Order Basic Algebraic Skills Essay

Order Basic Algebraic Skills Essay

Recall that the proper subsets of the real numbers are the natural numbers,

the whole numbers, the integers, the rational numbers, and the irrational

numbers.

(A) 15 is a natural number, a whole number, an integer, a rational number,

and a real number.

(B) is a rational, real number.

(C) –π is an irrational, real number.

(D) –100 is an integer, a rational number, and a real number.

(E) is an irrational, real number.

2. In interval notation, a square bracket means the endpoint is included, and a

parenthesis means the endpoint is not included. Open intervals do not include the

endpoints. Closed intervals include both endpoints. Half-open (or half-closed)

intervals include only one endpoint. Finite intervals are bounded intervals.

Intervals that extend indefinitely to the right and left are unbounded.

(A) (–∞, –4.5), unbounded below, bounded above, open

(B) [–12, 28], bounded, closed

(C) [–3, ∞), bounded below, unbounded above, half-open

(D) (–∞, 0), unbounded below, bounded above, open

(E) (–∞, ∞), unbounded, open

Order Basic Algebraic Skills Essay

3. (A) closure property of multiplication

(B) commutative property of addition

(C) multiplicative inverse property

(D) closure property of addition

(E) associative property of addition

(F) distributive property

(G) additive inverse property (H) zero factor property

(I) distributive property

(J) associative property of multiplication

4. The absolute value of a real number x is given by |x|= .

(A) 20.9

(B)

(C) –80

(D)

(E) –a

5. (A)

(C) =

(D) <

(E) <

6. To add two numbers that have the same sign, add their absolute values and

give the sum their common sign. Thus, –100 –50 = –150.

7. To add two numbers that have opposite signs, subtract the lesser absolute

value from the greater absolute value and give the sum the sign of the number

with the greater absolute value. Thus, 0.8 –1.9 = –1.1.

8. To subtract two signed numbers, add the opposite of the number that follows

the minus symbol. Thus, –34 – (–22) = –34 22 = –12.

9. To multiply two numbers that have opposite signs, multiply their absolute

values and make the product negative. Thus, .

Order Basic Algebraic Skills Essay

10. To divide two numbers, divide their absolute values (being careful to

make sure you don’t divide by 0) and then follow the rules for multiplication of

signed numbers. Thus, .

11. To multiply two numbers that have the same sign, multiply their absolute

values and keep the product positive. Thus, (–200)(–6) = 1200.

12. –175.54 3.48 1.23 = –170.83

13. 125–(–437) – 80 359 = 841

14. (–0.25)(–600)(4.5)(–50) = –33,750

15.

16. If x is any real number and n is a positive integer, then .

Thus, (–3)

4 = (–3)(–3)(–3)(–3) = 81.

17. –3

4 = –(3 · 3·3 · 3) = –81. Notice that the exponent applies only to the

number 3 and not to the negation symbol.

18. For a number x and a natural number n, , provided that when n is

even, x ≥ 0. Thus, .

19. A nonzero number raised to a negative exponent equals the reciprocal of

the number raised to the corresponding positive exponent. Thus, .

20. provided, in all cases, that x ≥ 0

when q is even and division by zero or 0

0 does not occur. Thus,

= 2

3 = 8.

21. Any nonzero number raised to the zero power is 1. Thus, .

22. x

mx

n = xm n

. Thus, x

5x

3 = x

5 3 = x

8

.

23. Thus, .

24. (x

n)

p = x

np

. Thus, (z

3)

4 = z

3⋅4 = z

12

.

25. . Thus, .

26. . Thus, .

27.

28.

29.

30.

31. (7 8)20 –10 = (15)20 –10 = 290

32. (–9

2)(5 – 8) = (–81)(–3) = 243

33.

34. 8(–2) – = –16 – (–3) = –16 3 = –13

35.

36. (–2)

4 · –3 – (15 – 4)

2 = 16 · –3 – (11)

2 = –48 –121 = –169

37. 3(–11 3 · 8 – 6 · 3)

2 = 3(–11 24 –18)

2 = 3(–5)

2 = 3(25) = 75

Having a hard time figuring out how to do your assignment?

Ask our experts for help and get it done in no time!

The price is based on these factors:

Academic level

Number of pages

Urgency

Basic features

- Free title page and bibliography
- Unlimited revisions
- Plagiarism-free guarantee
- Money-back guarantee
- 24/7 support

On-demand options

- Writer’s samples
- Part-by-part delivery
- Overnight delivery
- Copies of used sources
- Expert Proofreading

Paper format

- 275 words per page
- 12 pt Arial/Times New Roman
- Double line spacing
- Any citation style (APA, MLA, Chicago/Turabian, Harvard)

Delivering a high-quality product at a reasonable price is not enough anymore.

That’s why we have developed 5 beneficial guarantees that will make your experience with our service enjoyable, easy, and safe.

You have to be 100% sure of the quality of your product to give a money-back guarantee. This describes us perfectly. Make sure that this guarantee is totally transparent.

Read moreEach paper is composed from scratch, according to your instructions. It is then checked by our plagiarism-detection software. There is no gap where plagiarism could squeeze in.

Read moreThanks to our free revisions, there is no way for you to be unsatisfied. We will work on your paper until you are completely happy with the result.

Read moreYour email is safe, as we store it according to international data protection rules. Your bank details are secure, as we use only reliable payment systems.

Read moreBy sending us your money, you buy the service we provide. Check out our terms and conditions if you prefer business talks to be laid out in official language.

Read more