What fraction of a day are 7 minutes 12 seconds ?

Options

A. `(1)/(300)`
B. `(1)/(200)`
C. `(1)/(240)`
D. `(1)/(225)`

Answer

To find what fraction of a day is 7 minutes 12 seconds, we can follow these steps:

### Step 1: Convert the time into seconds
First, we need to convert 7 minutes and 12 seconds into total seconds.

\[ \text{Total seconds} = (7 \text{ minutes} \times 60 \text{ seconds/minute}) + 12 \text{ seconds} \]

Calculating this:

\[ 7 \times 60 = 420 \text{ seconds} \]
\[ 420 + 12 = 432 \text{ seconds} \]

### Step 2: Calculate the total number of seconds in a day
Next, we need to find out how many seconds are in a day.

\[ \text{Seconds in a day} = 24 \text{ hours} \times 3600 \text{ seconds/hour} \]

Calculating this:

\[ 24 \times 3600 = 86400 \text{ seconds} \]

### Step 3: Set up the fraction
Now we can set up the fraction of the day that 7 minutes 12 seconds represents.

\[ \text{Fraction} = \frac{\text{Total seconds}}{\text{Seconds in a day}} = \frac{432}{86400} \]

### Step 4: Simplify the fraction
To simplify the fraction, we can divide both the numerator and the denominator by their greatest common divisor (GCD).

Calculating the GCD of 432 and 86400, we find that it is 432.

Now we simplify:

\[ \frac{432 \div 432}{86400 \div 432} = \frac{1}{200} \]

### Final Answer
Thus, the fraction of a day that 7 minutes 12 seconds represents is:

\[ \frac{1}{200} \]

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