Final answer:
None of the statements provided by the student result in the number 9 when starting with 15. Correctly finding 9 from 15 would involve dividing 15 by itself and then multiplying by 9 to achieve the desired result.
Step-by-step explanation:
The student's question is asking to identify which mathematical operations correctly result in finding the value for 9 when starting with the number 15. None of the provided statements show correct reasoning because they all lead to results different than the number 9.
For instance, multiply 15 by 2, then divide by 9 results in 30/9, which simplifies to 10/3, not 9. The statement multiply 15 by 9, then divide by 2 leads to 135/2, which is 67.5, again not equal to 9. Both repeated statements about multiplying 15 by 9, then by 2, are incorrect since that leads to 15 x 9 x 2 = 270, which is far from the desired 9.
To precisely get 9 from 15, one should divide 15 by itself and then multiply by 9, i.e., (15/15) x 9, which simplifies to 9.
To find 9, you should multiply 15 by 2 and then divide by 9. This can be written as (15 * 2) / 9. By following the order of operations, you first multiply 15 and 2 to get 30, and then divide 30 by 9 to get 3. Therefore, the correct reasoning is to multiply 15 by 2 and then divide by 9.