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.
Let's start by finding 2/5 of 1/10.
2/5 * 1/10 = (2*1)/(5*10) = 2/50
To simplify the fraction, we can divide the numerator and the denominator by their greatest common factor, which is 2.
2/50 ÷ 2/2 = 1/25
So, the fraction of the U.S. population with undiagnosed diabetes is 1/25.
To find the fraction of the U.S. population that has undiagnosed diabetes, we first need to find the fraction of people with diabetes who have been diagnosed.
Given that 1/10 of the current U.S. population has diabetes, the fraction of people with diabetes who have been diagnosed is 1 - 2/5.
To subtract the fractions, we first need to find a common denominator. The common denominator here is 10.
Converting 2/5 to have a denominator of 10, we get 4/10.
Then, we subtract:
1 - 4/10 = 10/10 - 4/10 = 6/10
Therefore, the fraction of the U.S. population with undiagnosed diabetes is 6/10.
Simplifying the fraction, we divide both the numerator and denominator by their greatest common divisor, which is 2:
6/10 = 3/5
So, 3/5 of the U.S. population has undiagnosed diabetes.
To find the fraction of the U.S. population with undiagnosed diabetes, we need to multiply the fraction of the U.S. population with diabetes by the fraction of people with diabetes who have not been diagnosed.
1/10 represents the fraction of the U.S population with diabetes.
2/5 represents the fraction of people with diabetes who have not been diagnosed.
To calculate the fraction of the U.S population with undiagnosed diabetes, we multiply these two fractions:
(1/10) * (2/5) = 2/50
The fraction 2/50 can be simplified by dividing both the numerator and denominator by their greatest common factor, which is 2:
2/50 ÷ 2/2 = 1/25
Therefore, the fraction of the U.S. population with undiagnosed diabetes is 1/25.