User's Manual

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© Texas Instruments, 2007
General Math with the TI-84 Plus Silver Edition
Arithmetic Operations and Properties
Arithmetic Operations with the TI-84 Plus Silver Edition
Addition: valueA + valueB Returns valueA plus valueB √
Subtraction: valueA - valueB Subtracts valueB from valueA π
Multiplication: valueA
x
valueB Returns valueA times valueB Ø
Division: valueA ÷ valueB Returns valueA divided by valueB •
Properties of Addition & Multiplication
Commutative property of addition a+b = b+a
Commutative property of multiplication ab = ba
Associative property of addition a+(b+c) = (a+b)+c
Associative property of multiplication a(bc) = (ab)c
Distributive property of multiplication over addition a(b+c) = ab+ac
Distributive property of multiplication over subtraction a(b–c) = ab–ac
Numbers
Prime Numbers
A whole number with only two factors: itself and 1
EXAMPLES: 2, 3, 5, 7, 11, 13, 17
Common Factors
A number that divides exactly into two or more given numbers
EXAMPLES: 1, 2, 3, 4, 6, and 12 are factors of 12
Greatest Common Factor
The greatest number that is a factor of two or more numbers
EXAMPLE: 4 is the greatest common factor of 12 and 16.
To calculate the greatest common factor on your TI-84 Plus Silver Edition,
press ç ~ 9:gcd(. This will compute the greatest common factor of
valueA and valueB, which can be real numbers or lists.
Least Common Multiple
The smallest number that is a multiple of two or more numbers
EXAMPLE: 12 is the least common multiple of 2, 3, 4 and 6.
To calculate the least common multiple on your TI-84 Plus Silver Edition,
press ç ~ 8:lcm(. This will compute the least common multiple of
valueA and valueB, which can be real numbers or lists.
Order of Operations
General Rules
1 Do all operations within parentheses
2 Do all powers and roots
3 Do multiplication and division in order from left to right
4 Do addition and subtraction in order from left to right
Equation Operating System (EOS
™
) for the TI-84 Plus Silver Edition
EOS defines the order in which functions and expressions are entered and
evaluated. EOS evaluates the functions in an expression in this order:
1 Functions that precede the argument, such as √ (, sin(, or log(
2 Functions that are entered after the argument, such as
2
,
-1
, !, °, or
r
,
and conversions
3 Powers and roots, such as 2
5
or
5
√ 32
4 Permutations (nPr) and combinations (nCr)
5 Multiplication, implied multiplication, and division
6 Addition and subtraction
7 Relational functions, such as > or ≤
8 Logic operator and
9 Logic operators or and xor
Within a priority level, EOS evaluates functions from left to right.
Calculations within parentheses are evaluated first.
Math Symbols
To access many math symbols,
go to the TEST Menu on your
TI-84 Plus Silver Edition, by pressing
y : .
Powers and Roots
Square: value
2
The ° key returns a value multiplied by itself.
The value can be a real or complex number,
expression, or list.
Square root: √ (value) y C returns the square root of a real
or complex number, expression, or list.
Common Squares and Roots
Cube: value
3
Press ç. 3:
3
Returns the cube of a real or
complex number, expression, list, or square matrix.
Cube root:
3
√ (value) Press ç. 4:
3
√ ( Returns the cube root of a
real or complex number, expression, or list.
x
th
root:
x
√ value Press ç. 5:
x
√ ( Returns xth root of a value.
Power: value^power The õ key returns a value raised to a power. Value
can be a real or complex number or expression.
Power of 10: 10^(value) Press y G. Returns 10 raised to the value power.
Value can be a real or complex number or expression.
Fractions, Decimals and Percents
1=1.0 = 100%
1
/
2
= 0.5 = 50%
1
/
3
= 0.333 = 33.3%
1
/
4
= 0.25 = 25%
1
/
5
= 0.2 = 20%
1
/
6
= 0.166 = 16.7%
1
/
8
= 0.125 = 12.5%
1
/
9
= 0.111 = 11.1%
1
/
10
= 0.1 = 10%
1
/
12
= 0.083 = 8.3%
2
/
3
= 0.666 = 66.7%
3
/
4
= 0.75 = 75%
value ➧Dec Press ç. 2: ➧Dec Displays a real or complex
number, expression, list or matrix in decimal format.
value ➧Frac Press ç. 1: ➧Frac Displays a real or complex
number, expression, list or matrix as a fraction
simplified to its simplest terms.
n n
2
√n
9 81 3.0
10 100 3.162
15 225 3.873
20 400 4.472
25 625 5.0
100 10,000 10.0
1
/
2
1
/
4
0.707
1
/
4
1
/
1
6
1
/
2
n n
2
√n
111.0
241.414
391.732
4 16 2.0
5 25 2.236
6 36 2.449
7 49 2.646
8 64 2.828