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Welcome to Math 6

Welcome to Math 6. This lesson is a review of all the objectives from Lessons 1-10. When you finish the lesson and the assignments which follow, you will t ake an assessment of your progress so far. The assessment will be found in the assignments section. Objective:

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Welcome to Math 6

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  1. Welcome to Math 6 This lesson is a review of all the objectives from Lessons 1-10.

  2. When you finish the lesson and the assignments which follow, you will take an assessment of your progress so far. The assessment will be found in the assignments section.

  3. Objective: Each student will: Apply and use each of the rules and concepts which we have covered so far.

  4. Divisibility Rules

  5. Prime Factorization

  6. When we write a number as the product of its prime factors, we call it the Prime Factorization

  7. When we find the prime factorization of a number the divisibility rules can come in very handy Lets find the prime factorization of a number as a review.

  8. What is the prime factorization of 164?

  9. Divide 164 by 2 since it is even. Divide 82 by 2. 41 is odd. We cannot divide by 2. What else could we divide by?

  10. Here’s where we get to apply the divisibility rules.

  11. Is 41divisible by 3 ?

  12. Since the sum of its digits, 4+1=5 is not divisible by three, we know that 41 is not divisible by three.

  13. Is 41divisible by 5 ?

  14. Only numbers that have a five (5) or a zero (0) in the ones place are divisible by 5.So we know that 41 is not divisible by five.

  15. Is 41divisible by 7 ?

  16. Since we know our 7 times tables, we know that 42 and 49 are both divisible by 7 but 41 is not.

  17. Is 41divisible by 11 ?

  18. Since we know our 11 times tables, we know that 44 is divisible by 11 but 41 is not.

  19. Now we continue through the list of prime numbers to check if 41 could be divided by any of them.

  20. Prime and Composite Numbers

  21. A Prime Number has exactly two factors: itself and 1. A Composite Number is any number with more than two factors.

  22. It is not expected that you memorize all of the prime numbers. Since the set of prime numbers is infinite number, that would be impossible anyway. You are expected to be able to tell whether any number between 1 -100 is prime or composite. You could do that easily if you have all of your multiplication facts memorized.

  23. Prime Numbers between 1 and 50 are ---------- in Gray

  24. The prime factorization of 164 is 2 x 2 x 41 or 22 x 41

  25. What is the prime factorization of 96?

  26. Know the facts. That will make this skill easy and quick to master. I recommend that you memorize the multiplication tables up to 12 x 12.

  27. The prime factorization of 96 is 2x2x2x2x2x3 or 25x3.

  28. The prime factorization of 96 is 2x2x2x2x2x3 or 25x3. Do not circle composite numbers; only circle the prime numbers.

  29. Write decimals as fractions ormixed numbers

  30. First say the number. The ‘place’ that you named when you read it aloud is the denominator of the fraction. That place will either be “tenths,” or “hundredths” or “thousandths.”

  31. 0.28 is read as “twenty-eight hundredths.” As a fraction it would be written as 28/100.

  32. In most cases, fractions should be simplified. To do so, divide the numerator and denominator by the greatest common factor.

  33. 5.245 is read as “five and two hundred forty-five thousandths.” As a fraction (actually a mixed number) it would be written as 5 245/1000.

  34. Write fractions or mixed numbers as decimals

  35. Writing Fractions as Decimals To convert a fraction to a decimal, divide the numerator by the denominator. See examples: These two are examples of terminating decimals. 3÷4= 0.75 2÷5= 0.4

  36. If the denominator of the fraction is a ten, one hundred or one thousand, rewrite it using place value. 3/10 = 0.3 45/100 = 0.45

  37. In some cases it may be quicker and easier to convert a fraction to a decimal by renaming it (writing an equivalent fraction) so that it has 10, 100 or 1000 as a denominator. Then simply write as a decimal based on the place value system.

  38. A mixed number is part whole number and part fraction. When converting to a decimal, only the fraction is converted. The whole number remains unchanged. 2 ½ = 2.5

  39. Describe any ratio. “For every x, there are y”

  40. There are four birds in the sky. A fraction would describe the number of vultures to the total number of birds.

  41. A ratio describes the numerical relationship between one part to another part. The ratio of vultures to pelicans is “one to three.” It can be written as 1:3. It also can be

  42. So for every vulture there are three pelicans.

  43. Identify, write and compare ratios and rates.

  44. Ratio: is a comparison of two numbers by division.A ratio can compare “part to part” or “part to the whole.”

  45. Recipe 2 4 cups of orange juice 2 cups of soda 4 cups of pineapple juice Yield: 10 cups punch Recipe 1 5 cups of orange juice 3 cups of soda 2 cups of pineapple juice Yield: 10 cups punch

  46. Comparing Ratios 1) Which recipe has the most juice in it? Use evidence from the recipes to support your answer. 2) Which recipe has the most soda in it? Use evidence from the recipes to support your answer.

  47. Comparing Ratios 3) For Recipe #1, what is the ratio of orange juice to soda? Does this represent a part-to-part ratio or a part-to-whole ratio? Explain. 4) For Recipe #2, what is the ratio of orange juice to soda? Does this represent a part-to-part ratio or a part-to-whole ratio? Explain.

  48. George and Juan compared the fuel economy of their cars and found these rates: • George’s car went 580 miles on 20 gallons of gas. • Juan’s car went 450 miles on 15 gallons of gas. • a.) Compare the mileage (unit rate – miles per ONE gallon of gas).

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