| Algebra 1 Notes
Chapter One
Section1.1
Section1.2
Section 1.3
Section 1.4
Section 1.5
Section 1.6
Section 1.7
Section 1.8
Section 1.9
Section 1.10
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Section 1.1 :
Symbols and Expressions
Vocabulary
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variable
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numerical expression
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algebraic expression
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substituting
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evaluate an expression
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natural numbers
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whole numbers
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rational numbers
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grouping symbols
Remember
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A variable is a symbol that
represents two or more numbers.
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A numerical expression contains
one or more numbers and may also contain one or more operations.
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An algebraic expression
contains one or more variables and usually one or more operations.
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When we replace avariable with a
number, it is called substituting.
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To evaluate an expression,
replace each variable with a number and find the numerical value.
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Natural numbers
are the numbers used for counting: 1, 2, 3, ...
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Whole numbers
are the natural numbers and zero: 0, 1, 2, 3, ...
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Parentheses ( ) and brackets [ ] and
{ } are called grouping symbols.
Do operations within grouping symbols first. (See
Example 4 page 6). A
fraction bar is also a grouping symbol. Perform operations within
the numerator and the denominator before simplifying further.
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Translating an English Expression
into an Algebraic expression. |
|
Operation |
English Expression |
Algebraic Expression |
Value for x = 10 |
|
Addition |
x plus 5
5 added to x
x increased by 5
5 more than x
the sum of x and 5 |
x + 5 |
x + 5
10 + 5
15 |
|
Subtraction |
x minus 5
5 subtracted from x
5 less than x
x decreased by 5
the difference of x and 5 |
x - 5 |
x - 5
10 - 5
5 |
|
Multiplication |
5 times x
5 multiplied by x
the product of 5 and x |
5x |
5x
5(10)
50 |
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Division |
x divided by 5
the quotient of x ÷
5 |
x/5 |
x/5
(10)/5
2 |
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Rules for Order of Operation |
| 1. Compute within grouping symbols. |
| 2. Multiply and divide in
order from left to right. |
| 3. Add and subtract in order
from left to right |
Take class notes.
Rework the examples that are illustrated in
this section and the examples that I demonstrated in class.
Do your homework.
Write down questions (examples or concept that you do not
understand).......then.............. Ask these questions in class.
Quick Quiz Evaluate. 1.
8/x for x = 4 2. a - b for a
= 12 and b = 5 3. 3.2y for y
= 1.1 Write an algebraic expression
for each word description. 4.
7 books less than the number of books b on the shelf 5.
3 years more than Jim's age Answers:
1. 2 2. 7 3.
3.52 4. b - 7 5. j + 3
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