Math 105                 Practice     Exam 3    (with answers)       Name  ______________________

Do your work on this paper.  You may add additional sheets.  Harder questions are marked with a *.

1.  a.  Write the Hindu-Arabic number 379475 in expanded form.

                 3x105 + 7x104 + 9x103 + 4x102 + 7x101 + 5
    b.    What is the base 2 number 10101112   is equal to in base 10. 

                             87

2.  Convert each of the given numerals in to its equivalent in the other system:

           Hindu-Arabic	Roman	
     ?              164	CLXIV	
1498	?           MCDXCVIII	
    ?             5211	  		

3.  Perform the following fraction calculations (without a calculator) and reduce your answer to
     simplest form. Show your steps and indicate the answers clearly.  [ 1/2  means  1 over 2 ]

a.   3/16  + 5/12

	                 29/48

b.   5/12   x  8/25

                              2/15

c.   8/9    6/5

                                20/27

4.   Write the each of the following in the other two equivalent forms.   

Fraction	Decimal	Percent	
?     55/100 or 11/20    	.55	?          55%	
?	217/100	?              2.17	217%	
5/12	?              .417	?       41.7%	

5.   Circle the larger of the two numbers in each of the following.  Circle both if they are equal.

    a.       1/3      or     .3333333333333333333333
                                                                
    b.      23.51       or         2351%        

    c.      -34.46       or        -28.5
               _
    d.       .9          or          1         

6. Describe the rule of divisibility test for each of the following numbers: 

   a.   3      ______see text ________________________________________________

   b.   8     ______ see text________________________________________________

   c.   Use these tests to determine whether or not 52,189,026 is divisible by 3 and/or 8. 

              3 divides the number but 8 does not.  You should use the tests to get this answer.

7.  Solve each of the following percentage problems. (Round to tenths.)  Show how you did each.
    
a.  Find  123% of 1356.

     1667.9

b.   88 is what percent of 119?

     74%

c.  26  is 81% of what number?

        32.1

d.   A persons LDL cholesterol went from 273 to 191.  What was the percentage decrease?

             30%

e.   A restaurant bill was $218.33 with an 18% tip.  What was the cost without the tip?

               $185
8.  Circle T or F

     T    F     If a and b are integers then a/b is always a rational number.
  
     T    F     If x is negative then –x>x.
  
     T    F     A positive repeating decimal is always equal to a fraction.
     
     T    F      If a negative number is divided by positive number the result is always negative.
   
     T    F      If a divides b then a/b is an integer.

     T    F      x-y = y-x  for any numbers x and y.

9.  a.  Factor 420 into primes using a factor tree.                  b. Find the GCD of 90 and 135.

          22 x 3 x 5 x 7   (show the tree) 	  45

    c.  John sold some books for $12 each and used all of the money he got to buy concert tickets at $50 each.  He had no money left over after buying the tickets. What is the fewest number of books he could have sold? Explain.

                              25 books

10.  Evaluate/simplify the following:  [Do not use a calculator.]

       a.    -13   =   __   13   ____                b.   5-3x2   =   ____   -1     __  [x means times]

       b.  (-5)2   =    ____  25    _               * d. a2/a  =     ____    a         ____ 

       
11.   Find a rational number between 5/13   and   9/23.  Write is as a ratio of integers.

                       39/100
                        __ 
12.   Write   3. 17  as a fraction. [the bar is over the 17]    Show how you derived it.  

                                  314/99

13.  Circle Y(es) or N(o) to indicate whether the given number system has the given property.

	Additive	Subtractive	Positional	
Egyptian	Y     N	Y     N	Y     N	
Roman	Y     N	Y     N	Y     N	
Hindu-Arabic	Y     N	Y     N	Y     N	

14.  The base 12 number system is called the duodecimal system.  

a.     What would the number 325 in the duodecimal system be equal to in the base 10 system?

                                                    461

*b.    What would 267 in base 10 be in the duodecimal system?

	1A312

*15.   Suppose a person’s blood pressure was too high and they wanted to reduce it 30%.  If she could cut it 5% every 3 months, how long would it take to reduce it 30%.  Show your work. 

                             21 months