Understanding the Multiplication Property of Equality | Solving Equations and Manipulating Coefficients

Multiplication Property of Equality

The Multiplication Property of Equality is a fundamental principle in algebra that states that if you multiply both sides of an equation by the same non-zero number, the equality will still hold true

The Multiplication Property of Equality is a fundamental principle in algebra that states that if you multiply both sides of an equation by the same non-zero number, the equality will still hold true.

Formally, let’s consider an equation:

a = b

where ‘a’ and ‘b’ are two expressions or values that are equal to each other.

If we multiply both sides of the equation by the same non-zero number ‘c’, then we have:

c * a = c * b

The key point here is that ‘c’ must be non-zero. If ‘c’ were zero, we would end up with an undefined equation.

By applying the Multiplication Property of Equality, we can simplify and solve equations by getting rid of coefficients or isolating variables. Here’s an example:

2x = 6

To solve for ‘x’, we can divide both sides of the equation by the coefficient ‘2’ using the Multiplication Property of Equality:

(1/2) * (2x) = (1/2) * 6

x = 3

In this case, we multiplied both sides by the reciprocal of ‘2’ (which is ‘1/2’) to cancel out the coefficient ‘2’ on the left side and obtain the solution ‘x = 3’.

The Multiplication Property of Equality is a powerful tool that allows us to manipulate equations while maintaining equality, making it an essential concept in algebraic manipulation and problem-solving.

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