Express the following a)18 hours as the fraction of 1 day
The Correct Answer and Explanation is:
To express 18 hours as a fraction of 1 day, we need to understand the relationship between hours and a day.
Solution:
- We know that a day has 24 hours.
- So, the fraction of 1 day represented by 18 hours is:
[
\frac{18}{24}
] - To simplify (\frac{18}{24}), we divide both the numerator and the denominator by their greatest common divisor, which is 6:
[
\frac{18 \div 6}{24 \div 6} = \frac{3}{4}
]
Therefore, 18 hours is (\frac{3}{4}) of a day.
Explanation:
Fractions are used to represent parts of a whole. In this case, we are trying to determine what portion of an entire day (24 hours) is represented by 18 hours. To do this, we divide the part (18 hours) by the whole (24 hours). This results in the fraction (\frac{18}{24}), which can then be simplified by finding the greatest common divisor (GCD) of 18 and 24. The GCD is the largest number that can evenly divide both the numerator and the denominator; here, it is 6. Dividing both terms by 6 reduces the fraction to (\frac{3}{4}).
The fraction (\frac{3}{4}) tells us that 18 hours covers three-fourths of a full day. This means that if we divided a day into four equal parts of 6 hours each, 18 hours would account for three of those parts.
Understanding time in fraction form can be useful in various real-life applications, such as calculating work hours, dividing tasks, or planning schedules. For example, knowing that 18 hours is (\frac{3}{4}) of a day can help someone understand that they have three-fourths of their day dedicated to an activity or responsibility, leaving one-fourth of the day (or 6 hours) remaining. This understanding of time fractions aids in time management and resource allocation.