What is the Multiplication Property of Equality?
Multiplicative Property of Equality
The formal name for the property of equality that allows one to multiply the same quantity by both sides of an equation. This, along with the additive property of equality, is one of the most commonly used properties for solving equations.
Property:
If a = b then a·c = b·c.
Example:
x/5 = 7
(x/5)·5 = 7·5
x = 35
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The Multiplication Property of Equality is a fundamental principle in algebra that states that if you multiply the same non-zero number to both sides of an equation, the equality is still maintained. In other words, if a = b, then for any non-zero number c, ac = bc.
To understand why the Multiplication Property of Equality works, we can think about the basic concept of equality. In an equation, both sides represent the same value or quantity. When we multiply both sides of the equation by the same non-zero number, we are essentially scaling both sides by that factor.
Here's an example to illustrate the Multiplication Property of Equality:
Let's say we have the equation 2x = 8. We want to solve for x.
To isolate x, we can use the Multiplication Property of Equality. We can multiply both sides by 1/2 (or divide both sides by 2) since it is a non-zero number:
(1/2)(2x) = (1/2)(8)
x = 4
By multiplying both sides of the equation by 1/2, we were able to cancel out the coefficient of x on the left side and get the value of x.
It is important to remember that the Multiplication Property of Equality only applies to multiplication and not to addition, subtraction, or division. Each operation has its own properties that must be used correctly.