4 1414 x 3838 1 Multiplying Fractions & Mixed Numbers

22. Example #4: Find 3 / 8 x 1 1 / 4 1414 x 3838 1 5454 x 3838 Multiplying Fractions & Mixed Numbers = x +

23. Example #4: Find 3 / 8 x 1 1 / 4 1414 x 3 x 5 8 x 4 3838 = 1 5454 x 3838 Multiplying Fractions & Mixed Numbers = x +

24. Example #4: Find 3 / 8 x 1 1 / 4 1414 x 3 x 5 8 x 4 3838 = 1 5454 x 3838 15 32 = Multiplying Fractions & Mixed Numbers = x +

25. Example #5: Find 2 / 3 x 4 4 / 5 4545 x 2323 4 Multiplying Fractions & Mixed Numbers

26. Example #5: Find 2 / 3 x 4 4 / 5 4545 x 2323 4 = Multiplying Fractions & Mixed Numbers 24 5 x 2323

27. Example #5: Find 2 / 3 x 4 4 / 5 4545 x 2323 4 = Multiplying Fractions & Mixed Numbers 24 5 x 2323 = 2 x 24 3 x 5

28. Example #5: Find 2 / 3 x 4 4 / 5 4545 x 2323 4 = Multiplying Fractions & Mixed Numbers 24 5 x 2323 = 48 15 = 2 x 24 3 x 5

29. Example #5: Find 2 / 3 x 4 4 / 5 4545 x 2323 4 = Multiplying Fractions & Mixed Numbers 24 5 x 2323 = 48 15 = 3 15 3 2 x 24 3 x 5 =

30. Example #5: Find 2 / 3 x 4 4 / 5 4545 x 2323 1515 3 4 = Multiplying Fractions & Mixed Numbers 24 5 x 2323 = 48 15 = 3 15 3 2 x 24 3 x 5 =

31. Example #5: Find 2 / 3 x 4 4 / 5 4545 x 2 x 24 3 x 5 2323 1515 3 4 = = Multiplying Fractions & Mixed Numbers 24 5 x 2323 = 48 15 = 3 15 3 2 x 24 3 x 5 =

32. Example #5: Find 2 / 3 x 4 4 / 5 4545 x 2 x 24 3 x 5 2323 1515 3 4 = = = Multiplying Fractions & Mixed Numbers 24 5 x 2323 = 48 15 = 3 15 3 2 x 24 3 x 5 = 2 x 3 x 8 3 x 5

33. Example #5: Find 2 / 3 x 4 4 / 5 4545 x 2 x 24 3 x 5 2323 1515 3 4 = = = Multiplying Fractions & Mixed Numbers 24 5 x 2323 = 48 15 = 3 15 3 2 x 24 3 x 5 = 2 x 3 x 8 3 x 5

34. Example #5: Find 2 / 3 x 4 4 / 5 4545 x 2 x 24 3 x 5 2323 1515 3 4 = = 16 5 = Multiplying Fractions & Mixed Numbers 24 5 x 2323 = 48 15 = 3 15 3 2 x 24 3 x 5 = 2 x 3 x 8 3 x 5 =

35. Example #5: Find 2 / 3 x 4 4 / 5 4545 x 2 x 24 3 x 5 2323 1515 3 4 = = 16 5 = Multiplying Fractions & Mixed Numbers 24 5 x 2323 = 48 15 = 3 15 3 2 x 24 3 x 5 = 2 x 3 x 8 3 x 5 = 1515 3 =

36. Example #6: Find 3 1 / 3 x 2 2 / 5 2525 x 1313 23 Multiplying Fractions & Mixed Numbers

37. Example #6: Find 3 1 / 3 x 2 2 / 5 2525 x 1313 23 12 5 10 3 = Multiplying Fractions & Mixed Numbers x

38. Example #6: Find 3 1 / 3 x 2 2 / 5 2525 x 1313 23 10 x 12 3 x 5 = 12 5 10 3 = Multiplying Fractions & Mixed Numbers x

39. Example #6: Find 3 1 / 3 x 2 2 / 5 2525 x 1313 23 10 x 12 3 x 5 = 12 5 10 3 = = Multiplying Fractions & Mixed Numbers x 120 15

40. Example #6: Find 3 1 / 3 x 2 2 / 5 2525 x 1313 = 23 10 x 12 3 x 5 = 12 5 10 3 = = 8 Multiplying Fractions & Mixed Numbers x 120 15

41. Example #6: Find 3 1 / 3 x 2 2 / 5 2525 x 1313 = 23 10 x 12 3 x 5 = 12 5 10 3 2 x 5 x 4 x 3 3 x 5 = = 8 Multiplying Fractions & Mixed Numbers x 120 15

42. Example #6: Find 3 1 / 3 x 2 2 / 5 2525 x 1313 = 23 10 x 12 3 x 5 = 12 5 10 3 2 x 5 x 4 x 3 3 x 5 = = 8 Multiplying Fractions & Mixed Numbers x 120 15

43. Example #6: Find 3 1 / 3 x 2 2 / 5 2525 x 1313 = 23 10 x 12 3 x 5 = 12 5 10 3 2 x 5 x 4 x 3 3 x 5 = = 8 Multiplying Fractions & Mixed Numbers x 120 15

44. Example #6: Find 3 1 / 3 x 2 2 / 5 2525 x 2 x 4 1 1313 = 23 10 x 12 3 x 5 = 12 5 10 3 2 x 5 x 4 x 3 3 x 5 = = = 8 Multiplying Fractions & Mixed Numbers x 120 15

45. Example #6: Find 3 1 / 3 x 2 2 / 5 2525 x 2 x 4 1 1313 = 8181 = 23 10 x 12 3 x 5 = 12 5 10 3 2 x 5 x 4 x 3 3 x 5 = = = 8 Multiplying Fractions & Mixed Numbers x 120 15

46. Example #6: Find 3 1 / 3 x 2 2 / 5 2525 x 2 x 4 1 1313 = 8181 = 23 10 x 12 3 x 5 = 12 5 10 3 2 x 5 x 4 x 3 3 x 5 = = = 8 Multiplying Fractions & Mixed Numbers x 120 15 = 8

47. Independent Practice: Simplify (1) 1 / 2 x 3 / 5 (2) 5 / 6 x 2 / 3 (3) 2 / 3 x 7 (4) 1 / 3 x 3 / 4 (5) 5 / 6 x 6 / 5 Multiplying Fractions & Mixed Numbers

48. Independent Practice: Answers (1) 3 / 10 (2) 5 / 9 (3) 4 2 / 3 (4) 1 / 4 (5) 1 Multiplying Fractions & Mixed Numbers

49. Independent Practice 2: Simplify (1) 3 / 8 x 3 1 / 3 (2) 2 / 3 x 2 1 / 2 (3) 1 3 / 4 x 2 4 / 5 (4) 2 x 6 1 / 4 Multiplying Fractions & Mixed Numbers

50. Independent Practice 2: Answers (1) 1 1 / 4 (2) 1 2 / 3 (3) 4 9 / 10 (4) 12 1 / 2 Multiplying Fractions & Mixed Numbers

51. Real World: The state of Rhode Island has an area of 1,545 square miles. Water makes up about 1 / 3 of the total area of the state. About how many square miles of water does the state of Rhode Island have? 515 miles Multiplying Fractions & Mixed Numbers

52. Real World: Mr. Williams is baking 4 ½ batches of brownies for the school bake sale. If each batch requires 2 ¾ cups of brownie mix, how much brownie mix will he need? * Since each batch uses 2 ¾ cups, multiply 2 ¾ by 4 ½. 4 ½ x 2 ¾ = 9 / 2 x 11 / 4 = 99 / 8 = 12 3 / 8 Multiplying Fractions & Mixed Numbers

53. HOMEWORK p.218 #24-36, even