Answer:
Well to solve the expression 2 1/6 - (-8/3) + (-4 7/9), we need to simplify each fraction and combine the whole numbers with the fractions.
First, let's simplify the fractions:
2 1/6 can be written as an improper fraction: 2 * 6 + 1 = 13/6
-8/3 remains the same.
-4 7/9 can be written as an improper fraction: -4 * 9 + 7 = -29/9
Now we can rewrite the expression as:
13/6 - (-8/3) + (-29/9)
Next, let's simplify the negative signs by changing the subtraction and addition to their equivalent operations:
13/6 + 8/3 + (-29/9)
To add fractions, we need a common denominator. In this case, the common denominator is 6 * 3 * 9 = 162.
Now, let's convert the fractions to have a denominator of 162:
13/6 = (13 * 27) / (6 * 27) = 351/162
8/3 = (8 * 54) / (3 * 54) = 432/162
-29/9 remains the same.
Now, we can add the fractions:
351/162 + 432/162 + (-29/9)
When we have the same denominator, we can simply add the numerators:
(351 + 432 - 29) / 162 = 754/162
To simplify this fraction, we can divide both the numerator and denominator by their greatest common divisor, which is 2:
754/162 = 377/81
Therefore, the answer to the expression 2 1/6 - (-8/3) + (-4 7/9) is 377/81