NAME DATE PERIOD 1-2 Study Guide and Intervention · Lesson 1-2 PDF Pass Chapter 1 11 Glencoe...
Transcript of NAME DATE PERIOD 1-2 Study Guide and Intervention · Lesson 1-2 PDF Pass Chapter 1 11 Glencoe...
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NAME DATE PERIOD
Less
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1-2
PDF Pass
Chapter 1 11 Glencoe Algebra 2
1-2 Study Guide and InterventionProperties 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 {all numbers that can be represented in the form m − 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, …}
Name the sets of numbers to which each number belongs.
a. - 11 −
3 rationals (Q), reals (R)
b. √ ��
25
√
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25 = 5 naturals (N), wholes (W), integers (Z), rationals (Q), reals (R)
Exercises
Name the sets of numbers to which each number belongs.
1. 6 −
7 2. -
√
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81 3. 0 4. 192.0005
5. 73 6. 34 1 −
2 7. √�
36 −
9 8. 26.1
9. π 10. 15 −
3 11. - 4.
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2 13. -1 14. √�
42
15. -11.2 16. - 8 −
13 17.
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18. 33. −
3 19. 894,000 20. -0.02
Example
Q, R Z, Q, R W, Z, Q, R Q, R
N, W, Z, Q, R Q, R Q, R Q, R
I, R N, W, Z, Q, R Q, R
Q, R Z, Q, R I, R
Q, R Q, R I, R
Q, R N, W, Z, Q, R Q, R
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NAME DATE PERIOD
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Chapter 1 12 Glencoe Algebra 2
Study Guide and Intervention (continued)
Properties of Real Numbers
1-2
Properties of Real Numbers
Simplify 9x + 3y + 12y - 0.9x.
9x + 3y + 12y - 0.9x = 9x + (- 0.9x) + 3y + 12y Commutative Property (+)
= (9 + (- 0.9))x + (3 + 12)y Distributive Property
= 8.1x + 15y Simplify.
ExercisesSimplify each expression.
1. 8(3a - b) + 4(2b - a) 2. 40r + 18t - 5t + 11r 3. 1 − 5 (4j + 2k -6j + 3k)
4. 10(6g + 3h) + 4(5g - h) 5. 12( a − 3 - b −
4 ) 6. 8(2.4r - 3.1t) - 6(1.5r + 2.4t)
7. 4(20 - 4p) - 3 − 4 (4 - 16p) 8. 5.5j + 8.9k - 4.7k -10.9j 9. 1.2(7x - 5y) - (10y - 4.3x)
10. 9(7d - 4f ) - 0.6(d + 5f ) 11. 2.5(12m - 8.5p) 12. 3 − 4 p - 1 −
5 r - 3 −
5 r - 1 −
2 p
13. 4(10g + 80h) - 20(10h - 5g) 14. 2(15d + 45c) + 5 − 6 (12d + 18c)
15. (7y - 2.1x)3 + 2(3.5x - 6y) 16. 2 − 3 (18m - 6p + 12m + 3p)
17. 14( j - 2k) - 3j(4 - 7k) 18. 50(3a - b) - 20(b - 2a)
Example
Real Number Properties
For any real numbers a, b, and c
Property Addition Multiplication
Commutative a + b = b + a a � b = b · a
Associative (a + b) + c = a + (b + c) (a � b) � c = a � (b � c)
Identity a + 0 = a = 0 + a a � 1 = a = 1 � a
Inverse a + (-a) = 0 = (-a) + a a � 1 − a = 1 = 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
20a k - 2 − 5 j
80g + 26h 4a - 3b
77 - 4p 12.7x - 16y
62.4d - 39f 30m - 21.25p
140g + 120h
0.7x + 9y
2j - 7k
51r + 13t
10.2r - 39.2t
4.2k - 5.4j
1 − 4 p - 4 −
5 r
40d + 105c
20m - 2p
190a - 70b
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