Download 1.1 Numbers and Number Operations

1-1 Symbols and Expressions
Terms to Know:
Variable: A symbol that represents a
number.
Algebraic Expression: Is a collection of
numbers, operators, variables, and
grouping symbols.
Algebra 1c
1-1 Symbols and Expressions
Terms to Know:
Substitution: When a variable is
replaced by a number.
Evaluate: To substitute a number for
each variable and calculate (simplify).
Algebra 1c
1-1 Symbols and Expressions
Objective (things to learn): How to represent
numbers and number operations and how to use
grouping symbols.
First we will start off with learning the
terms that identify specific types of numbers.
The following terms are types of numbers:
Natural Numbers
Rational Numbers
Whole Numbers
Real numbers
Integers
Algebra 1c
1-1 Symbols and Expressions
Natural Numbers
N := {1, 2, 3, 4, …}
Whole Numbers
W := {0, 1, 2, 3, …}
Integers
Z := {… ,-3, -2, -1, 0, 1, 2, 3, …}
Rational Numbers
Real Numbers
Q := { All Fractions ie.
R := { All Numbers }
Algebra 1c
1 3
5
,
,  , ...}
2
4
6
1-1 Symbols and Expressions
The four basic
operations to
remember are:
Algebra 1c
1-1 Symbols and Expressions
•Addition:
268
Sum
** The sum of 2 and 6 is 8 **
•Subtraction:
Difference
95 4
** The difference of 9 and 5 is 4 **
•Multiplication:
Product
4(6)  24
** The product of 4 and 6 is 24 **
•Division:
Quotient
** The quotient of 63 Algebra
and 7
is 9 **
1c
63
9
7
1-1 Symbols and Expressions
Examples:
1. What is the sum of 15 and 19?
** 15 +19 = 34 **
2. What is the difference of 9 and 5?
** 9 - 5 = 4 **
Algebra 1c
1-1 Symbols and Expressions
Examples:
1. What is the product of 4 and 8?
** 4 (8) = 32 **
2. What is the quotient of 36 and 6?
** 36 ÷ 6 = 6 **
Algebra 1c
1-1 Symbols and Expressions
Evaluating expressions containing grouping
symbols
Recall: Order of Operations ( PEMDAS )
Please Excuse My Dear Aunt Sally
3
[( )]

6

1st
2nd
3rd
L
R
Algebra 1c
+ 4th
L
R
1-1 Symbols and Expressions
Evaluating expressions containing grouping
symbols
Examples:
22  (4  5)  6  22  20  6
 22  14
=8
Algebra 1c
Simplify
45
Simplify 20  6
Simplify
22  14
1-1 Symbols and Expressions
Evaluating expressions containing grouping
symbols
Examples:
(45  9)  (12  6)  5  6 Simplify 45  9 and 12  6
 11
Simplify 5  6
Algebra 1c
1-1 Symbols and Expressions
Evaluating expressions containing grouping
symbols
Examples:
64
64
Simplify 12  4

4(12 - 4) 4(8)
64
Simplify 4  8

32
Simplify 64  2
2
Algebra 1c
Algebra 1c