Final answer:
To solve 2 2/3 divided by 2/3, convert the mixed number to an improper fraction, 8/3, and multiply by the reciprocal of 2/3, resulting in 4.
Step-by-step explanation:
The question asks us to divide a mixed number by a fraction. We approach this by converting the mixed number to an improper fraction and then multiplying by the reciprocal of the divisor. In this case, 2 2/3 needs to be converted to an improper fraction before dividing it by 2/3.
To convert 2 2/3 into an improper fraction, multiply the whole number by the denominator of the fraction part and add the numerator of the fraction part. This gives us:
2 * 3 + 2 = 6 + 2 = 8
Therefore, 2 2/3 equals 8/3.
Now, we divide 8/3 by 2/3. Dividing by a fraction is the same as multiplying by its reciprocal. Hence, we multiply 8/3 by 3/2, the reciprocal of 2/3.
8/3 × 3/2 = 24/6, which simplifies to 4.
The answer is 4.