8.13 Real Number System and Properties
Complete the "Think About a Plan" ­ Order of Operations and Evaluating Expressions Worksheet.
Homework Answers:
pages 7 ­ 8
pages 13 ­ 14
9. p + 4
27. 8 ­ 9r
11. n/8
29. (3/7)y ­ 4
13. t/82
32. 13b
15. 5n + 6.7
17. 5 more than a number q
19. the product of 12 and x
21. one more than the product of 9
and a number n
23. the difference of 15 and the quotient
36. a) 24.0 cubic inches
b) 2.0 cubic inches
37. 256
39. 5
41. 12
45. 27
47. 6
49. 68
51. 3
of 1.5 and d
25. 5 more than the product of 9 and a number n; 9n + 5
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8.13 Real Number System and Properties
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8.13 Real Number System and Properties
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8.13 Real Number System and Properties
1.3 The Real Number System
If the pattern continues, which will be the first figure to contain more than 200 square units? Explain your reasoning.
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1
3
4
A. Understanding Square Roots
A number "a" is a square root of a number if
Example: If You can simplify certain square roots and determine the exact answers. 1. 2.
3.
4.
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8.13 Real Number System and Properties
B. Subsets of the Real Number System
*rational number:
* integer:
*whole number:
*natural number:
* irrational number:
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8.13 Real Number System and Properties
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8.13 Real Number System and Properties
Apply it: To which subsets of real numbers does each
number belong?
a. 15
d.
b. -1.4583
e.
c.
f. -4
Look at the lesson check on page 20 in your book. 1.4 Properties of Real Numbers
1. Commutative Properties of Addition and Multiplication
­ Changing the order of the addends does not change the sum. ­ Changing the order of the factors does not change the product.
2. Associative Properties of Additon and Multiplication.
­Changing the grouping of the addends does not change the sum. ­Changing the grouping of the factors does not change the product. 3. Identity Properties of Addition and Multiplication
­The sum of any real number and 0 is the original number. ­The product of any real number and 1 is the original number. 7
8.13 Real Number System and Properties
4. Zero Property of Multiplication
­­The product of "a" and 0 is zero. 5. Multiplication Property of -1
­­The product of ­1 and "a" is negative 1. What property is illustrated by each statement?
a. 42 * 0= 0
b. (y +2.5) +28 = y + (2.5 +28)
c. (y + 2.5) + 28 = 28 + (y + 2.5)
d. 10x + 0 = 10x
Explain the properties used in the following scenario:
A movie ticket costs $7.75. A drink costs $2.40. Popcorn costs $1.25. what is the total cost of a ticket, a drink, and popcorn? Use mental math.
(7.75 +2.40) + 1.40 = (2.40 + 7.75) + 1.25
= 2.40 + (7.75 + 1.25)
= 2.40 + 9
= 11.40
** Look at lesson check on pg. 26
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8.13 Real Number System and Properties
1.7 - The Distributive Property
6. The Distributive Property
a(b+c) = ab +ac
(20 +6)4 = 20(4) + (6)4
1. ­3(x +8)
2. (5b ­ 4)(­7)
3. 12(3 ­ )
4. 5(x + y ­ z) + 4(2x ­ 3y + 6z)
5. 2(­3x + 5y ­ 4z) ­ 6( x ­ y + 2z)
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8.13 Real Number System and Properties
6. 7. Homework:
pg 20 #9-36 (odd), 52-55, 57-63
pg. 26 # 7-19 (all), 36-46 (all)
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8.13 Real Number System and Properties
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