Math 131
Exam 2 Winter 2011
Name: __________________________
Score: 100
Please show all appropriate work clearly and write all explanations in
complete sentences. You may use a scientific calculator only for all
problems. Graphing calculators are not allowed on this exam. You
may not use notes or scratch paper.
All application problems must be answered in complete sentences.
1. Write an application (word problem) that illustrates 8 ÷ 4 in each
of the following ways. (5 points each)
a. Partitive model
b. Subtractive model.
2. Simplify each in the indicated base. No explanation is needed if
you show your work clearly. (5 points each)
a. 235 six + 44 six
b. 431 five – 40 five
c. 103 eight – 76 eight.
d. 23 four x 3 four
3. Identify each of the following properties. No explanation is
needed. (2 points each)
a. _____________________________ 4 x (5 x 3) = (4 x 5) x 3
b. _________________________ 4 x (5 + 3) = (4 x 5) + (4 x 3)
c. _____________________________ 2 x 1 = 2
d. _____________________________ 6 + (2 + 5) = 6 + (5 + 2)
e. _____________________________ 2 + 0 = 2
4. List the numbers that you must check to see if 817 is a prime
number. No explanation is needed. (5 points)
6. Use the prime factorization method to find the following:
No explanation is needed if you show your work clearly. (5 points
each)
a. LCM(64, 50)
b. GCF(64, 50)
7. Simplify the following using the stated alternative algorithm.
No explanation is needed if you show your work clearly. (5
points each)
a. Partial Products
32 x 53
b. Lattice multiplication 342 x 98
8. Explain the divisibility test for 4 using 264 as an example. (10
points)
9. Explain the divisibility test for 9 using 1.234 as an example. (10
points)
10. Is the set of all whole numbers closed under division? If yes,
explain how you know. If no, give a specific counterexample. (10
points)