Final answer:
The discussed properties include multiplication and division properties of equality, along with rules for the signs when multiplying or dividing numbers. Operations must be applied equally to both sides of an equation to maintain balance, drawing an analogy with a balanced see-saw.
Step-by-step explanation:
The question revolves around the properties of equality and the application of mathematical operations to both sides of an equation. When we multiply or divide both sides of an equation by the same number, we are using the multiplication properties of equality or the division properties of equality, respectively. It's crucial to apply these operations to every term on either side of the equality, encasing any side with more than one term in brackets before performing multiplication or division to ensure each term is properly affected.
The signs of numbers within an equation also play a role when multiplying and dividing. When two positive numbers or two negative numbers multiply, the answer has a positive sign, while a positive number multiplied by a negative number results in a negative sign. The same rules apply when dividing numbers. Keep in mind that division is simply multiplication by the inverse of a number.
Thinking of an equation as a balanced see-saw can help you understand the importance of performing operations equally on both sides. In the case of Ohm's Law, dividing by R on both sides maintains the balance and helps derive a different form of the equation. This is the essence of keeping equations balanced through the application of equal operations on both sides.