Download math_130_sample test 4

Sample Test, Math 130 Test #4 Spring 2014
Chapters 10-11
Instructor: Smith-Subbarao
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Name
1. Put the following numbers in order from smallest to largest.
-8/13, 0.63, -3 1/5, 0, -1.45, 4/5
2. The set of rational numbers is dense. That is we can always find another rational number in between
any two rational numbers.
a) To show this is true. Find four fractions in between -3/8 and – 2/9.
b) Is the set of integers dense? (Yes or No)
3. A student is having a hard time understanding the problem -15 + 20.
a) Explain the problem using temperature.
b) Explain the problem using money.
4. Another student is having trouble understanding 8 – (-6).
a) Explain the problem using the chips model where black chips are negative numbers and
white chips are positive numbers.
b) Explain the problem using the standard rule for subtraction. Be sure to address the topic of
additive inverses.
5. Use repeat subtraction to explain the problem −18 ÷ ( −3) .
7. A field is a set of numbers for which the following properties hold for addition and multiplication
(Identity, Inverse, Commutative, Associative, Closure, and Distributive properties). Does the set of
integers (… -3, -2, -1, 0,1,2,3,…) make up a field? (Yes or No). If yes, give an example of each
property using both addition and multiplication. If no, give a counter example where at least one of
the properties fails.
6. True or False?
7.
a)
8 is a factor of 108
b)
3 is a multiple of 99
c)
36 is a divisor of 9
d)
69 is divisible by 13
a) Give all the factors of 36.
b) List the first eight multiples of 7.
8.
a) Find the prime factorization of 480.
b) Use the prime factorization of 480 in part (a) to tell how many factors 480 has?
(Note: You do not need to find them. Just tell how many there are.)
9. Explain to a student how to find the Greatest Common Factor of 36 and 120 using the prime
factorization approach.
10. Explain to a student how to find the LCM of 18 and 24 using the multiple lists method.
11. Determine whether the number 147,015 is divisible by 2, 3, 4, 5, 6, 8, 9, 10 or 11? Use the
divisibility tests instead of long division.
12. Reduce the following fractions using prime factorization:
a) 2860/4095
b) 5544/11,880
13. A class is having an argument about the prime factorization of 504. Which of the following is true?
Do not use long division to calculate your answer.
a) Using a sieve approach, if we try prime factors below 25, we have gone far enough.
b) The number 9 is a divisor.
c) The number 4 is a factor
d) The number 6 is a prime factor
14. Use prime factors to allow mental computation of the following. Explain your reasoning:
a) 140/28
b) 48 x 15