Final answer:
The mixed number 4 1/2 is equivalent to the improper fraction 9/2, which is obtained by converting 4 to an improper fraction with the same denominator as 1/2 and then summing them up.
Step-by-step explanation:
To convert the mixed number 4 1/2 into a quotient of two integers, we can follow a straightforward mathematical approach. First, we recognize that 4 1/2 is equivalent to 4 + 1/2. In terms of improper fractions, we can express 4 as ⅔ or ⅙ because four wholes can be represented by any fraction where the numerator is four times the denominator.
Looking specifically at the given options: a) 9/2, b) 7/2, c) 5/2, d) 3/2, we want to find which one represents 4 1/2. We know that 4 can be written as ⅔7 and 1/2 remains the same. Adding these together, we get ⅔7 + 1/2 = ⅙ + 1/2. To add these fractions, they must have the same denominator, so we convert 4 into ⅔9 (8/2) and then add the 1/2 by making it 1x2/2x2 (1/4). The resulting fraction is 8/2 + 1/4 = 9/2.
This shows that the mixed number 4 1/2 expressed as an improper fraction is 9/2, which aligns with answer choice a).