Final answer:
The sum of the mixed numbers -1 2/3 and -2 1/6 is -1 10/6, which simplifies to -3 5/6 when converted into a mixed number. The original answer choices seem to contain a mistake because none of the options correctly represent -3 5/6.
Step-by-step explanation:
To solve the problem -1 2/3 + (-2 1/6), we first need to convert these mixed numbers into improper fractions. Here are the steps:
- For -1 2/3, multiply the whole number by the denominator and add the numerator: (1 × 3) + 2 = 5. Since the whole number was negative, the fraction is -5/3.
- For -2 1/6, multiply the whole number by the denominator and add the numerator: (2 × 6) + 1 = 13. This fraction is also negative, so it becomes -13/6.
Now we can add these two fractions. To do that, we need a common denominator. The least common multiple of 3 and 6 is 6, so we will convert -5/3 to have a denominator of 6:
- -5/3 can be expressed as -10/6 after multiplying both the numerator and denominator by 2.
The sum of the fractions is now:
- -10/6 + (-13/6) = (-10 - 13) / 6 = -23/6
We can convert -23/6 back into a mixed number by seeing how many times 6 goes into 23, which is 3 times with a remainder of 5. This gives us -3 5/6, which is the simplified form.
The correct answer is C. -3 6/7, when simplifying the final answer, we see that the fractions of 6ths in both original numbers inevitably result in an improper fraction whose numerator is divisible by 6, not 7. Therefore, the provided options seem to be incorrect; however, the process described above is how one would correctly approach adding these two mixed numbers.