-6 5/6 + 2 1/3
To solve the problem, we need to add these mixed numbers:
-6 5/6 + 2 1/3
First, we need to convert these mixed numbers into improper fractions, which have a common denominator. To do this, we multiply the whole number by the denominator and add the numerator. The result becomes the new numerator, while the denominator remains the same.
For -6 5/6:
- Multiply -6 by 6 and add 5 to get -35 as the new numerator.
- The denominator remains as 6, so the improper fraction is -35/6.
For 2 1/3:
- Multiply 2 by 3 and add 1 to get 7 as the new numerator.
- The denominator remains as 3, so the improper fraction is 7/3.
Now that both mixed numbers are converted into improper fractions, we can add them together. Since the fractions have the same denominator, we can simply add the numerators and keep the denominator unchanged.
-35/6 + 7/3
To add these fractions, we need a common denominator. In this case, the least common multiple (LCM) of 6 and 3 is 6.
To make the denominators match, we need to multiply the numerator and denominator of the first fraction (-35/6) by 1/2, and the numerator and denominator of the second fraction (7/3) by 2/2.
(-35/6) * (1/2) = -35/12
(7/3) * (2/2) = 14/6
Now we can add the fractions:
-35/12 + 14/6
Since the fractions have the same denominator, we can simply add the numerators:
-35 + 14 = -21
The denominator remains the same: 12.
So, the answer is -21/12.