Download 1-2 Study Guide and Intervention Properties of Real Numbers

NAME
DATE
1-2
PERIOD
Study Guide and Intervention
Properties of Real Numbers
Real Numbers All real numbers can be classified as either rational or irrational. The
set of rational numbers includes several subsets: natural numbers, whole numbers,
and integers.
R
real numbers
{all rationals and irrationals}
Q
rational numbers
m
{all numbers that can be represented in the form −
n , where m and n are integers and
n is not equal to 0}
I
irrational numbers
{all nonterminating, nonrepeating decimals}
Z
integers
{…, -3, -2, -1, 0, 1, 2, 3, …}
W
whole numbers
{0, 1, 2, 3, 4, 5, 6, 7, 8, …}
N
natural numbers
{1, 2, 3, 4, 5, 6, 7, 8, 9, …}
Example
3
rationals (Q), reals (R)
Lesson 1-2
11
a. - −
Name the sets of numbers to which each number belongs.
25
b. √
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
√
25 = 5
naturals (N), wholes (W), integers (Z), rationals (Q), reals (R)
Exercises
Name the sets of numbers to which each number belongs.
6
1. −
Q, R
2. - √
81 Z, Q, R
3. 0 W, Z, Q, R
5. 73 N, W, Z, Q, R
1
6. 34 −
Q, R
2
7. − Q, R
7
4. 192.0005 Q, R
√
36
9
8. 26.1 Q, R
15
10. −
3 N, W, Z, Q, R
−−
11. - 4. 17 Q, R
12. − Q, R
2
13. -1 Z, Q, R
14. √
42 I, R
15. -11.2 Q, R
8
16. - −
Q, R
13
17. − I, R
2
−
18. 33.3 Q, R
19. 894,000 N, W, Z, Q, R
20. -0.02 Q, R
9. π I, R
√
25
Chapter 1
11
√5
Glencoe Algebra 2
NAME
1-2
DATE
PERIOD
Study Guide and Intervention
(continued)
Properties of Real Numbers
Properties of Real Numbers
Real Number Properties
For any real numbers a, b, and c
Property
Addition
Multiplication
Commutative
a+b=b+a
ab=b·a
Associative
(a + b) + c = a + (b + c)
(a b) c = a (b c)
Identity
a+0=a=0+a
a1=a=1a
Inverse
a + (-a) = 0 = (-a) + a
1
1
a−
a =1= −
a · a, a ≠ 0.
Closure
a + b is a real number.
a b is a real number.
Distributive
a(b + c) = ab + ac and (b + c)a = ba + ca
Example
Simplify 9x + 3y + 12y - 0.9x.
9x + 3y + 12y - 0.9x = 9x + (- 0.9x) + 3y + 12y
= (9 + (- 0.9)) x + (3 + 12)y
= 8.1x + 15y
Commutative Property (+)
Distributive Property
Simplify.
Exercises
Simplify each expression.
1. 8(3a - b) + 4(2b - a)
2. 40r + 18t - 5t + 11r
2
j
k-−
51r + 13t
4. 10(6g + 3h) + 4(5g - h)
5
b
a -−
5. 12 −
4
3
(
80g + 26h
)
6. 8(2.4r - 3.1t) - 6(1.5r + 2.4t)
4a - 3b
3
(4 - 16p)
7. 4(20 - 4p) - −
4
10.2r - 39.2t
8. 5.5j + 8.9k - 4.7k -10.9j
77 - 4p
62.4d - 39f
9. 1.2(7x - 5y) - (10y - 4.3x)
4.2k - 5.4j
12.7x - 16y
3
3
1
1
p-−
r-−
r-−
p
12. −
10. 9(7d - 4f ) - 0.6(d + 5f ) 11. 2.5(12m - 8.5p)
4
5
5
2
4
1
−
p-−
r
30m - 21.25p
5
4
5
(12d + 18c)
14. 2(15d + 45c) + −
13. 4(10g + 80h) - 20(10h - 5g)
6
140g + 120h
40d + 105c
2
(18m - 6p + 12m + 3p)
16. −
15. (7y - 2.1x)3 + 2(3.5x - 6y)
3
0.7x + 9y
20m - 2p
17. 14( j - 2k) - 3j(4 - 7k)
18. 50(3a - b) - 20(b - 2a)
2j - 7k
Chapter 1
5
190a - 70b
12
Glencoe Algebra 2
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
20a
1
3. −
(4j + 2k -6j + 3k)