Calculating Time Spent Watching the Movie

Oct 13, 2025 by miodeya.com 13 views

Introduction

Watching a movie can be a great way to relax and unwind, but what if you accidentally turn it off before it's over? In this scenario, we'll explore a mathematical problem that involves calculating the time spent watching a movie. Given that a movie was $$3 \frac{1}{2}$$ hours long and Lily turned it off $$\frac{1}{4}$$ of the way through, we need to determine how much time she spent watching it.

Understanding the Problem

To solve this problem, we need to first convert the mixed number $$3 \frac{1}{2}$$ to an improper fraction. This can be done by multiplying the whole number part (3) by the denominator (2) and then adding the numerator (1). The result is $$\frac{7}{2}$$ hours.

Next, we need to find $$\frac{1}{4}$$ of the total time. To do this, we can multiply the total time ($$\frac{7}{2}$$ hours) by $$\frac{1}{4}$$. This can be represented as:

\frac{7}{2} \times \frac{1}{4} = \frac{7}{8}

Calculating Time Spent Watching the Movie

Now that we know $$\frac{1}{4}$$ of the total time, we can calculate the time spent watching the movie. Since Lily turned it off $$\frac{1}{4}$$ of the way through, we need to find the time equivalent to $$\frac{3}{4}$$ of the total time. This can be done by subtracting $$\frac{1}{4}$$ from 1 (or $$\frac{4}{4}$$). The result is:

1 - \frac{1}{4} = \frac{3}{4}

To find the time spent watching the movie, we can multiply the total time ($$\frac{7}{2}$$ hours) by $$\frac{3}{4}$$. This can be represented as:

\frac{7}{2} \times \frac{3}{4} = \frac{21}{8}

Converting the Answer to a Mixed Number

To make the answer more understandable, we can convert the improper fraction $$\frac{21}{8}$$ to a mixed number. This can be done by dividing the numerator (21) by the denominator (8). The result is:

2 \frac{5}{8}

Conclusion

In conclusion, if a movie was $$3 \frac{1}{2}$$ hours long and Lily turned it off $$\frac{1}{4}$$ of the way through, she spent $$2 \frac{5}{8}$$ hours watching it. This problem requires a good understanding of fractions and how to manipulate them to solve real-world problems.

Discussion

What if the movie was longer or shorter than $$3 \frac{1}{2}$$ hours? How would this affect the calculation?
Can you think of any real-world scenarios where this type of calculation would be useful?
How would you explain this problem to someone who is not familiar with fractions?

Additional Practice

A movie is $$2 \frac{3}{4}$$ hours long. If someone turns it off $$\frac{1}{3}$$ of the way through, how much time did they spend watching it?
A book is $$5 \frac{1}{2}$$ hours long. If someone reads $$\frac{2}{5}$$ of the book, how much time did they spend reading it?

Answer Key

A movie is $$2 \frac{3}{4}$$ hours long. If someone turns it off $$\frac{1}{3}$$ of the way through, they spent $$1 \frac{1}{3}$$ hours watching it.
A book is $$5 \frac{1}{2}$$ hours long. If someone reads $$\frac{2}{5}$$ of the book, they spent $$2 \frac{2}{5}$$ hours reading it.
A Movie Watching Dilemma: Calculating Time Spent Watching a Film ===========================================================

Q&A: A Movie Watching Dilemma

Q: What if the movie was longer or shorter than $$3 \frac{1}{2}$$ hours? How would this affect the calculation?

A: If the movie was longer or shorter than $$3 \frac{1}{2}$$ hours, the calculation would be affected. To calculate the time spent watching the movie, you would need to convert the new length of the movie to an improper fraction and then multiply it by $$\frac{3}{4}$$.

Q: Can you think of any real-world scenarios where this type of calculation would be useful?

A: Yes, this type of calculation can be useful in real-world scenarios such as:

Calculating the time spent watching a movie or TV show
Determining the amount of time spent reading a book
Figuring out the time spent working on a project
Calculating the time spent traveling to a destination

Q: How would you explain this problem to someone who is not familiar with fractions?

A: To explain this problem to someone who is not familiar with fractions, you would need to break it down into simpler terms. Here's an example:

Imagine you have a pizza that is cut into 8 slices. If you eat 2 slices, you have eaten $$\frac{2}{8}$$ of the pizza.
If the pizza is 7 slices long, and you eat $$\frac{2}{8}$$ of it, you would have eaten $$\frac{7}{8}$$ of the pizza.
To find the time spent watching the movie, you would need to multiply the total time by $$\frac{3}{4}$$.

Q: What if the movie was $$2 \frac{3}{4}$$ hours long and someone turned it off $$\frac{1}{3}$$ of the way through? How much time did they spend watching it?

A: To calculate the time spent watching the movie, you would need to convert the mixed number $$2 \frac{3}{4}$$ to an improper fraction. This can be done by multiplying the whole number part (2) by the denominator (4) and then adding the numerator (3). The result is $$\frac{11}{4}$$ hours.

Next, you would need to find $$\frac{1}{3}$$ of the total time. To do this, you can multiply the total time ($$\frac{11}{4}$$ hours) by $$\frac{1}{3}$$. This can be represented as:

\frac{11}{4} \times \frac{1}{3} = \frac{11}{12}

To find the time spent watching the movie, you would need to multiply the total time ($$\frac{11}{4}$$ hours) by $$\frac{2}{3}$$. This can be represented as:

\frac{11}{4} \times \frac{2}{3} = \frac{22}{12} = 1 \frac{2}{3}

Q: What if the movie was $$5 \frac{1}{2}$$ hours long and someone read $$\frac{2}{5}$$ of the book? How much time did they spend reading it?

A: To calculate the time spent reading the book, you would need to convert the mixed number $$5 \frac{1}{2}$$ to an improper fraction. This can be done by multiplying the whole number part (5) by the denominator (2) and then adding the numerator (1). The result is $$\frac{11}{2}$$ hours.

Next, you would need to find $$\frac{2}{5}$$ of the total time. To do this, you can multiply the total time ($$\frac{11}{2}$$ hours) by $$\frac{2}{5}$$. This can be represented as:

\frac{11}{2} \times \frac{2}{5} = \frac{22}{10} = 2 \frac{2}{10}

To make the answer more understandable, you can convert the improper fraction $$\frac{22}{10}$$ to a mixed number. This can be done by dividing the numerator (22) by the denominator (10). The result is:

2 \frac{2}{10} = 2 \frac{1}{5}

Conclusion

In conclusion, the time spent watching a movie or reading a book can be calculated using fractions. By converting mixed numbers to improper fractions and multiplying them by the desired fraction, you can determine the time spent on an activity. This type of calculation can be useful in real-world scenarios and can help you understand fractions in a more practical way.

Discussion

Can you think of any other real-world scenarios where this type of calculation would be useful?
How would you explain this problem to someone who is not familiar with fractions?
Can you think of any other ways to calculate the time spent on an activity?