Find the ratio of each of the in simplest form :
2 hours 45 minutes to 1 hour 15 minutes

Answer

To find the ratio of 2 hours 45 minutes to 1 hour 15 minutes in simplest form, follow these steps:

### Step 1: Convert hours to minutes
First, we need to convert both time durations into minutes.

- For 2 hours 45 minutes:
\[ 2 \text{ hours} = 2 \times 60 = 120 \text{ minutes} \]
Adding the extra 45 minutes:
\[ 120 + 45 = 165 \text{ minutes} \]

- For 1 hour 15 minutes:
\[ 1 \text{ hour} = 1 \times 60 = 60 \text{ minutes} \]
Adding the extra 15 minutes:
\[ 60 + 15 = 75 \text{ minutes} \]

### Step 2: Write the ratio
Now that we have both durations in minutes, we can write the ratio:
\[ \text{Ratio} = \frac{165 \text{ minutes}}{75 \text{ minutes}} \]

### Step 3: Simplify the ratio
To simplify the ratio, we divide both the numerator and the denominator by their greatest common divisor (GCD).

- The GCD of 165 and 75 can be found by factoring:
- \(165 = 15 \times 11\)
- \(75 = 15 \times 5\)

Thus, the GCD is 15.

Now, divide both numbers by 15:
\[ \frac{165 \div 15}{75 \div 15} = \frac{11}{5} \]

### Final Result
The ratio of 2 hours 45 minutes to 1 hour 15 minutes in simplest form is:
\[ \text{Ratio} = 11:5 \]

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