In the solution to the equation shown, what property allows you to transform from one step to the next?
4/5x=1
5/4⋅4/5x=1⋅5/4
A. Addition Property of Equality
B. Subtraction Property of Equality
C. Multiplicative Inverse Property
D. Multiplicative Identity Property
C. Multiplicative Inverse Property
The correct answer is C. Multiplicative Inverse Property.
To understand why, let's go through the steps of the solution:
1. The original equation is 4/5x = 1.
2. To eliminate the fraction, we need to multiply both sides of the equation by the reciprocal of 4/5, which is 5/4. This multiplication is allowed by the Multiplicative Inverse Property. According to this property, any number multiplied by its reciprocal equals 1, which does not change the value of the original number. Therefore, we have (4/5x)(5/4) = 1(5/4).
3. Simplifying the left-hand side, we have (4/5) * (5/4) * x = 1 * (5/4). The reciprocal multiplication cancels out the fraction on both sides, leaving us with x = 5/4.
In this case, the Multiplicative Inverse Property allows us to transform the equation from step 2 to step 3.
The correct answer is C. Multiplicative Inverse Property.
Explanation: In the given equation, the property that allows us to transform from one step to the next is the Multiplicative Inverse Property. This property states that if we multiply both sides of the equation by the reciprocal (or multiplicative inverse) of a non-zero number, the equation will still hold true.
In this case, we multiplied both sides of the equation by the reciprocal of 4/5, which is 5/4. This step is valid because the Multiplicative Inverse Property allows us to multiply both sides of the equation by the reciprocal of a non-zero number without changing the equality.