To subtract mixed numbers, we first convert them into improper fractions. The mixed number 1 2/3 can be converted to an improper fraction by multiplying the whole number (1) by the denominator (3) and adding the numerator (2), resulting in 5/3. Similarly, the mixed number 2 1/3 converts to 7/3. Now, we can perform the subtraction: 5/3 - 7/3. Since the denominators are the same, we subtract the numerators: 5 - 7 = -2. Thus, we have -2/3 as the result. Therefore, 1 2/3 - 2 1/3 equals -2/3.