Which property allows you to multiply or divide both sides of an equation by the same nonzero value without changing the solution?

Which property allows you to multiply or divide both sides of an equation by the same nonzero value without changing the solution?

• A. Additive Property of Equality
• B. Multiplicative Identity
• C. Multiplicative Property of Equality
• D. Substitution Property

Answer: (C)

When you have two expressions that are equal, you can perform the same nonzero operation on both sides and the equality stays true. Specifically, multiplying both sides by a nonzero number (and likewise dividing by a nonzero number) preserves the relationship because it scales both sides by the same factor. If a = b, then ca = cb for any nonzero c, and a/c = b/c for any nonzero c. This lets you isolate a variable, for example turning 3x = 12 into x = 4 by dividing both sides by 3, or by multiplying each side by 1/3. The requirement that the multiplier be nonzero avoids collapsing the equation to something like 0 = 0, which would lose information. This is the multiplicative property of equality.

When you have two expressions that are equal, you can perform the same nonzero operation on both sides and the equality stays true. Specifically, multiplying both sides by a nonzero number (and likewise dividing by a nonzero number) preserves the relationship because it scales both sides by the same factor. If a = b, then ca = cb for any nonzero c, and a/c = b/c for any nonzero c. This lets you isolate a variable, for example turning 3x = 12 into x = 4 by dividing both sides by 3, or by multiplying each side by 1/3. The requirement that the multiplier be nonzero avoids collapsing the equation to something like 0 = 0, which would lose information. This is the multiplicative property of equality.