Math - Arithmetic

Arithmetic is the study of numbers and basic operations like addition, subtraction, multiplication and division.

Addition

Addition is the process of combining two or more values.
The result of a addition = “sum”

$1 + 1 = 2\\ 8 + 4 = 12\\ -12 + 37 = 25\\ -128 + 371 = 243\\ 42.4 + 6.27 = 48.67\\ -21.72 + 10.5 = -11.22$

Subtraction

Subtraction is the process of compute the difference between two or more values.
The result of a subtraction = “difference”

$2 - 2 = 0\\ 24 - 6 = 18\\ -7 - 3 = -10\\ -14 - 32 = -46\\ 5.325 - 1.125 = 4.2\\ -32.64 - 32.64 = -64.128$

Multiplication

Multiplication is the process of repeating a sum of the same number.
The result of a multiplication = “product”

$10 \times 5 = 50\\ 4 \times 8 = 32\\ -12 \times 3 = -36\\ -7 \times -5 = 35$

Division

Division is the process of distributing a quantity into equal parts or groups.
The result of a division = “quotient”

$36 \div 6 = 6\\ 55 \div 4 = 13.75\\ -100 \div 8 = -12.5\\ -128 \div -4 = 32$

Identity Property

The identity property says that a special number (the identity element) keeps any number unchanged in an operation.

Additive Identity

$a+0=a$

The additive identity is $0$.

Subtractive Identity

$a-0=a$

The subtractive identity is $0$.

Multiplicative Identity

$a*1=a$

The multiplicative identity is $1$.

Divisive Identity

$a\div1=a$

The divisive identity is $1$.

Law of Signs

Addition & Subtraction

$(-)(-) = (-)\\ (+)(+) = (+)\\ \LARGE(-)\normalsize (+) = (-)\\ \LARGE(+)\normalsize (-) = (+)$

Multiplication & Division

$(-)(-) = (+)\\ (+)(+) = (+)\\ (-)(+) = (-)\\ (+)(-) = (-)$