Final answer:
Julio incorrectly believes the quotient of 6 ÷ 12 is 3, but the correct answer is ½. Division determines how many times one number is contained within another, and understanding the inverse relationship between multiplication and division helps in avoiding such mistakes.
Step-by-step explanation:
Julio's error lies in his understanding of division. The quotient of 6 ÷ 12 is not 3. To correct this, we understand that division is the process of finding how many times one number is contained within another. In this case, 12 is double the size of 6, hence, 6 is contained within 12 only ½ (one half) of the time. Therefore, the correct quotient of 6 ÷ 12 is ½, not 3.
To ensure that we avoid similar errors, it's critical to reinforce the concept of division and common denominators, and remember the relationship between multiplication and division. For instance, dividing by a number is the inverse operation of multiplying by that number's reciprocal. If Julio were to use this understanding, he would see that 6 ÷ 12 is the same as 6 ÷ (1/12), which equals 6 × (1/12), giving the correct answer of ½.