MATH 081 Exam 2 Review Solutions 

1.	Five are shaded and there are eight total squares.   represents the shaded area.

2.	= =,  = =, because both fractions simplify to , they are equivalent.
(Alternative method: 18  35 = 630, and 42  15 = 630, so they are equivalent.)

3.	 = =

4.	 =  == =

5.	Simplify by dividing:  
6.	Simplify by dividing:(Cannot divide by zero)

7.	Perform the indicated operation.  Write the answer as a mixed number in simplest form:  
8.	Write the fraction in simplest form:  

9.	Add or subtract as indicated.  Write the answer in simplest form. 
   or 

10.	Add or subtract as indicated.  Write the answer in simplest form:  

11.	Add or subtract as indicated.  Write the answer in simplest form:  

12.	Determine whether the proportion is true or false:  
                                                                              
                                                                                         True

13.	Determine whether the proportion is true or false:  
                                                                            
                                                                                  False
14.	Evaluate.  Write the answer in simplest form.  

15.	Evaluate.  Write the answer in simplest form.  

16.	Divide and simplify:   or 

17.	Divide and simplify:  

18.	Simplify the complex fraction:  

19.	Solve the proportion for the given variable:  

      
20.	Solve the proportion for the given variable:  

    
21.	Solve the proportion for the given variable:  

 

22.	Solve the proportion for the given variable:  

      
      
23.	Perform the indicated operation.  Write the answer in simplest form.  

24.	Perform the indicated operation.  Write the answer in simplest form.  

25.	Perform the indicated operation.  Write the answer in simplest form.  

26.	Perform the indicated operation.  Write the answer in simplest form.  

27.	Perform the indicated operation.  Write the answer in simplest form.  

28.	Perform the indicated operation.  Write the answer in simplest form.  

29.	Perform the indicated operation.  Write the answer in simplest form.  

30.	Give the prime factorization of 1536.

31.	Give the prime factorization of 405.

32.	Determine whether the pair of fractions is equivalent:  and 
              Not equivalent.

(You can also check to see if the cross products are equivalent.  Is   Is ?  No, so the two fractions are not equivalent.)

33.	Determine whether the pair of fractions is equivalent:  and 
             Equivalent.

(You can also check to see if the cross products are equivalent.  Is   Is ?  Yes, so the two fractions are equivalent.)

34.	Evaluate the expression for the given replacement values.  Write the answer in simplest form.   for  and 
 or 

35.	Add or subtract as indicated.  Write the answer as a mixed number in simplest form.  

36.	Add or subtract as indicated.  Write the answer as a mixed number in simplest form.  

37.	Add or subtract as indicated.  Write the answer as a mixed number in simplest form.  
   =   

38.	Add or subtract as indicated.  Write the answer as a mixed number in simplest form.  
         =    
                                  
39.	Solve the equation:  

                                    

(You could also have cleared denominators.)  

40.	Solve the equation:  

                                       
41.	Solve the equation:  

                                         
42.	Solve the equation:  

                                            
                                              
43.	For the proportion, find the unknown number, x:  

44.	For the proportion, find the unknown number, x:  

                                                                                  
45.	Betty has  cups of flour.  She uses  cups of flour to make a cake.  How many cups of flour does she have left?
 (cups)

46.	Simplify by combining like terms.  

47.	Find the exact circumference of the circle.  Then use the approximation 3.14 for .  Label your answers.

48.	It takes Bob 20 minutes to do and check 12 math problems.  Find how long it takes him to do and check 40 problems of the same difficulty level.  Round answers to the nearest whole number, if necessary.

   (minutes)
49.	Write the ratio as a ratio of whole numbers using fractional notation.  Write the fraction in simplest form:  48 inches to 15 inches

50.	How many feet of fencing are needed to fence a circular yard with a diameter of 30 feet?  Use 3.14 for, and give your answer to the nearest tenth of a foot.

51.	Find the area of a circle with a radius of 7 miles.  Use 3.14 for , and give your answer to the nearest tenth.  Label your answer.

52.	Write the fraction as a decimal.  If necessary, use repeating decimal notation:  

53.	Write the fraction as a decimal.  If necessary, use repeating decimal notation:  

54.	Write the fraction as a decimal.  Round to the nearest hundredth:  

55.	Solve the equation:  

56.	Write a fraction to represent the shaded area.

Count up 4 shaded, 7 total
4 shaded/7 total 

57.	Perform the indicated operation:  

58.	Perform the indicated operation.  Write the answer as a mixed number in simplest form:  

59.	Write the rate as a unit rate:  21 garage sales in 3 blocks
 
60.	There are 20 mg of a compound in 1 mL of solution.  If a chemist needs 35 mg of the compound for an experiment, how many mL of solution should he use?

          
61.	Find which is the better buy (lower cost per ounce by finding each unit price rounded to three decimal places if necessary.  Assume that different sizes of the same brand are being compared.  
Laundry detergent:  $$3.59 for 96 ounces or $4.12 for 128 ounces.
 per oz
 per oz.    The $4.12 for 128 oz is a better buy.
62.	The following weights were recorded for a group of children:  67, 81, 56, 92, 107, 83.  Find the mean, median, and mode.

median:  First put the weights in ascending order:  56, 67, 81, 83, 92, 107
 	         The median is the middle number if there are an odd number of data values and the 
 	         average of the two middle numbers if there is an even number of data values.  Since   
 	         we have an even number of data values, 

mode:       There is no mode, since no data value occurs more than any other data value.

63.	Solve.  If necessary, round answers to the nearest hundredth.  
The grades are given for a student for a given semester.  Find the grade point average.  The point values of grades are given below:  
A:4		B:3		C:2		D:1		F:0

Grade	Grade Values	Credit Hours	Products	
B	3	2	 6	
C	2	4	 8	
A	4	3	12	
F	0	3	 0	
Totals		12	26	

   	

64.	In a model village, a triangular garden is to have the same shape as an actual triangular garden.  Use the diagram to find the length of the miniature garden’s missing side.  Round to the nearest hundredth, if necessary.

                   14 ft            17.5 ft                                x ft
                                                                 .5 ft             

                                                                          .375 ft
                                   10.5 ft                                

   

65.	Determine whether the pair of triangles is congruent.  If congruent, state the reason why, such as SSS, SAS, or ASA.         

                                      6 in      7 in            7 in             
                                                                                 6 in
                                                       
                                                             4 in
                                             4 in                                         Yes, because of SSS.