there are 240 patients in a hospital with health insurance, while 60 patients are without health insurance. write a simplified ratio to express the number of insured patients to the number without insurance
240/60 = 4:1
To write a simplified ratio to express the number of insured patients to the number without insurance, we need to find the greatest common divisor (GCD) of the two numbers.
First, let's label the number of insured patients as "insured" and the number of patients without insurance as "uninsured."
It is given that the number of insured patients is 240, and the number of patients without insurance is 60.
Now, let's find the GCD of these two numbers, 240 and 60, to simplify the ratio.
The GCD of 240 and 60 can be found by listing their common factors:
Factors of 240: 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 40, 48, 60, 80, 120, 240
Factors of 60: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60
The common factors are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, and 30.
The largest common factor, which is also the GCD, is 30.
To simplify the ratio, divide both the numerator and denominator by the GCD (30):
Insured patients: 240 ÷ 30 = 8
Uninsured patients: 60 ÷ 30 = 2
Therefore, the simplified ratio of insured patients to uninsured patients is 8:2.