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1) 12 • (–28) 2) –23 + (–15) 3) 28 ÷ ( –12)
4) 0.314, 0.0978, 0.309, 0.3131
1.1 Warm-UpSimplify.
Order the numbers from least to greatest.
-336 -38 7
3
0.0978, 0.309, 0.3131, 0.314
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Alg2 Lesson 1-1Properties of Real Numbers
Objectives:
1. Identify the subsets of real numbers.
2. Identify the properties of real numbers.
3. Find the opposite and reciprocal of a number.
4. Order real numbers and graph on a number line.
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SUBSETS OF THE REAL NUMBERS
WHOLE NUMBERS: 0, 1, 2, 3, …………….
INTEGERS: ……., -3, -2, -1, 0, 1, 2, 3, ………….
RATIONAL NUMBERS: A ratio of two integers (3/4, 1/3, -4/1, ….) when written as decimals, rational numbers terminate or repeat. (3/4 = 0.75, or 1/3 = 0.3333….)
IRRATIONAL NUMBERS: They neither terminate or repeat. (л, 2, etc.)
NATURAL NUMBERS: 1, 2, 3, …………….
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Example 1
Graph the real numbers , 3, and – 1.8 5 2
–5 –4 –3 –2 –1 1 2 5430
Where is the origin?
–5 –4 –3 –2 –1 1 2 5430
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Properties of Real Numbers
• Opposite or Additive Inverse of any number a is –a– The sum of any two opposites is 0
• The Reciprocal or Multiplicative Inverse of any nonzero number a is 1/a– The product of reciprocals is 1
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• Example 4
Find the opposite and the reciprocal of each number
a) -3 b)
Opposite: Opposite:
Reciprocal: Reciprocal:
3
5
5
3
1
3
3
5
3
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PROPERTIES OF ADDITION AND MULT.
ASSOCIATIVE: (a + b) + c = a + (b + c) & (ab)c = a(bc)
COMMUTATIVE: a + b = b + a & ab = ba
DISTRIBUTIVE: a(b + c) = ab + ac
IDENTITY: a + 0 = a & a • 1 = a
INVERSE: a + (-a) = 0 & a • = 1 1 a
CLOSURE: a + b is a real number & ab is a real number
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Example 2
Identify the property shown.
a. 14 + 7 = 7 + 14 b. 5 • = 1
Commutative property of addition
Inverse Property of multiplication
1 5
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Operations with Real Numbers.
Example 3
a. The difference of -3 and -15 is:
b. The Quotient of -18 and 1/6 is:
Sum +Difference –
Product x
÷Quotient
-3 – -15
18
-3 + 15 = 12
1 6
6 1
6 1•
•-18 • 6 = -108
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• The Absolute Value of a real number is its distance from zero on the number line
Example 5
Find the absolute value of:
a) |-4|
b) |0|
c) |-1 (-2)|
4
0
2
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HOMEWORKDue Wednesday:
Pg. 8 – 9
12 – 24, 34 – 36, 42 – 62 even