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Mat 391 Chapter 3 Assessment Questions

..(Disclaimer: There is no guarantee anything typed here is worded or spelled correctly Consequently, there may be errors in both the statements and answers of the following problems.)

1. What number precedes MLXV in the Roman system?

a. M L X I V
d. M L X I X

b.. M L X X I
e none of these

c. M L I I I Answer: a

2. Write-out the following numbers in Hindu-Arabic numerals.

a. Answer: 611

b. LXV - XLII Answer: 23

3 Arrange these Roman numerals from smallest to largest LXIV, XLV, LXVI, LXIX

Answer: XLV, LXIV, LXVI, LXDC

4. Find the sum of each pair of numbers in Hindu-Arabic numerals.

a. Answer: 536

b. MCXLII and DXXXII Answer: 1674

5. a. Write 534(six) as a base ten numeral.
Answer: 202

b. Write 37 as a base two numeral.
Answer: 10010(two)

c. Write E2(twelve) as a base ten numeral.
Answer: 134

d. How many different digits are needed for base fifteen? Answer-fifteen covering from 0 to14: 0, 1, 2, 3,...,9 ,T, E, W, H, R(fourteen),10(fifteen), 11(sixteen or fifteen+one), 12, 13, etc..

6. Find the base indicated by the letter b for 55(ten)=313(base b)

a. four d. seven

b . five e. none of these

c. six Answer: a

7. Choose the largest number from the following list.

a. E-(twelve)-
d. 1101(two)..

b. 62(seven)
e. none of these

c. 212(three)
Answer: b.

8. Perform the following operations:

a. 153(six) + 241(six)
Answer: 434(six)

b. 46(seven)*22(seven)

Answer: 1405(seven)

c. 11110(two) 1111(two)
Answer: 1O(two)

9. Which of the following is 111011(two) in base 4?

a. 113(four)
d. 1221(four)

b. 233(four)
e. none of these

c. 323(four)

Answer: c

10. Write the value of three quarters, four dimes, two nickels, and six pennies in base Eleven.

Answer:10(eleven)

answer: one quarter = 23(eleven), one dime=T(eleven), one nickel=5(eleven), one penney=1(eleven), so add 3*23(eleven)=69(eleven), 4*T(eleven)=37(eleven), 2*5(eleven)=T(eleven), and 6*1(eleven)=6(eleven)

11. Find the solution set on the domain of whole numbers for the following open sentences.

a. x<8 and x>3 Answer: {5, 14)

b. x+3=8 or x-5=9 Answer: {4, 5, 6, 7, 8}

c. (3x-5)>7 Answer: {5, 6, 7, 8,....}

12. a. Use each of the digits 8, 7, 5, and 3 exactly once to create two two-digit numbers, so that when you multiply them, the product is a minimum.

Answer: 37*58=2146

b. 225 is a three-digit numeral If you were permitted to change one of its digits, which would you change to alter the size of the number the least? What digit would you change it to?

Answer: change the five to a four or the five to a six

13. Write-out the solution to the subtraction 852 - 354 in expanded form using a place value chart in each of the following two ways:

a.) subtract directly from ten after regrouping, then add column digit to the difference (all sums and differences involve integers < ten

i.) from five tens, keep four tens and trade one ten for ten ones

ii.) from eight of the ten squared keep seven of the ten squared and trade one ten squared in for ten many tens.

iii.) in the ones column: subtract four ones from ten ones to get six ones; then add two ones to get eight ones.

iv.) in the tens column: subtract five tens from the ten tens to get five tens left to which you add the four tens to get nine tens.

v.) in the ten squared column: subtract three of the ten squared from seven of the ten squared to get four many ten squared.

vi.) the answer is 498

i.) ii.)

iii.), iv.), v.)

..vi.)

b.) add regrouped ten to column digit then subtract from the resulting two-digit number

vii.) Skip over steps iii.) to vi.) and subtract column digit from the regrouped two digit number sum.

i.-ii.) vii).

14. Illustrate 6*148 by the doubling and halving method.

Answer: We know that(1/2)*2=1, so multiple the lhs column number by 1/2 and multiply the rhs column number by 2 in each row to get the next row Cross out all rows with remainder 0,(i.e all rows that have an even number in the lhs column), then add the numbers in all the rows not crossed out in the rhs column For this example, add the colored numbers in the rhs column 314+628=942

15. Consider the multiplication problem(15)*(24).

a Use a rectangular array to show the product of the two numbers visually with rectangles

Answer: 10*20+10*4+5*20+5*4=360

b Write-out the multiplication problem, , using partial products as you would encourage a student to do who is just learning the vertical multiplication algorithm.

Answer: 5*4=20, 5*20=100, 10*4=40, 10*20=200 -

written vertically showing 360 in the fifth row

16. a Pedro learned to play a card game after 3 lessons If he increased his score by 150 points each lesson and had a final score of 660 points, what was his score after the first lesson?

Answer: 70

b The width of a rectangle is 12 units less than its length Find the dimensions of the rectangle if its perimeter is 204 units.

Answer: length = 57 units, width = 45 units

17. Tell whether the following are (A) Always true, (S) Sometimes true or,

(N) Never true

by placing the appropriate letter by the question and justifying your answer.

N a In the expression "'8/2 = 4", the 2 is called the dividend; the 8 is called an addend.

S b Subtraction on the set of whole numbers is closed 3-5=-2 is not a whole number.

A c.(ab)c = a(bc) for all whole numbers a, b and c associativity holds for multiplication

18. From the list of properties given below, identify the property illustrated in each of the examples Upper Case letters represent sets, and a, b, and c represent whole numbers in W.

Associative
Closure
Commutative
Distributive
Identity Ele.

Reflexive
Symmetric
Transitive
Zero Prop for Multiplication

a.) a+(b+c)=(a+b)+c
----Answer: Associative Property------------

b.) a(b+c)=ab+ac
---Answer: Distributive

c.) (a + b) W
---Answer: Closure

..From the list of properties given below, identify the property illustrated in each of the examples A, B, and C represent sets, and a, b, and c represent whole numbers W.

Associative
Closure
Commutative
Distributive Identity Ele.

Reflexive
Symmetric
Transitive

Zero Prop for Multiplication

a. b*O = 0
---Answer: Zero property for multiplication

b. ab = ba
---Answer: Commutative Property

c. a*1=1*a=a
---Answer: one is the mult iplicative Identity element

19. For the following division problems,

a Show the division 84613 in scaffold format.

d

b Find the q and r of the division algorithm for the division of 352 by 50

Answer: q = 7, r = 2

20. Use the tables below for the set S={e, o} and the operations and to answer the questions which follow.

a Is S closed under(? Explain

Answer: Yes, all the answers are from the set S.

b Is S closed under? Explain

Answer: Yes, all the answers are from the set S

c Does S have an identity element for ? If so, what is it?

Answer: Yes, e

d Does S have an identity element for If so, what is it?

Answer: Yes, o.

e Is commutative on S?

Answer: Yes

f Is commutative on S?

Answer: Yes

Home,

1. What number precedes MLXV in the Roman system?
a. M L X I V	d. M L X I X
b.. M L X X I	e none of these
c. M L I I I		Answer: a

2. Write-out the following numbers in Hindu-Arabic numerals.
a.		Answer: 611
b. LXV - XLII		Answer: 23

4. Find the sum of each pair of numbers in Hindu-Arabic numerals.
a.		Answer: 536
b. MCXLII and DXXXII		Answer: 1674

5. a. Write 534(six) as a base ten numeral.			Answer: 202
b. Write 37 as a base two numeral.		Answer: 10010(two)
c. Write E2(twelve) as a base ten numeral.		Answer: 134
d. How many different digits are needed for base fifteen?	Answer-fifteen covering from 0 to14: 0, 1, 2, 3,...,9 ,T, E, W, H, R(fourteen),10(fifteen), 11(sixteen or fifteen+one), 12, 13, etc..

6. Find the base indicated by the letter b for 55(ten)=313(base b)
a. four	d. seven
b . five	e. none of these
c. six		Answer: a

a. E-(twelve)-	d. 1101(two)..
b. 62(seven)	e. none of these
c. 212(three)		Answer: b.

8. Perform the following operations:
a. 153(six) + 241(six)	Answer: 434(six)
b. 46(seven)*22(seven)	Answer: 1405(seven)
c. 11110(two) 1111(two)	Answer: 1O(two)

9. Which of the following is 111011(two) in base 4?
a. 113(four)	d. 1221(four)
b. 233(four)	e. none of these
c. 323(four)		Answer: c

11. Find the solution set on the domain of whole numbers for the following open sentences.
a. x<8 and x>3	Answer: {5, 14)
b. x+3=8 or x-5=9	Answer: {4, 5, 6, 7, 8}
c. (3x-5)>7	Answer: {5, 6, 7, 8,....}

12. a. Use each of the digits 8, 7, 5, and 3 exactly once to create two two-digit numbers, so that when you multiply them, the product is a minimum.
Answer: 37*58=2146
b. 225 is a three-digit numeral If you were permitted to change one of its digits, which would you change to alter the size of the number the least? What digit would you change it to?
	Answer: change the five to a four or the five to a six

13. Write-out the solution to the subtraction 852 - 354 in expanded form using a place value chart in each of the following two ways:

a.) subtract directly from ten after regrouping, then add column digit to the difference (all sums and differences involve integers < ten

i.) from five tens, keep four tens and trade one ten for ten ones
ii.) from eight of the ten squared keep seven of the ten squared and trade one ten squared in for ten many tens.
iii.) in the ones column: subtract four ones from ten ones to get six ones; then add two ones to get eight ones.
iv.) in the tens column: subtract five tens from the ten tens to get five tens left to which you add the four tens to get nine tens.
v.) in the ten squared column: subtract three of the ten squared from seven of the ten squared to get four many ten squared.
vi.) the answer is 498
	i.)		ii.)
iii.), iv.), v.)		..vi.)

b.) add regrouped ten to column digit then subtract from the resulting two-digit number vii.) Skip over steps iii.) to vi.) and subtract column digit from the regrouped two digit number sum.
	i.-ii.)		vii).

17. Tell whether the following are (A) Always true, (S) Sometimes true or,
		(N) Never true
by placing the appropriate letter by the question and justifying your answer.
N	a In the expression "'8/2 = 4", the 2 is called the dividend; the 8 is called an addend.
S	b Subtraction on the set of whole numbers is closed 3-5=-2 is not a whole number.
A	c.(ab)c = a(bc) for all whole numbers a, b and c associativity holds for multiplication

18. From the list of properties given below, identify the property illustrated in each of the examples Upper Case letters represent sets, and a, b, and c represent whole numbers in W.

Associative	Closure	Commutative			Distributive		Identity Ele.
Reflexive	Symmetric	Transitive					Zero Prop for Multiplication

a.) a+(b+c)=(a+b)+c				----Answer: Associative Property------------
b.) a(b+c)=ab+ac				---Answer: Distributive
c.) (a + b) W				---Answer: Closure

..From the list of properties given below, identify the property illustrated in each of the examples A, B, and C represent sets, and a, b, and c represent whole numbers W.

Associative	Closure		Commutative		Distributive	Identity Ele.
Reflexive	Symmetric		Transitive			Zero Prop for Multiplication

a. b*O = 0			---Answer: Zero property for multiplication
b. ab = ba			---Answer: Commutative Property
c. a1=1a=a			---Answer: one is the mult iplicative Identity element

20. Use the tables below for the set S={e, o} and the operations and to answer the questions which follow.

a Is S closed under(? Explain
Answer: Yes, all the answers are from the set S.
b Is S closed under? Explain
Answer: Yes, all the answers are from the set S
c Does S have an identity element for ? If so, what is it?
Answer: Yes, e
d Does S have an identity element for If so, what is it?
Answer: Yes, o.
e Is commutative on S?
Answer: Yes
f Is commutative on S?
Answer: Yes