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LCM using the Ladder Method

Learn how to find the least common multiple (LCM) using the ladder method with step-by-step examples. Practice multiplying fractions and mixed numbers, simplifying before multiplying, and understand exponents and prime factorization.

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LCM using the Ladder Method

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  1. Thursday, August 16, 2018 • Find the LCM using the ladder method. • 64 and 28 2) 48 and 72

  2. Homework Answers

  3. Multiplying Fractions and Mixed Numbers

  4. Multiplying Fractions • Multiply the numerators, multiply the denominators, and simplify the fraction. 1 2 1 3 1 x = 6 3 5 1 2 3 x = 10

  5. Multiplying Fractions by a whole number 3 4 Change the whole number to a fraction. 2 x 2 1 3 4 6 1 1 x = = 4 2

  6. Simplifying Before MultiplyingIf any numerator and denominator have a common factor, you can simplify before multiplying. This will keep you from working with big numbers a lot of the time. 1 2 7 3 8 x 4 1 7 3 4 3 x = 28

  7. Simplifying Before Multiplying 1 1 3 3 7 x 1 1 1 1 7 1 x = 7

  8. Simplifying Before Multiplying 1 1 5 6 3 5 x 1 2 1 2 1 1 1 x = 2

  9. Multiplying Mixed Numbers • Rename the mixed numbers as improper fractions. Simplify then multiply. 19 1 4 76 9 1 4 4 9 x 8 x = 1 1 1 19 9 1 19 2 = x = 9 9

  10. You Try…. 1) 1 8 1 9 3 12 4 5 1 2) 1 x x = = 72 5 1 3 1 3 6 7 2 7 3) 4) x = 6 x 2 6 2 =

  11. Notes: Keep this sheet in the Math section of your binder. Just remember…..Although it is not in these notes, it is always better to simplify before you multiply.

  12. Exponents and Prime Factorization

  13. What is an exponent? • An exponent is a little number high and to the right of a regular or base number. Exponent 3 4 Base

  14. Definition of Exponent Exponent 3 4 • An exponent tells how many times a number is multiplied by itself. Base 4 = 3 x 3 x 3 x 3 3

  15. What is Exponential Form? Expressed in terms of a designated power Ex: 2 3 This is written in exponential form

  16. What is Standard Form? • When you simplify/solve the expression you put it in standard form. • Ex: 2 3 = 2 x 2 x 2 = 8 • 8 is standard form

  17. How to read an Exponent • This exponent is read three to the fourth power. Exponent 3 4 Base

  18. How to read an Exponent • This exponent is read three to the 2nd power or three squared. Exponent 3 2 Base

  19. How to read an Exponent • This exponent is read three to the 3rd power or three cubed. Exponent 3 3 Base

  20. Let’s see who can read these exponents… 3 2 6 7 2 3 5 4

  21. How would we write this in exponential form? 3 2 x 2 x 2 = 2

  22. How would we write this in exponential form? 2 3 x 3 = 3

  23. How would we write this in exponential form? 4 5 x 5 x 5 x 5 = 5

  24. How to Multiply an Exponent to Find the Standard Form 4 3 = 3 x 3 x 3 x 3 9 27 81

  25. Write in Standard Form 2 4 16 =

  26. Write in Standard Form 3 2 8 =

  27. Write in Standard Form 2 3 9 =

  28. Write in Standard Form 3 5 125 =

  29. Now Let’s Look at Prime Factorization

  30. Prime numbers are numbers that only have two factors: one, and the number itself. EXAMPLES: 3, 5, 7, 11, 31 Composite numbers have more than two factors. EXAMPLES: 6, 15, 18, 30, 100 Prime and Composite Numbers

  31. A Product of Primes • Every composite number can be expressed as a product of prime numbers. • This is called prime factorization.

  32. Example 15 is a composite number. The product of the primes or primes factorization for 15 is 3 x 5

  33. Let me show you an example: Prime Factorization of 100. 100 100 ÷ 2 = 50. Two is the first prime number that goes into 100. 2 is a prime number, so we are done with it. 2 X 50 Now we deal with the 50. Divide it by 2 to get the next factors. 25 is not divisible by the first prime, 2. The next prime, 3, does not work either. We must divide by 5 to get a factor. 2 X 25 5 x 5 Both numbers are prime, leaving us with all primes.

  34. What’s the Answer? Just list the circled prime numbers in order from least to greatest with a multiplication sign between them. 2 x 2 x 5 x 5

  35. Exponential Form • We have just listed our prime factorization for 100 as being 2 x 2 x 5 x 5. This is repeated multiplication. Repeated multiplication can be expressed with exponents. • 2 x 2 can be expressed in exponential form: 22 • 5 x 5 can be expressed as 52 • Put it together, and 2 x 2 x 5 x 5 is more simply put as 22 x 52

  36. Let’s do this one together… 420 2 x 210 2 x 105 Expanded Form: 2 x 2 x 3 x 5 x 7 3 x 35 or 22 x 3 x 5 x 7 5 x 7 Exponential Form:

  37. Now, You Try! Find the Prime Factorization and Exponent of 16? 16 / \ 2 8 / \ 2 4 / \ 2 2 The prime factors of 16 are: 4 or 2 2 x 2 x 2 x 2

  38. Class Practice

  39. Class PracticeAnswers

  40. Homework Time! You may use a calculator for Section C of homework. There is no work/justification needed on tonight’s homework.

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