Final answer:
To simplify -2 1/3 - (-10 1/6), convert the mixed numbers to improper fractions, change subtraction to addition and the sign of the number being subtracted to add negative, find a common denominator, add the fractions, and convert the improper fraction back to a mixed number. The simplified form is 7 5/6.
Step-by-step explanation:
To simplify -2 1/3 - (-10 1/6), we need to subtract the second number from the first. When subtracting mixed numbers, we first need to convert them to improper fractions. -2 1/3 can be written as -7/3, and -10 1/6 can be written as -61/6. Subtracting -61/6 from -7/3 gives us (-7/3) - (-61/6). In order to subtract a negative, we change the subtraction to addition and change the sign of the number being subtracted. This becomes (-7/3) + (61/6). To add these fractions, we need to find a common denominator, which is 6 in this case. Converting -7/3 to have a denominator of 6 gives us -14/6. Adding this to 61/6 gives us (-14/6) + (61/6) = 47/6. Finally, we can convert the improper fraction 47/6 back to a mixed number, which is 7 5/6. Therefore, the simplified form of -2 1/3 - (-10 1/6) is 7 5/6. Therefore, the correct answer is option c) 7 5/6.