Evaluate the expression shown below and write your answer as a fraction in simplest form.

Question

(1/10 + 0.4) / 2/11

Answer 1

To evaluate the expression \((\frac{1}{10} + 0.4) / \frac{2}{11}\), let's follow these steps:

1. Convert 0.4 to a fraction: \[ 0.4 = \frac{4}{10} = \frac{2}{5} \]

2. Add the fractions: We have \(\frac{1}{10} + \frac{2}{5}\). To add these fractions, we need a common denominator. The least common denominator (LCD) of 10 and 5 is 10.

   Convert \(\frac{2}{5}\) to have the denominator of 10: \[ \frac{2}{5} = \frac{2 \times 2}{5 \times 2} = \frac{4}{10} \]

   Now we can add: \[ \frac{1}{10} + \frac{4}{10} = \frac{1 + 4}{10} = \frac{5}{10} = \frac{1}{2} \]

3. Divide by \(\frac{2}{11}\): Now we need to divide \(\frac{1}{2}\) by \(\frac{2}{11}\): \[ \frac{1}{2} \div \frac{2}{11} = \frac{1}{2} \times \frac{11}{2} = \frac{1 \times 11}{2 \times 2} = \frac{11}{4} \]

Thus, the final answer is: \[ \frac{11}{4} \]