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Unit 1; Part 2: Using Factors for Fractions and Solving Problems

Unit 1; Part 2: Using Factors for Fractions and Solving Problems. You need to be able to find the GCF, LCM and solve problems using them. Advanced Homework Answers pp. 222-223. CHECK CHAPTER % FOR LAST YEARS SHOW. THERE WERE CHANGES!!!!.

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Unit 1; Part 2: Using Factors for Fractions and Solving Problems

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  1. Unit 1; Part 2:Using Factors for Fractions and Solving Problems You need to be able to find the GCF, LCM and solve problems using them.

  2. Advanced Homework Answers pp. 222-223

  3. CHECK CHAPTER % FOR LAST YEARS SHOW. THERE WERE CHANGES!!!!

  4. Unit 1, Lesson 10Advanced – LCM(least common multiple) Assignment – p. 226; #8-18 even (also find GCF) & 28-31.

  5. LCM • Multiples are any number multiplied by 1, 2, 3, etc. • Multiples of 12: 12, 24, 36, 48, 60… • Multiples get bigger where factors get smaller. • Factors of 12: 1, 2, 3, 4, 6, 12

  6. LCM • Least common multiple (LCM) is the smallest common multiple of 2 or more original numbers. • This is used to find the least common denominator. (Oh, boy. Can’t wait to that! Yuck!!!) • So, use LCM to find LCD.

  7. LCM • THE GCF of 2 or more numbers with nothing in common, is always 1. • The LCM of 2 or more numbers with nothing in common is found by simply multiplying them together.

  8. LCM • Find the GCF and LCM of 7 and 25. • There are no common factors, so… • GCF = 1 and • LCM = 7(25) = 175

  9. LCM • The LCM of 2 numbers with common factors is done exactly the same as GCF, using the same ladder as before. • The GCF is the numbers down the left side multiplied together just like before.

  10. LCM • The LCM is all the numbers on the side and across the bottom multiplied together. • Down the side and across the bottom form a big L for LCM.

  11. GCF and LCM 24 60 12 30 6 15 2 5 ) 2 ) 2 ) 3 LCM= 2x2x3x2x5=120 GCF= 2x2x3=12

  12. GCF and LCM 300 18 150 9 50 3 ) 2 ) 3 GCF=2x3=6 LCM=2x3x50x3=900

  13. GCF and LCM 625 30 125 6 ) 5 GCF=5 LCM=5x125x6=3750

  14. GCF and LCM of 3 Numbers • The GCF works the same way with 3 numbers. • You are done when there are no common factors for ALL 3 numbers.

  15. GCF and LCM of 3 Numbers 18 42 60 9 21 30 3 7 10 ) 2 ) 3 GCF=2x3=6

  16. GCF and LCM of 3 Numbers 18 42 60 9 21 30 3 7 10 ) 2 ) 3 Since the bottom numbers have nothing in common, this example works the same as before. LCM=2x3x3x7x10=1260

  17. GCF and LCM of 3 Numbers 56 14 70 28 7 35 4 1 5 ) 2 ) 7 GCF=2x7=14 LCM=14x20=280

  18. GCF and LCM of 3 Numbers • If there are any repeated factors on the bottom, you must do some additional work to find the LCM. • BUT, you first need to figure the GCF, since the common factors must be from all three numbers.

  19. GCF and LCM of 3 Numbers 200 120 180 100 60 90 50 30 45 10 6 15 ) 2 ) 2 ) 5 GCF=2x2x5=20

  20. GCF and LCM of 3 Numbers • After you find the GCF: • Keep dividing by factors that are common to 2 of the 3 numbers. • The 3rd number that can’t be divided is brought down as is. • Keep going until there are no common factors at all. • The LCM is the product of all the numbers (side and bottom).

  21. GCF and LCM of 3 Numbers 200 120 180 100 60 90 50 30 45 10 6 9 5 3 9 5 1 3 ) 2 ) 2 LCM= 2x2x5x2x3x5x1x3 =1800 ) 5 ) 2 ) 3

  22. GCF and LCM of 3 Numbers 12 18 28 6 9 14 3 9 7 1 3 7 ) 2 ) 2 ) 3 GCF=2 LCM=2x2x3x1x3x7=252

  23. GCF and LCM of 3 Numbers 32 80 96 16 40 48 8 20 24 4 10 12 2 5 6 1 5 3 ) 2 ) 2 ) 2 ) 2 ) 2 GCF=24=16 LCM=25x1x5x3=252

  24. GCF and LCM of 3 Numbers • REMEMBER!!!!!! • You may only work with 2 out of 3 numbers on LCM. • GCF MUST be all 3 numbers.

  25. LCM Find the GCF and LCM of 12 and 15.

  26. LCM Find the GCF and LCM of 3 and 15.

  27. LCM Find the GCF and LCM of 60 and 80.

  28. LCM Find the GCF and LCM of 24 and 36.

  29. LCM • Find the GCF and LCM of 2, 3 & 49. • There are no common factors, so… • GCF = 1 and • LCM = 2(3)(49) = 294

  30. LCM Find the GCF and LCM of 2, 6 and 10.

  31. LCM Find the GCF and LCM of 18, 42 & 60.

  32. LCM Be careful when doing 3 numbers! Check the numbers at the bottom. Do they have ANY common factors? (doesn’t have to be in all 3)

  33. LCM If so: • Find the GCF on the side. (The ones that went into all three.) • Write it down now! • Don’t wait until the end.

  34. LCM • Then keep dividing by factors that are common to 2 of the 3 numbers. • The 3rd number that can’t be divided is brought down as is. • Keep going until there are no common factors at all. The LCM is the product of all the numbers (the L on the side and bottom).

  35. LCM Find the GCF and LCM of 4, 10 and 9.

  36. LCM Find the GCF and LCM of 10, 12 & 15.

  37. LCM Find the GCF & LCM of 200, 120 & 180.

  38. End of Slide Show

  39. End of Lesson 7

  40. Advanced Homework Answersp. 226

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