Final answer:
To divide 2/3 by -1 1/3, convert the mixed number -1 1/3 into an improper fraction. Multiply 2/3 by the reciprocal of -4/3, which is -3/4. Simplify the resulting fraction to get the answer, which is -1/2.
Step-by-step explanation:
To divide 2/3 by -1 1/3, we can convert the mixed number -1 1/3 into an improper fraction. -1 1/3 is equal to -4/3. Now, we can write the problem as 2/3 ÷ -4/3. To divide fractions, we multiply the first fraction by the reciprocal of the second fraction. So, the reciprocal of -4/3 is -3/4.
Therefore, the division problem 2/3 ÷ -1 1/3 is the same as multiplying 2/3 by -3/4. To multiply fractions, multiply the numerators together and multiply the denominators together. So, the answer is (2 * -3)/(3 * 4) = -6/12. Finally, we can simplify the fraction -6/12 to -1/2. Therefore, 2/3 ÷ -1 1/3 is equal to -1/2.