20 19/30-7 2/15

To solve \(20 \frac{19}{30} - 7 \frac{2}{15}\), we first convert the mixed numbers into improper fractions.

1. Convert \(20 \frac{19}{30}\): \[ 20 \frac{19}{30} = \frac{20 \times 30 + 19}{30} = \frac{600 + 19}{30} = \frac{619}{30} \]

2. Convert \(7 \frac{2}{15}\): \[ 7 \frac{2}{15} = \frac{7 \times 15 + 2}{15} = \frac{105 + 2}{15} = \frac{107}{15} \]

Next, we need a common denominator to subtract the fractions. The least common multiple (LCM) of 30 and 15 is 30.

3. Rewrite \(\frac{107}{15}\) with a denominator of 30: \[ \frac{107}{15} \times \frac{2}{2} = \frac{214}{30} \]

Now we can subtract the two fractions: \[ \frac{619}{30} - \frac{214}{30} = \frac{619 - 214}{30} = \frac{405}{30} \]

4. Simplify \(\frac{405}{30}\): \[ \frac{405 \div 15}{30 \div 15} = \frac{27}{2} \]

Finally, convert \(\frac{27}{2}\) to a mixed number: \[ \frac{27}{2} = 13 \frac{1}{2} \]

Thus, the final result is: \[ 20 \frac{19}{30} - 7 \frac{2}{15} = 13 \frac{1}{2} \]