1.1 Real Numbers and Number Operations

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1.1

• 1.1 Real Numbers and Number Operations

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At the end of this lesson you will

• Use a number line to graph and order real
  numbers.
• Identify properties of and use operations with
  real numbers.

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First some Warm up
or
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Order the numbers from least to greatest.
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Real Numbers

• These are the numbers most often used in algebra.
• Subsets of real numbers whole, integers,
  rational, and irrational.
• You can picture real numbers as points on a
  line.called a real number line.
• There are no holes or gaps in this number
  line. It is complete.
• The point on a number line that corresponds to a
  real number is the graph of the number.
• The number that corresponds to a point on a
  number line is the coordinate of the point.

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The point labeled 0 is the origin.
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A number line can be used to order real numbers.
The inequality symbols, lt, lt,gt,and gt can be used
to show the order of two numbers.

• 1lt 2 since 1 is to the left of 2
• 3gt-3 since 3 is to the right of -3

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When you add or multiply real numbers, there are
several properties to remember
Let a, b, and c be real numbers.
Property
Addition
Multiplication
Closure
ab is a real number
ab is a real number
Commutative
ab ba
ab ba
(ab)c a(bc)
(ab)c a(bc)
Associative
Identity
a0 a, 0aa
a1a, 1aa
Inverse
a(-a)0
The following property involves both addition and
multiplication.
Distributive
a(bc) ab ac
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Subtraction is defined as adding the opposite,
and division as multiplying by the reciprocal.
a b a (-b)
Definition of subtraction
Definition of division
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The difference between 7 and 10 is

• 7-(-10) 7 10
• Subtract by adding the opposite.

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The quotient of 24 and 1/3 is
Division is defined as multiplying by the
reciprocal.
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When you use the operations of addition,
subtraction, multiplication, and division in real
applications, you should use unit analysis to
check that your units make sense.
345 miles 187 miles 158 miles
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Homework 15-53 odd 55, 65