8 2/3-6 3/5- 2 2/5+1 7/9

To solve the expression, first we need to convert each mixed number to an improper fraction so that we can more easily add and subtract them.

The expression is 8 2/3 - 6 3/5 - 2 2/5 + 1 7/9.

For 8 2/3, there are 3 parts in each whole number, so: 8 * 3 + 2 = 24 + 2 = 26 So 8 2/3 = 26/3.

For 6 3/5, there are 5 parts in each whole number, so: 6 * 5 + 3 = 30 + 3 = 33 So 6 3/5 = 33/5.

For 2 2/5, there are again 5 parts in each whole number, so: 2 * 5 + 2 = 10 + 2 = 12 So 2 2/5 = 12/5.

For 1 7/9, there are 9 parts in each whole number, so: 1 * 9 + 7 = 9 + 7 = 16 So 1 7/9 = 16/9.

Now the expression with the improper fractions is 26/3 - 33/5 - 12/5 + 16/9. To do the operations, we need to find a common denominator which is a multiple of 3, 5, and 9. The smallest common multiple for these numbers is 45. Convert each fraction to an equivalent fraction with a denominator of 45.

For 26/3, the equivalent fraction with a denominator of 45 is: 26 × 15 / (3 × 15) = 390/45

For 33/5, the equivalent fraction with a denominator of 45 is: 33 × 9 / (5 × 9) = 297/45

For 12/5, the equivalent fraction with a denominator of 45 is: 12 × 9 / (5 × 9) = 108/45

For 16/9, the equivalent fraction with a denominator of 45 is: 16 × 5 / (9 × 5) = 80/45

Now you can combine these numbers using the common denominator of 45:

390/45 - 297/45 - 108/45 + 80/45 = (390 - 297 - 108 + 80) / 45 = (390 - 405 + 80) / 45 = (-15 + 80) / 45 = 65 / 45

This fraction can be simplified. Both the numerator and the denominator are divisible by 5:

65 ÷ 5 / 45 ÷ 5 = 13/9

And 13/9 as a mixed number is 1 4/9.

So the result of the expression 8 2/3 - 6 3/5 - 2 2/5 + 1 7/9 is 1 4/9.