The equivalent expression to "1/3(3p - 12)" is simply "p - 4".

To determine if the expression "1/3(3p - 12)" is equivalent to "p - 4", we should simplify the first expression. Here's how we do it:

We start with the expression: 1/3(3p - 12)

Next, we apply the distributive property to remove the parentheses. This involves multiplying each term inside the parentheses by the fraction that is outside: 1/3 * 3p - 1/3 * 12

Now, simplify each term: The "1/3 * 3p" simplifies to "p" because 1/3 of 3 is 1, and 1 times p is just p. The "1/3 * 12" simplifies to "4" because 1/3 of 12 is 4. So, the simplified expression is: p - 4

Indeed, "1/3(3p - 12)" is equivalent to "p - 4".

Extra: When simplifying algebraic expressions, it's important to make use of properties of arithmetic, including the distributive property. The distributive property states that a(b + c) = ab + ac.

Simplifying an expression means reducing it to its simplest form, so that it is easier to understand or work with. This often involves removing parentheses, combining like terms, and reducing fractions.

In the given expression, dividing each term inside parenthesis by 3 (which is the same as multiplying by 1/3) has the effect of simplifying the expression so that it’s clear how 'p' relates to the constant term without any additional multiplication or division needed to understand the relationship. It transforms the expression into a simple linear expression in the format "mx + b", which is a typical format for a linear equation or linear function, where 'm' is the slope and 'b' is the y-intercept. In this case, 'm' is 1 (as represented by 'p') and 'b' is -4.