Final answer:
To find the rational number one-third of the way between 47/74 and 23/32, first find common denominator, then subtract the fractions, divide the difference by 3, and finally add it to the smaller fraction.
Step-by-step explanation:
The question requires finding a rational number that is positioned at one-third of the distance between the two given rational numbers, 47/74 and 23/32. First, we need to find the difference between these two numbers. To do this, we have to find a common denominator and subtract the smaller fraction from the larger one. After calculating the difference, we divide this difference by 3 to find the value of one-third of the distance between the numbers. Finally, we add this value to the smaller fraction to find the rational number that is one-third of the way from the smaller number.
Let's start with finding a common denominator for 47/74 and 23/32, which would be 74*32. We’ll convert both fractions to have this common denominator and then subtract. Once we have the difference, we'll divide that by 3 to calculate one-third of the distance, and then add that value to the smaller original fraction (47/74).