Final answer:
The correct answer is (d), where '5 1/2 of three-fourths' is exactly one in '4 1/8'. This is determined by converting mixed numbers to improper fractions, multiplying, and then finding reciprocals to divide fractions correctly.
Step-by-step explanation:
The correct answer is option (d). To interpret the quotient based on the fraction model, we can follow the given example A.4.1 which tells us to multiply the numerators and divide by the denominators when multiplying fractions. If we apply this to the expression '5 1⁄2 of three-fourths', first we must convert the mixed number to an improper fraction. We would get 11⁄2 × 3⁄4 which equals 33⁄8 after multiplying. The quotient of the improper fraction 33⁄8 into '4 1⁄8' simply follows the concept of dividing by a fraction, which is the same as multiplying by its reciprocal.
To do this, convert '4 1⁄8' to an improper fraction, which is 33⁄8, and then multiply by the reciprocal of 33⁄8, which is 8⁄33. Multiplying 33⁄8 by 8⁄33 equals 1, indicating that there is exactly one '5 1⁄2 of three-fourths' in '4 1⁄8'. Hence, using your intuitive understanding of fractions and applying the rules of multiplying and finding the reciprocal should help you interpret quotients correctly.
There are 5 1/2 three-fourths in 4 1/8. To interpret this quotient based on the fraction model, we can think of three-fourths as the fraction 3/4. So, we need to find out how many times 3/4 can fit into 4 1/8.
First, we convert the mixed numbers 4 1/8 and 5 1/2 to improper fractions. 4 1/8 can be written as the improper fraction 33/8, and 5 1/2 can be written as the improper fraction 11/2.
Next, we divide 33/8 by 3/4. To divide fractions, we multiply the numerator of the first fraction by the reciprocal of the second fraction. So, we have (33/8) * (4/3) = (33*4) / (8*3) = 132/24.
Finally, we simplify the fraction 132/24. Both the numerator and denominator are divisible by 12, so we can divide them by 12 to get the simplified fraction 11/2. Therefore, there are 5 1/2 three-fourths in 4 1/8.