Final answer:
The equivalent expression to 2/3 x 5 is (c) 2x5÷3 because multiplying by a fraction is the same as dividing by its reciprocal, and using the associative property of multiplication gives us the same result.
Step-by-step explanation:
The question asks which expression is equivalent to the original multiplication problem 2/3 x 5. To find an equivalent expression, we can rearrange the multiplication and division in a way that preserves the value of the expression. For example, multiplying by a fraction is the same as dividing by its reciprocal.
Starting from the expression 2/3 x 5, we can convert the multiplication of 5 into division. This gives us the equivalent expression 2 x 5 ÷ 3, which matches option C from the provided selections. Thus, the correct answer to the question is (c) 2x5÷3. The associative property of multiplication allows us to multiply 2 by 5 first, obtaining 10, and then divide that result by 3 to get the same answer as multiplying 2/3 times 5 directly.