The _______ property states that If a = b then ac = bc
The multiplicative property of equality
The property you are referring to is called the "Multiplicative Property of Equality."
The property you are referring to is called the Multiplication Property of Equality. It states that if two quantities are equal, then multiplying both sides of the equation by the same number does not change the equality.
To demonstrate this property, consider the equation "a = b." To show that "ac = bc," where "c" is a constant:
1. Start with the equation "a = b."
2. Multiply both sides of the equation by the constant "c."
3. Since the Multiplication Property of Equality states that multiplying both sides by the same number does not change the equality, we have "a * c = b * c."
4. Simplify the equation by performing the multiplication on both sides: "ac = bc."
By applying the Multiplication Property of Equality, you can see that if "a = b," then "ac = bc" when multiplying both sides by the same constant "c."