Math Help 2!

PART I: EXERCISES

 

Directions: Answer each of the following questions.  When appropriate, please show work.

 

1. 1.Find all the factors of 210.

 

1. 2.Defined a prime number and a composite number.  Give an example of each.

 

1. 3.Determine whether the number 15 is prime, composite, or neither.

 

1. 4.Determine whether the number 41 is prime, composite, or neither.

 

1. 5.Determine whether the number 1 is prime, composite, or neither.

 

1. 6.Define prime factorization.

 

1. 7.Find the prime factorization of the number 66.

 

1. 8.Find the prime factorization of the number 81.

 

1. 9.Determine whether 348 is divisible by 3.

 

1. 10.Determine whether 2842 is divisible by 6.

 

1. 11.Determine whether 4933 is divisible by 9.

 

1. 12.Identify the numerator and the denominator of  .

 

1. 13.What is a ratio and how does it relate to a fraction?

 

1. 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?

 

1. 15.What number can we never divide by?  Why not?

 

1. 16.Simplify:  

 

1. 17.Simplify:  

 

1. 18.Simplify:  

 

1. 19.Simplify:  

 

1. 20.Simplify:  

 

1. 21.Multiply and simplify:  

 

1. 22.Multiply and simplify:  

 

1. 23.Multiply and simplify:  

 

1. 24.Multiply and simplify:  

 

1. 25.Find the reciprocal:  

 

1. 26.Find the reciprocal: 7

 

1. 27.Divide and simplify:  

 

1. 28.Divide and simplify:  

 

1. 29.Solve for t.  

 

1. 30.Evaluate and simplify:  

 

1. 31.Evaluate and simplify:  

 

1. 32.At North Spring College there are 576 students, and  of them are registered for December graduation.  How many are registered to graduate in December?

 

1. 33.A piece of ribbon m long is cut into 4 equal pieces.  How long is each piece?

 

1. 34.A gas tank held 24 gal when it was  full.  How much gas could it hold when full?

 

1. 35.After driving 180 miles, Larry notes that he has completed  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.

 

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.

 

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.

 

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