Understanding Fractions of Time: A Simple Calculation

Have you ever come across a problem that requires you to find a fraction of a fraction of a fraction of a day? More specifically, how many hours are in one-half of one-third of one-fourth of a day? In this article, we will break down the problem step-by-step, ensuring clarity and ease of understanding.

Step-by-Step Calculation

Definition of a Full Day in Hours

To solve the given problem, we first need to understand that a full day comprises 24 hours.

Step 1: One-Fourth of a Day

One-fourth of a day is calculated by dividing 24 hours by 4.

Calculation:

24 hours / 4 6 hours

Step 2: One-Third of One-Fourth of a Day

Next, we need to find one-third of the 6 hours obtained in the previous step.

Calculation:

6 hours / 3 2 hours

Step 3: One-Half of One-Third of One-Fourth of a Day

Finally, we need to find one-half of the 2 hours obtained in the previous step.

Calculation:

2 hours / 2 1 hour

Therefore, one-half of one-third of one-fourth of a day is 1 hour.

Alternative Methods and Proofs

Alternative One: Replacing Numbers Directly

An alternative approach involves replacing the numerical operations directly. Starting with 24 hours, we calculate each fraction step-by-step.

24 hours / 4 6 hours (one-fourth of a day)

6 hours / 3 2 hours (one-third of 1/4 of a day)

2 hours / 2 1 hour (one-half of 1/3 of 1/4 of a day)

Mathematical Proof

Mathematically, we can express the problem as follows:

y One-half of one-third of one-fourth of a day in hours

Let 24 hours the number of hours in 1 day

Let 1 hour 1/24 of a day

y 1/2 × 1/3 × 1/4 × 24 hours

y 1/2 × 3 × 4 × 24 hours

y 1/24 × 24 hours

y 24 hours / 24

y 1 hour

Therefore, the solution to the expression 1/2 × 1/3 × 1/4 × 24 hours is 1 hour.

Verification via Direct Multiplication

Another method involves multiplying the fractions directly and then performing the division:

24 × 1/2 × 1/3 × 1/4 24/24 1 hour

Thus, confirming that the answer is indeed 1 hour.

Conclusion

In conclusion, the problem of finding one-half of one-third of one-fourth of a day simplifies to a straightforward calculation, resulting in 1 hour. This method can be applied to similar time fraction problems, reinforcing the importance of understanding basic mathematical operations.

Citations and References

1. Basic Arithmetic and Fractions (Math is Fun)

2. Time Conversion (Time Calculator)