What is the multiplication property of equality?

The multiplication property of equality is a fundamental principle in mathematics that states that if you multiply both sides of an equation by the same non-zero number, then the two sides remain equal.

Mathematically, it can be stated as follows:

If a = b, then for any non-zero number c, a * c = b * c.

This property allows us to simplify equations and solve for unknown variables. By multiplying both sides of an equation by the reciprocal or a suitable non-zero number, we can eliminate fractions or other complicating factors.

For example, if we have the equation 2x = 8, we can use the multiplication property of equality to isolate the variable x. By multiplying both sides by 1/2, we get (1/2) * 2x = (1/2) * 8, which simplifies to x = 4.

It is important to note that this property holds true only for non-zero numbers. Multiplying both sides by zero is undefined, as any number multiplied by zero equals zero. So, if we multiply both sides of an equation by zero, we lose information and cannot guarantee that the equation remains true.

Overall, the multiplication property of equality is a valuable tool in algebraic manipulations, providing a systematic and reliable method for solving equations and simplifying mathematical expressions.