# algebra

These problems are labeled as Natural numbers, Prime numbers, Integers, Rational numbers, Irrational numbers, Groups Felds and Real numbers, Discrete Mathematics,and Crytography.

p.188 #26 Classify as an example of the commutative property, the associative property, or both: (3+5)+(2+4)=(3+4)+(5+2)

p.188 #30 Think of three nonassociative word triples (i.e., (word1 word2) word3 has a different meaning than word1 (word2 word3), e.g., (man eating) tiger and man (eating tiger).

p.190 #59 (Solve two different ways) Put the appropriate plus or minus signs between the numbers, in the correct places, so that the sum total will equal 1.

0 1 2 3 4 5 6 7 8 9 = 1

p.203 #18 Write the prime factorizations for each of the numbers. If the number is prime, so state.

a. 108 b. 740 c. 699 d. 123

p.203 #20 Write the prime factorizations for each of the numbers. If the number is prime, so state.

a. 490 b. 4,752 c. 143 d. 51

p.203 #32 Find the canonical representation of the number 111.

p.203 #46 Two movie theatres, UAI and UAII, start their movies at 7:00 PM. 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?

p.203 #50 Pairs of consecutive 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?

p.212 #20 Simplify the expressions:

a. -5(8-12) b. [-5(8)]-12

p. 212 #30 Simplify the expressions:

a. -14-21 b. -9+16+(-11)

p. 212 #32 Simplify the expressions:

a. -46-(-46) b. |7-(-3)|

p. 212 #46 Simplify the expressions:

a. [-54(-9)] 3 b. -54[(-9)3]

p.220 #26 Perform the indicated operations:

a. 1/2 + 1/3 + 1/5 b. 2-1 + 3-1 + 5-1

p. 220 #32 Perform the indicated operations:

a. 1/10 * (-2)/5 b. -5/18 * 9/25

p. 220 #36 Perform the indicated operations:

a. 2/3 - 7/12 b. -7/24 + (-13/16)

p. 220 #38 Perform the indicated operations:

#### Solution Summary

The solution is composed of detailed explanations to various algebra questions, such as fractions, natural numbers, prime factorizations, and irrational numbers.