Download 1.8 Notes Beginning Algebra

Chapter 1
Real
Numbers
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2011,Pearson
2007 Pearson
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Chapter
Chapter1-1
1-1
1
Chapter Sections
1.1 – Study Skills for Success in Mathematics
1.2 – Problem Solving
1.3 – Fractions
1.4 – The Real Number System
1.5 – Inequalities and Absolute Value
1.6 – Addition of Real Numbers
1.7 – Subtraction of Real Numbers
1.8 – Multiplication and Division of Real Numbers
1.9 – Exponents, Parentheses and Order of Operations
1.10 – Properties of the Real Number System
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2015, 2007
2011,Pearson
2007 Pearson
Education,
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Education,
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Chapter
Chapter1-2
1-2
2
Multiplication and
Division of Real
Numbers
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2007 Pearson
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Chapter
Chapter1-3
1-3
3
Sign of the Product Rule
The product of two numbers with like signs
is a positive number.
The product of two numbers with unlike
signs is a negative number.
Example:
a.) 4(– 5) = – 20
b.) (– 6)(7) = -42
c.) (– 9)(-3) = 27
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2015, 2007
2011,Pearson
2007 Pearson
Education,
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Chapter
Chapter1-4
1-4
4
Helpful Hint
At this point some students begin confusing
problems like -2 – 3 with (-2)(-3) and problems
like 2-3 and (-2)(-3). Make sure you understand
the difference between these problems.
Subtraction Problems
Multiplication Problems
2–3 =–5
(-2) (– 3) = 6
2- 3 = – 1
(2)(-3)= – 6
–
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2011,Pearson
2007 Pearson
Education,
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Education,
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Chapter
Chapter1-5
1-5
5
Divide Numbers
The Sign of the Quotient of Two Real Numbers
1. The quotient of two numbers with like signs
is a positive number.
2. The quotient of two numbers with unlike
signs is a negative number.
Example:
a.)
b.)
10   2
5
 45  -9
5
c.)
36  6
6
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2015, 2007
2011,Pearson
2007 Pearson
Education,
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© 2015,
Education,
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Chapter
Chapter1-6
1-6
6
Helpful Hint
For multiplication and division of two real numbers:
(+)(+) = +
(+)(+) = +
(–)(–) = +
(–)(–) = +
(+)(–) = –
(+)(–) = –
(–)(+) = –
(–)(+) = –
Like signs give
positive products and
quotients.
Unlike signs give
negative products and
quotients.
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2011,Pearson
2007 Pearson
Education,
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Education,
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Chapter
Chapter1-7
1-7
7
Remove Negative Signs from Denominators
If a and b represent any real numbers, b 0, then
a  a   a
b
b
b
We generally do not write fractions with a negative
sign in the denominator. When a negative sign
appears in a denominator, we can move it to the
numerator or place it in front of the fraction.
The fraction
5
7
would be written as
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2011,Pearson
2007 Pearson
Education,
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5
7
or
5

7
.
Chapter
Chapter1-8
1-8
8
Real Number Operations
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2015, 2007
2011,Pearson
2007 Pearson
Education,
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Chapter
Chapter1-9
1-9
9
Evaluate Divisions Involving Zero
If a represents any real number except 0, then
0  a = a0 = 0
Division by 0 is undefined.
a ?
0
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© 2011,
2015, 2007
2011,Pearson
2007 Pearson
Education,
Copyright
© 2015,
Education,
Inc. Inc.
Chapter
Chapter1-10
1-10
10