There are 800 doctors and 3600 patients in a hospital. Find the ratio of the number of doctors to the number of patients.

Answer

To find the ratio of the number of doctors to the number of patients in the hospital, follow these steps:

### Step 1: Identify the number of doctors and patients.
- The number of doctors is given as 800.
- The number of patients is given as 3600.

### Step 2: Write the ratio in fraction form.
- The ratio of the number of doctors to the number of patients can be expressed as:
\[ \text{Ratio} = \frac{\text{Number of Doctors}}{\text{Number of Patients}} = \frac{800}{3600} \]

### Step 3: Simplify the fraction.
- To simplify the fraction \(\frac{800}{3600}\), we can divide both the numerator and the denominator by their greatest common divisor (GCD).
- The GCD of 800 and 3600 is 800.
- Dividing both by 800:
\[ \frac{800 \div 800}{3600 \div 800} = \frac{1}{4.5} \]
- To express this in a simpler form, we can multiply both the numerator and the denominator by 2 to avoid decimals:
\[ \frac{1 \times 2}{4.5 \times 2} = \frac{2}{9} \]

### Step 4: Write the final ratio.
- The final simplified ratio of the number of doctors to the number of patients is:
\[ 2:9 \]

### Final Answer:
The ratio of the number of doctors to the number of patients is \(2:9\).

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