Final answer:
To divide fractions, multiply the first fraction by the reciprocal of the second fraction. Convert the mixed number to an improper fraction and compute the division.
Step-by-step explanation:
To calculate the quotient, 6/7 divided by 7 1/2, we need to convert the mixed number 7 1/2 to an improper fraction. To do this, we multiply the whole number (7) by the denominator (2), which is 14. Then we add the numerator (1) to get 15. The improper fraction is therefore 15/2.
To divide fractions, we multiply the first fraction by the reciprocal of the second fraction. The reciprocal of 15/2 is 2/15. So, our division becomes (6/7) * (2/15).
Now, we can multiply the numerators (6 * 2 = 12) and the denominators (7 * 15 = 105) to get the final quotient. The answer is 12/105.