10 16/26-6 10/27+4 5/27

To solve the expression \(10 \frac{16}{26} - 6 \frac{10}{27} + 4 \frac{5}{27}\), we first convert the mixed numbers into improper fractions.

1. Convert \(10 \frac{16}{26}\): \[ 10 \frac{16}{26} = \frac{10 \times 26 + 16}{26} = \frac{260 + 16}{26} = \frac{276}{26} \]

2. Convert \(6 \frac{10}{27}\): \[ 6 \frac{10}{27} = \frac{6 \times 27 + 10}{27} = \frac{162 + 10}{27} = \frac{172}{27} \]

3. Convert \(4 \frac{5}{27}\): \[ 4 \frac{5}{27} = \frac{4 \times 27 + 5}{27} = \frac{108 + 5}{27} = \frac{113}{27} \]

Now we need to substitute these improper fractions back into the expression: \[ \frac{276}{26} - \frac{172}{27} + \frac{113}{27} \]

To combine these fractions, we will need to get a common denominator. The denominators are 26 and 27, so the least common denominator (LCD) is \(26 \times 27 = 702\).

Next, we convert each fraction:

1. For \(\frac{276}{26}\): \[ \frac{276}{26} = \frac{276 \times 27}{702} = \frac{7452}{702} \]

2. For \(\frac{172}{27}\): \[ \frac{172}{27} = \frac{172 \times 26}{702} = \frac{4472}{702} \]

3. For \(\frac{113}{27}\): \[ \frac{113}{27} = \frac{113 \times 26}{702} = \frac{2938}{702} \]

Now substitute back into our expression: \[ \frac{7452}{702} - \frac{4472}{702} + \frac{2938}{702} \]

Now simplify: \[ \frac{7452 - 4472 + 2938}{702} = \frac{7452 - 4472 + 2938}{702} = \frac{7452 - 4472 + 2938}{702} = \frac{7452 - 4472 = 2980}{702} \] The next step is \( 2980 + 2938 = 5918 \)

So we get: \[ \frac{5918}{702} \]

To simplify \(\frac{5918}{702}\), find the GCD of 5918 and 702: 5918 ÷ 2 = 2959 702 ÷ 2 = 351

Final fraction: \(\frac{2959}{351}\)

Therefore, the final answer is: \[ \frac{2959}{351} \] or as a mixed number: \(8 \frac{41}{351}\)