2(1)/(2)div (1)/(10)+(9)/(10)

To solve the expression \(2\frac{1}{2} \div \frac{1}{10} + \frac{9}{10}\), follow these steps:<br /><br />1. Convert the mixed number \(2\frac{1}{2}\) to an improper fraction:<br /> \[<br /> 2\frac{1}{2} = \frac{5}{2}<br /> \]<br /><br />2. Divide \(\frac{5}{2}\) by \(\frac{1}{10}\). Dividing by a fraction is equivalent to multiplying by its reciprocal:<br /> \[<br /> \frac{5}{2} \div \frac{1}{10} = \frac{5}{2} \times \frac{10}{1} = \frac{5 \times 10}{2 \times 1} = \frac{50}{2} = 25<br /> \]<br /><br />3. Add \(\frac{9}{10}\) to the result:<br /> \[<br /> 25 + \frac{9}{10}<br /> \]<br /><br />4. Convert 25 to a fraction with a denominator of 10 to add the fractions:<br /> \[<br /> 25 = \frac{250}{10}<br /> \]<br /><br />5. Add the fractions:<br /> \[<br /> \frac{250}{10} + \frac{9}{10} = \frac{250 + 9}{10} = \frac{259}{10}<br /> \]<br /><br />So, the final answer is:<br />\[<br />\frac{259}{10} \text{ or } 25.9<br />\]