Express 45 minutes as the fraction of one day

Options

A. `(1)/(40)`
B. `(1)/(32)`
C. `(1)/(60)`
D. `(1)/(24)`

Answer

To express 45 minutes as a fraction of one day, we can follow these steps:

### Step 1: Understand the total minutes in one day
One day consists of 24 hours. To find out how many minutes are in one day, we multiply the number of hours by the number of minutes in an hour:
\[ \text{Total minutes in one day} = 24 \text{ hours} \times 60 \text{ minutes/hour} = 1440 \text{ minutes} \]

### Step 2: Set up the fraction
Now we can express 45 minutes as a fraction of the total minutes in one day:
\[ \text{Fraction} = \frac{45 \text{ minutes}}{1440 \text{ minutes}} \]

### Step 3: Simplify the fraction
To simplify the fraction, we can divide both the numerator and the denominator by their greatest common divisor (GCD). The GCD of 45 and 1440 is 15. So we divide both by 15:
\[ \frac{45 \div 15}{1440 \div 15} = \frac{3}{96} \]

### Step 4: Further simplify the fraction
Now, we can simplify \(\frac{3}{96}\) by dividing both the numerator and the denominator by 3:
\[ \frac{3 \div 3}{96 \div 3} = \frac{1}{32} \]

### Final Answer
Thus, 45 minutes expressed as a fraction of one day is:
\[ \frac{1}{32} \]

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