Rules for operations on like and unlike terms
Addition
Like terms
Sum the absolute values and add the negative sign afterwards.
$$ \\begin{split} -4 + -3 \\ = 4 + 3 \\ = -7 \\end{split} $$
Unlike terms
Subtract smaller from larger amount and then affix the sign of the larger amount to the sum.
Negative plus positive
$$ \\begin{split} -8 + 5 \\ = 8 - 5 \\ = 3 \\ = -3 \\end{split} $$
Positive plus negative
$$ \\begin{split} 4 + -1 \\ = 4 - 1 \\ = 3 \\end{split} $$
Subtraction
Like terms
Turn the operator and second negative into a plus sign and execute as an addition.
$$ \\begin{split} -4 - -3 = \\ = -4 + 3 \\ = -1 \\end{split} $$
Unlike terms
Positive subtract negative
Turn the negative after the operator to a positive. (Same as previous.)
$$ \\begin{split} 2 - -3 = \\ = 2 + 3 \\ = 5 \\end{split} $$
Negative subtract positive
Start at the negative value and count backwards on the number-line
$$ -2 - 3 = -5 $$
Multiplication
Like terms
The product of two negative numbers will always be a positive number.
$$ -15 \cdot -3 = 45 $$
Unlike terms
The product of a positive and a negative number will always be a negative number.
$$ -3 \cdot 5 = -15 $$
Division
Division follows the same rules as multiplication.
Like terms
The quotient of two negative numbers will always be a positive number.
$$ -15 / -3 = 5 $$
Unlike terms
The quotient of a positive and a negative number will always be a negative number.
$$ -15 / 3 = -5 $$
