Order Basic Algebraic Skills Essay

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
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