1/10 of the current U.S. population has diabetes. 2/5 of the people with diabetes have not been diagnosed with the disease. What fraction of the U.S. population has undiagnosed diabetes? Write the answer in simplest form

Answer 1

Let's denote the current U.S. population as \( P \).

1. The fraction of the U.S. population that has diabetes is given as \( \frac{1}{10} \). Therefore, the number of people with diabetes is: \[ \frac{1}{10}P \]

2. We know that \( \frac{2}{5} \) of those with diabetes have not been diagnosed. To find the number of people with undiagnosed diabetes, we calculate: \[ \frac{2}{5} \times \frac{1}{10} P = \frac{2}{5 \times 10} P = \frac{2}{50} P = \frac{1}{25} P \]

Thus, the fraction of the U.S. population that has undiagnosed diabetes is: \[ \frac{1}{25} \]

Therefore, the answer in simplest form is: \[ \boxed{\frac{1}{25}} \]