These four properties can be summed up briefly by saying, to remain equal (balanced), whatever operation you carry out on an equation you must carry out on both sides of the equality (to all terms):
Addition property
If \(a=b\), then \(a+c=b+c\)
If two expressions are equal, then they remain equal after adding the same quantity to each expression.
Subtraction property
If \(a=b\), then \(a-c=b-c\)
If two expressions are equal, then they remain equal after subtracting the same quantity from each expression.
Multiplication property
If \(a=b\), then \(a\cdot c=b\cdot c\)
If two expressions are equal, then they remain equal after multiplying each expression by the same quantity.
Division property
\[\text{If }a=b\text{ and }c\neq0\text{, then }\frac{a}{c}=\frac{b}{c}\]
If two expressions are equal, then they remain equal after dividing each expression by the same quantity, as long as the dividing quantity is not zero.
