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.(1 point)
To find the fraction of the U.S. population with undiagnosed diabetes, we first need to find the fraction of people with diabetes who have not been diagnosed with the disease.
2/5 of people with diabetes have not been diagnosed, so the fraction of people with undiagnosed diabetes is 2/5.
Since 1/10 of the U.S. population has diabetes, the fraction of the U.S. population with undiagnosed diabetes can be found by multiplying 1/10 by 2/5.
(1/10) * (2/5) = 2/50
The fraction of the U.S. population with undiagnosed diabetes is 2/50.
However, we can simplify this fraction by dividing the numerator and denominator by their greatest common divisor.
The greatest common divisor of 2 and 50 is 2.
When we divide the numerator and denominator by 2, we get:
(2/2) / (50/2) = 1/25
Therefore, the fraction of the U.S. population with undiagnosed diabetes is 1/25 in simplest form.