Final answer:
To perform the division 6/7 ÷ 2 1/3, convert the mixed number to an improper fraction. Then, multiply the first fraction by the reciprocal of the second fraction. The simplified form of the division is 18/49.
Step-by-step explanation:
To perform the division 6/7 ÷ 2 1/3, we need to convert the mixed number 2 1/3 to an improper fraction. Multiplying the whole number part (2) by the denominator (3) and adding the numerator (1), we get 7. So, 2 1/3 can be written as the improper fraction 7/3.
Now, to divide fractions, we multiply the first fraction (6/7) by the reciprocal of the second fraction (7/3). The reciprocal of 7/3 is 3/7.
Multiplying 6/7 by 3/7, we get (6/7) × (3/7) = 18/49.
Therefore, the simplified form of 6/7 ÷ 2 1/3 is 18/49.