repost Math Help 2
coolcat
[INSERT TITLE HERE] 1
Running head: [INSERT TITLE HERE]
[INSERT TITLE HERE]
Student Name
Allied American University
Author Note
This paper was prepared for [INSERT COURSE NAME], [INSERT COURSE
ASSIGNMENT] taught by [INSERT INSTRUCTOR’S NAME].
[INSERT TITLE HERE] 2
PART I: EXERCISES
Directions: Answer each of the following questions. When appropriate, please show work.
1. Find all the factors of 210.
2. Defined a prime number and a composite number. Give an example of each.
3. Determine whether the number 15 is prime, composite, or neither.
4. Determine whether the number 41 is prime, composite, or neither.
5. Determine whether the number 1 is prime, composite, or neither.
6. Define prime factorization.
7. Find the prime factorization of the number 66.
8. Find the prime factorization of the number 81.
9. Determine whether 348 is divisible by 3.
10. Determine whether 2842 is divisible by 6.
11. Determine whether 4933 is divisible by 9.
12. Identify the numerator and the denominator of 9 10.
13. What is a ratio and how does it relate to a fraction?
14. In 2008, there were 325 mammals considered to be endangered. Of these, 69 were in the U.S. What was the ratio of endangered U.S. mammals to total endangered mammals?
What was the ratio of endangered foreign mammals to total endangered mammals?
15. What number can we never divide by? Why not?
16. Simplify: 5
10−10
17. Simplify: 20 4
18. Simplify: 8 48
19. Simplify: 0 17
20. Simplify: 30 252
[INSERT TITLE HERE] 3
21. Multiply and simplify: 1 2 ×
3 4
22. Multiply and simplify: 5 6 ×
3 20
23. Multiply and simplify: 1 3 ×
9 10
24. Multiply and simplify: 4 × �
25. Find the reciprocal: 3 8
26. Find the reciprocal: 7
27. Divide and simplify: 1 3 ÷
1 6
28. Divide and simplify: 6 ÷ ��
29. Solve for t. 2 3� = 18
30. Evaluate and simplify: 1 4 ×
3 8 ÷
3 4
31. Evaluate and simplify: �12� 2
32. At North Spring College there are 576 students, and 1 9 of them are registered for December
graduation. How many are registered to graduate in December?
33. A piece of ribbon 3 5m long is cut into 4 equal pieces. How long is each piece?
34. A gas tank held 24 gal when it was 4 5 full. How much gas could it hold when full?
35. After driving 180 miles, Larry notes that he has completed 3 5 of his trip. How far is his trip?
PART II: PRACTICAL APPLICATION
Directions: Find all the prime numbers less than 100, using the Sieve of Eratosthenes.
[INSERT TITLE HERE] 4
Focus Prime and composite numbers
Background: One of the methods for finding prime numbers was developed around 200 BC by a
mathematician named Eratosthenes. He used the process of elimination to “sift” out the
composite numbers, leaving only prime numbers. His method became known as the Sieve of
Eratosthenes.
1. In Section 2.1 of your textbook, a prime number is defined as a natural number that has
exactly two different factors, itself and 1. For example, the number 7 is prime, because it has
only the factors 1 and 7. The number 14, on the other hand, is not prime because 7 is a factor of
14. Looking at the definition from another point of view, any number that is a multiple of
another number will not be prime. In the example above, 14 is a multiple of 7, and so 14 is not
prime.
In this activity, you will cross off all multiples of prime numbers from a grid of numbers. When
you are done, the remaining numbers will be prime.
2. Look at the grid on the next page. The number 1 has already been highlighted blue, as it is not
a prime number. The smallest number that is not crossed off is 2. Begin by highlighting the
number 2 yellow on the grid.
List the first 10 multiples of 2 in the space below:
Now, highlight these numbers blue from the grid. Continue highlighting multiples of 2 blue until
you reach the end of the grid.
3. Next, look for the smallest number that is not highlighted blue and highlight it yellow. This is
the next prime number.
List the first 10 multiples of this number in the space below:
Highlight these numbers blue on the grid. Continue, as before, highlighting multiples of the
number blue until you reach the end of the grid.
Note: Prime numbers should be highlighted yellow.
Composite numbers should be highlighted blue.
[INSERT TITLE HERE] 5
1 2 3 4 5 6 7 8 9 10
11 12 13 14 15 16 17 18 19 20
21 22 23 24 25 26 27 28 29 30
31 32 33 34 35 36 37 38 39 40
41 42 43 44 45 46 47 48 49 50
51 52 53 54 55 56 57 58 59 60
61 62 63 64 65 66 67 68 69 70
71 72 73 74 75 76 77 78 79 80
81 82 83 84 85 86 87 88 89 90
91 92 93 94 95 96 97 98 99 100
4. Repeat step 3 until all multiples are highlighted blue. The numbers highlighted yellow are the
prime numbers less than 100.
Write the list of prime numbers less than 100 in the space below:
5. Compare this list with the table of primes given in section 2.1 of your textbook. Are there any
differences between the lists? If there are, check your grid to see if you crossed off all multiples.
Check also that you did not accidentally cross off a number that is not a multiple.
6. In your own words, describe how The Sieve of Eratosthenes works. Was there a point when
you had highlighted all of the composite numbers less than 100? If so, at what number did that
happen? Do you think that you could develop a rule from this?
Conclusion: The Sieve of Eratosthenes can be used anytime you need to list the first few prime
numbers. For example, if you need all the prime numbers up to 50, make a list of the numbers
from 1 to 50, and start crossing out the multiples of 2, 3, 5, etc.
PART III: JOURNAL ACTIVITY
Directions: Write a page about where you use fractions in your everyday lives. Address how
you use them (mostly in a concept of reading gages, estimating time, or calculations). Also,
explore the idea of multiplying by a fraction and its relationship to division.