© Scarborough
Math 365
Exam 3
Spring 2013
Scarborough
Spring 2013
Math 365-501
Exam III
1
NEATLY PRINT NAME: ______________________________________
STUDENT ID: __________________________
DATE: _________________________
"On my honor, as an Aggie, I have neither given nor received unauthorized aid on this academic work."
________________________________
Signature of student
Academic Integrity Task Force, 2004
http://www.tamu.edu/aggiehonor/FinalTaskForceReport.pdf
My signature in this blank allows my instructor to pass back my graded exam in class or allows me to pick up
my graded exam in class on the day the exams are returned. If I do not sign the blank or if I am absent from
class on the day the exams are returned, I know I must show my Texas A&M student ID during my instructor’s
office hours to pick up my exam.
Signature of student ____________________________________________
Write all solutions in the space provided as full credit will not be given without complete, correct accompanying
work, even if the final answer is correct. Use techniques taught in class to solve; do not use brute force (do not
use “list by exhaustion” unless that is the only way to solve the problem). Fully simplify all your answers, and
give exact answers unless otherwise stated. Make sure that you indicate your answer clearly by circling your
response.
What is so special about the number 1729? It is the smallest whole number that can be written as the sum of two
positive cubes in two different ways: 1 7 2 9  13  1 2 3  9 3  1 0 3
© Scarborough
Spring 2013
Math 365-501
Exam III
2
(10 pts: 1 pt for each TF) On problems 1 through 10, circle either “True” or “False.”
1. True or False: An orchard had 25 pear trees and 26 apple trees. The number of apples trees to the total
number of trees is the ratio 25: 51.
2. True or False:
6
is an improper fraction.
6
3. True or False: 0 .6 6 
2
%
3
4. True or False: The following numbers are rational:
5. True or False: The multiplicative inverse of  2
6. True or False:
3

4
7. True or False: If
5
7
a
17

3
11
66
275
is
11
25
,  43 ,
2
3
.
8
9
is a rational number in simplest form, such that 0  a  17 , the repetend has at
most 17 digits.
8. True or False:  4
9. True or False:
46
115
9
11
means  4 
9
11
.
can be written as a terminating decimal.
10. True or False: The Law of Fractions applies to only rational numbers.
# 11 – 15 Short Answer (1 pt each – no work needed)
11. What is the fractional meaning (expanded fractional form) of 5.89? _____________________________
12. Convert 1.476  10  2 into a standard numeral. ______________________________
13. Using congruent circles, model the fraction
3
5
. __________________________________
14. Give an example of a ratio of integers such that its decimal form is non-terminating. ________________
15. Using nonzero rational numbers, give an example of the exponent law
________________________________________________
a
n
a
m
1

a
mn
a
nm
.
© Scarborough
Spring 2013
Math 365-501
Exam III
16. (4 pts) Using base-ten blocks where a block represents one, model and compute 1.36 + 0.053.
17. (4 pts) Model and compute
18. (6 pts) Model and compute
4 2

5 3
4

5
19. (4 pts) Calculate 3.58  1.432 .
.
1
3
.
3
© Scarborough
Spring 2013
Math 365-501
Exam III
4
20. (4 pts) In a photograph of an adult and young child, the child’s height is 3 cm and the adult’s height is
5.7 cm. If the adult is actually 190 cm, how tall is the child?
21. (4 pts) Use the Fundamental Law of Fractions to solve
22. (5 pts) Write
57
75
3
x

5
7
for x.
as a terminating decimal, if possible, using the methods discussed in class (not using
long division). If it is not possible, explain why.
2
1
9
2
23. (4 pts) Fully simplify 3 

24. (3 pts) Define rational number.
5
6
.
© Scarborough
Spring 2013
Math 365-501
Exam III
5
25. (5 pts) Convert 2.0 45 to a ratio of integers in simplest terms.
26. (5 pts) Prove
a
b

c
d

ad
bc
where
c
d
 0.
27. (5 pts) A store has a jacket that is 20% off of the original price, and with a coupon you can get an
additional 10% off. What is your total percent discount?
28. (4 pts) Find a rational number between
7
12
and
7
11
. Show your work. Give your answer using inequality
symbols.
29. (5 pts) Either show that the fractions are equal or put the correct inequality sign between the numbers:
15
85
and
9
51
.
© Scarborough
Spring 2013
Math 365-501
Exam III
30. (6 pts) Correctly and properly write the number 2.508 in words.
31. (4 pts) Simplify fully, using positive exponents in your answer:   3 x 
32. (5 pts) Fully simplify
1
 
2
 13
6  2
10
 16
3
4

7
where x  y .
3
 x 2  y 2   y  x 1
6
© Scarborough
Spring 2013
Math 365-501
Exam III
33. Dividing a nonzero rational number by zero.
a. (4 pts) Prove why you cannot divide a nonzero rational number r by zero.
b. (4 pts) Explain to your ‘student’ why they cannot divide
1
2
by 0.
5-point Bonus: Explain why when I divide 6 by one-half, I get a bigger number.
7