Question

$$ \text {} 8 \frac{9}{10}+1 \frac{1}{5} $$

Short answer

The sum of \(8 \frac{9}{10} + 1 \frac{1}{5}\) is \(10 \frac{1}{10}\).

Step-by-step solution

Convert Mixed Numbers into Improper Fractions

Transform both mixed numbers into improper fractions. The first mixed number, \(8 \frac{9}{10}\), when converted to an improper fraction will be \( \frac{8 \times 10 + 9}{10} = \frac{89}{10} \). The second one, \(1 \frac{1}{5}\), can be converted to \( \frac{1 \times 5 + 1}{5} = \frac{6}{5} \).

Add the Improper Fractions

Add the two improper fractions together. To add two fractions, they must have the same denominator. In this case, the denominators are 10 and 5. The least common multiple of 10 and 5 is 10, and 5 can be converted to 10 by multiplying by 2. So we have \( \frac{89}{10} + \frac{6 \times 2}{10} = \frac{89 + 12}{10} = \frac{101}{10} \).

Convert Back to Mixed Number

The improper fraction \( \frac{101}{10} \) can be converted back into a mixed number. Divide the numerator by the denominator: \(101 \div 10 = 10\) with remainder 1, so the fraction \( \frac{101}{10} \) is equivalent to the mixed number \(10 \frac{1}{10}\).