Preferred language style: English(U.S.)

Question 1:

Classify each as an example of the commutative property, the associative property, or both:

2+3+5=2+5+3 = commutative property

Question 2:

Write the prime factorization for each the numbers. If the number is prime, so state:

a. 24 = 3 x 2 x 2 x 2

b. 30 = 5 x 3 x 2

c. 300 = 5 x 5 x 3 x 2 x 2

d. 144 = 3 x 3 x 2 x 2 x 2 x 2

Question 3:

Simplify the expressions:

a. 14(-5) = -70

b. -14(-5) = 70

Question 4:

Perform the indicated operations.(Recall that negative exponents are sometimes used to denote fractions)

a.5/3 divid 7/12 = 60/21 or 2 18/21 or 2 6/7

b. -2/9 divid 6/7 = -14/54 or -7/27

Question 5:

In your own words, explain the word or concepts:

Natural numbers- are numbers used for counting, also referred to as counting or positive numbers. Written in order, each number is succeeded or preceded by adding or subtracting 1. (e.g. 1, 2, 3)

Question 6:

Classify each as an example of the commutative property, the associative property, or both:

(3+5)+(2+4)=(3+4)+(5+2)= both associative and commutative properties

Question 7:

Think of three nonassociative word triples as shown in below: Monkey eating Eagle, social climbing girl, blue flame burner

In the English language, the meaning of certain phrases can be very different depending on the association of the words. For example, (Man eating)Tiger is not the same as Man(eating tiger). Decide whether each of the following groups of words is associative.

a. High school student- non-associative

b. Slow curve sign- associative

C. Bare facts person- non-associative

d. Red fire engine- non-associative

E. Traveling salesman joke- non-associative

f. Brown smoking jacket- associative

Question 8:

Write the prime factorization for each of the numbers. If the number is prime, so state:

a. 108 = 3 x 3 x 3 x 2 x 2

b. 740 = 37 x 5 x 2 x 2

c. 699 = 233 x 3

d. 123 = 41 x 3

Question 9:

Same as question 8:

a. 490 = 7 x 7 x 5 x 2

b. 4,752 = 11 x 3 x 3 x 3 x 2 x 2 x 2 x 2

c. 143 = 13 x 11

d. 51 = 17 x 3

Question 10:

Find the canonical representation for each of the numbers:

111

Question 11:

Two movie theaters, UAI and UAII, start their movies at 7:00pm. The movie at UAI takes 75 minutes and the movie at UAII takes 90 minutes. If the shows run continuously, when will they again start at the same time. 2:30 am, Solution 90 x 5, 75 x 6 = 450 minutes or 7 hours and 30 minutes

Question 12:

Pairs of consecuitive odd numbers that are primes are called prime twins. For example, 3 and 5, 11 and 13, and 41 and 43 are prime twins. Can you find any others? 5 and 7, 17 and 19, 29 and 31, 59 and 61, 71 and 73

Question 13:

Simplify the expressions:

a. -5(8-12) = 20

b. [-5(8)]-12 = [-40]-12 = -52

Question 14:

Same as question 13:

a. -14-21 = -35

b. -9+16+(-11) = -4

Question 15:

Same question:

a. -46-(-46) = 0

b. l7-(-3)l = 20

Question 16:

Simplify the expressions:

a. [-54 divid(-9)] divid 3 = 2

b. -54 divid [(-9) divid 3] = 18

Question 17:

Perform the indicated operations.(Recall that negative exponents are sometimes used to denote fractions)

a. 1/2+1/3+1/5 = 31/30 or 1 1/30

b. 2 -1square+3 -1square+5 -1 square = ¼ + 1/9 + 1/25 = 361/900

Question 18:

Same question:

a. 1/10 . -2/5 = -2/50 or -1/25

b. -5/18.9/25 = -45/450 or -1/10

Question 19:

Same question:

a. 2/3-7/12 = 1/12

b. -7/24+-13/16 = -53/48 or -1 5/48

Question 20:

Perform the indicated operations

a. 1/2+-2/3 3/6 + (-4/6) -1/6 -1 30 -30 -5

——– = ———– = ——- = — X —- = —- or —

5/6–3/5 25/30 – (-18/30) 43/30 6 43 258 43

b. 1/3–1/4 4/12 – (-3/12) 7/12 7 16 112 28

——– = —————– = —— = — X — = —– or —-

7/8-3/16 14/16 – 3/16 11/16 12 11 132 33