Final answer:
The student is asked to multiply the number 4 by a fraction, which results in the numerator being 36. To find the denominator that pairs with this numerator to correspond with the answer options, we divide 36 by the whole number provided and multiply the result by the denominator in the given fraction.
Step-by-step explanation:
The student is asked to multiply the whole number 4 by the fraction 9/something. To do so, we apply the rule that states when mulitplying fractions, you multiply the top numbers (numerators) and multiply the bottom numbers (denominators). Here we have a whole number and a fraction, so we can think of the whole number 4 as the fraction 4/1. Multiplying 4/1 by 9/x gives us 36/x. Now, we need to find what x should be for each answer option by converting the provided fractions to have 36 as a numerator.
Let's consider option a. 12; 1/18. The goal is to get 36 as the numerator; we see that 36 divided by 12 gives us 3. So, the x we are looking for is 3 times the denominator in the fraction, which would be 3*18=54. However, this does not match the original denominator of 1, hence a is not correct.
Applying the same calculation to other options will help us identify the correct answer, which will have 36 as the numerator and the correct denominator when the given whole number is divided into 36.