6 2/25+7 23/25-8 1/30

To solve the expression \( 6 \frac{2}{25} + 7 \frac{23}{25} - 8 \frac{1}{30} \), we should first convert the mixed numbers to improper fractions.

1. Convert \( 6 \frac{2}{25} \): \[ 6 \frac{2}{25} = \frac{6 \times 25 + 2}{25} = \frac{150 + 2}{25} = \frac{152}{25} \]

2. Convert \( 7 \frac{23}{25} \): \[ 7 \frac{23}{25} = \frac{7 \times 25 + 23}{25} = \frac{175 + 23}{25} = \frac{198}{25} \]

3. Convert \( 8 \frac{1}{30} \): \[ 8 \frac{1}{30} = \frac{8 \times 30 + 1}{30} = \frac{240 + 1}{30} = \frac{241}{30} \]

Now, we can rewrite the expression using the improper fractions: \[ \frac{152}{25} + \frac{198}{25} - \frac{241}{30} \]

Next, we combine the first two fractions, since they have a common denominator: \[ \frac{152 + 198}{25} = \frac{350}{25} = 14 \]

Now we need to subtract \( \frac{241}{30} \) from \( 14 \): First, we convert \( 14 \) to a fraction with a denominator of 30: \[ 14 = \frac{14 \times 30}{30} = \frac{420}{30} \]

So now our expression becomes: \[ \frac{420}{30} - \frac{241}{30} = \frac{420 - 241}{30} = \frac{179}{30} \]

Thus, the final answer is: \[ \frac{179}{30} \]

If needed, we can convert it back to a mixed number: \[ \frac{179}{30} = 5 \frac{29}{30} \]

So the final result is: \[ 5 \frac{29}{30} \]