Final answer:
Priya is correct in thinking that the mystery number '?' in division is less than 24. Dividing 24 by any number less than 24 will create a valid number of groups for sharing apples. Understanding reciprocals and the universal consistency of mathematical operations supports this reasoning.
Step-by-step explanation:
Priya is working with the concept of division to share apples equally among her friends. When Priya divides 24 apples by a number to see how many people can receive an equal share, she is essentially determining how many groups of that number can be made from the 24 apples. For instance, 24÷4 equals 6, meaning if each person gets 4 apples, there will be 6 people in total who can receive apples.
When Priya considers the mystery number represented by "?" and thinks it's less than 24, she is basing this on the fact that dividing 24 by any whole number less than 24 will result in more than one group, which aligns with the context of sharing apples among multiple friends. Hence, it's reasonable to agree with Priya's assumption that "?" is less than 24. On the other hand, dividing by a number greater than 24 would not work as it would suggest a fractional or non-whole number of groups, which is not possible when sharing a whole number of apples.
Reciprocals are relevant when thinking about division and multiplication as related operations. By understanding this relationship, we can use multiplication by the reciprocal of a number, instead of division, to achieve the same result. This is evident when we multiply 24 by 5 instead of dividing by 2, which results in a 12-like number, hinting to the outcome being 12 or close to it.
The rules of mathematics are universal and do not change regardless of the context or location. This concept reinforces the understanding that mathematical operations produce consistent results.