Download 1.1 Real Numbers and Number Operations

1.1 Real Numbers and Number Operations
Vocabulary
Real Numbers ­ all rational and irrational numbers.
Whole Numbers ­ 0, 1, 2, 3, …
Integers ­ …, ­3, ­2, ­1, 0, 1, 2, 3, …
Rational Numbers ­ any number that can be written as a ratio of 2 integers (or easier, any number that can be written as a fraction).
Irrational Numbers ­ real numbers that are not rational.
Graph ­ the point on a number line that corresponds to a real number.
Coordinate ­ the number that corresponds to a point on a number line.
Origin ­ the point labeled 0 on a number line.
1.
What is ­7 + 10?
2.
Find the area of a circle with diameter 11.
3.
The Venn diagram below shows subsets of the real numbers, the numbers used most often in algebra. Place these numbers in the diagram:
4 1/2, ­sqrt(7), 0.122333..., 5/9, ­7/1, 0.184, ­0.666..., sqrt(7), ­47, 0.238614..., 293, ­0.42, pi, 6/3, ­sqrt(9), 4.
Order the real numbers in example 3 from least to greatest.
­47, ­7/1, ­sqrt(9), ­sqrt(7), ­0.666..., ­0.42, 0.122333..., 0.184, 0.238614..., 5/9, 6/3, sqrt(7), pi, 4 1/2, 293
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5.
Graph the 1st 5 real numbers in example 3.
Properties of Addition and Multiplication
Let a, b and c be real numbers.
Property
Addition
Closure
Commutative
Associative
Identity
Inverse
Distributive
a + b is real
ab is real
a + b = b + a
ab = ba
(a + b) + c = a + (b + c)
(ab)c = a(bc)
a + 0 = 0 + a = a
a ∙ 1 = 1 ∙ a = a
a + (­a) = ­a + a = 0
a ∙ 1/a = 1/a ∙ a = 1
a(b + c) = ab + ac
Multiplication
(Sometimes called the distributive property of multiplication over addition)
Identify the property.
6.
12(1) = 12
7.
7(2 + 3) = 7 ∙ 2 + 7 ∙ 3
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Vocabulary
Additive Inverse (Opposite) ­ the additive inverse of any number a is ­a.
Multiplicative Inverse (Reciprocal) ­ the multiplicative inverse of any number a is 1/a.
Subtraction ­ addition of the opposite. Such as: a ­ b = a + (­b)
Division ­ multiplication by the reciprocal. Such as: a ÷ b = a ∙ 1/b, b ≠ 0.
8.
Use the definitions above to find the difference of ­1 and ­10?
9.
Use the definitions above to find the quotient of ­14 and 7/4?
Unit Analysis ­ Simplify.
10.
11.
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MATH HOMEWORK
1. Homework should show the page number and problem numbers of the assignment.
2. Problems must be copied onto your paper as you do them, with the exception of word problems and multiple choice problems. Ask if you are not sure!
3. All calculations and operations needing to be written must be near the original problem, not in the margin or on a separate paper.
4. Leave an empty line between problems.
5. NEATNESS MATTERS!
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Assignment: Pg 6, #1­3, 7, 10­16, 25­47 odd, 40, 60, 64.
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