Final answer:
To make the expressions 5/8x - 4 and 1/2x - 4 equivalent, you would multiply the 5/8x term by 4/5, but since both expressions already have the same constant term (-4), no additional terms need to be added.
Step-by-step explanation:
The question is asking for terms to add to the expression 5/8x-4 to make it equivalent to 1/2x-4. The key to solving this is understanding the relationship between fractions, multiplication, and division. It requires a familiarity with fractions and their equivalents.
Firstly, we acknowledge that dividing by 8 is the same as multiplying by 1/8 and that multiplying by 1/2 is the same as dividing by 2. Since multiplication and division are inverse operations, we can use this knowledge to find equivalent fractions. To make the expressions equivalent, we need to find a term that makes 5/8x equal to 1/2x.
To turn 5/8x into 1/2x, we need to multiply it by a fraction that when multiplied by 5/8 gives 1/2. This fraction would be 4/5 since (5/8) * (4/5) = 1/2. We can write down the term to multiply as 4/5x but to maintain equality we must add this term to both sides of the equation. However, since the question asks for additional terms to be added to 5/8x - 4 to make it equivalent to 1/2x - 4, and the two expressions already have the same constant term, -4, we do not need to add anything more to the equation.