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If a movie lasts 2 hours and 45 minutes, how many minutes long is it?

Mathematics

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Here are the solutions for Practice :

  1. 360 minutes = 6\boxed{\text{6}} hours

  1. Convert minutes to hours using the conversion factor 1 hour=60 minutes1 \text{ hour} = 60 \text{ minutes}.

    $$
360 \text{ minutes} \times \frac{1 \text{ hour}}{60 \text{ minutes}} = \frac{360}{60} \text{ hours} = 6 \text{ hours}
$$

    2. 120 seconds = 2\boxed{\text{2}} minutes

  2. Convert seconds to minutes using the conversion factor 1 minute=60 seconds1 \text{ minute} = 60 \text{ seconds}.

    $$
120 \text{ seconds} \times \frac{1 \text{ minute}}{60 \text{ seconds}} = \frac{120}{60} \text{ minutes} = 2 \text{ minutes}
$$

    3. 10 minutes = 600\boxed{\text{600}} seconds

  3. Convert minutes to seconds using the conversion factor 1 minute=60 seconds1 \text{ minute} = 60 \text{ seconds}.

    $$
10 \text{ minutes} \times \frac{60 \text{ seconds}}{1 \text{ minute}} = 10 \times 60 \text{ seconds} = 600 \text{ seconds}
$$

    4. 3 hours = 180\boxed{\text{180}} minutes

  4. Convert hours to minutes using the conversion factor 1 hour=60 minutes1 \text{ hour} = 60 \text{ minutes}.

    $$
3 \text{ hours} \times \frac{60 \text{ minutes}}{1 \text{ hour}} = 3 \times 60 \text{ minutes} = 180 \text{ minutes}
$$

    5. 4 days = 96\boxed{\text{96}} hours

  5. Convert days to hours using the conversion factor 1 day=24 hours1 \text{ day} = 24 \text{ hours}.

    $$
4 \text{ days} \times \frac{24 \text{ hours}}{1 \text{ day}} = 4 \times 24 \text{ hours} = 96 \text{ hours}
$$

    6. 3 weeks = 21\boxed{\text{21}} days

  6. Convert weeks to days using the conversion factor 1 week=7 days1 \text{ week} = 7 \text{ days}.

    $$
3 \text{ weeks} \times \frac{7 \text{ days}}{1 \text{ week}} = 3 \times 7 \text{ days} = 21 \text{ days}
$$

    7. 1\boxed{\text{1}} hour = 3 600 seconds

  7. Convert seconds to hours using the conversion factor 1 hour=3600 seconds1 \text{ hour} = 3600 \text{ seconds}.

    $$
3600 \text{ seconds} \times \frac{1 \text{ hour}}{3600 \text{ seconds}} = \frac{3600}{3600} \text{ hours} = 1 \text{ hour}
$$

    8. 72 hours = 3\boxed{\text{3}} days

  8. Convert hours to days using the conversion factor 1 day=24 hours1 \text{ day} = 24 \text{ hours}.

    $$
72 \text{ hours} \times \frac{1 \text{ day}}{24 \text{ hours}} = \frac{72}{24} \text{ days} = 3 \text{ days}
$$

    9. 2122\frac{1}{2} years = 30\boxed{\text{30}} months

  9. Convert the mixed number to a decimal.

    $$
2\frac{1}{2} \text{ years} = 2.5 \text{ years}
$$

  10. Convert years to months using the conversion factor 1 year=12 months1 \text{ year} = 12 \text{ months}.

    $$
2.5 \text{ years} \times \frac{12 \text{ months}}{1 \text{ year}} = 2.5 \times 12 \text{ months} = 30 \text{ months}
$$

    10. 48 months = 4\boxed{\text{4}} years

  11. Convert months to years using the conversion factor 1 year=12 months1 \text{ year} = 12 \text{ months}.

    $$
48 \text{ months} \times \frac{1 \text{ year}}{12 \text{ months}} = \frac{48}{12} \text{ years} = 4 \text{ years}
$$

    11. 2 decades = 20\boxed{\text{20}} years

  12. Convert decades to years using the conversion factor 1 decade=10 years1 \text{ decade} = 10 \text{ years}.

    $$
2 \text{ decades} \times \frac{10 \text{ years}}{1 \text{ decade}} = 2 \times 10 \text{ years} = 20 \text{ years}
$$

    12. 20 years = 2\boxed{\text{2}} decades

  13. Convert years to decades using the conversion factor 1 decade=10 years1 \text{ decade} = 10 \text{ years}.

    $$
20 \text{ years} \times \frac{1 \text{ decade}}{10 \text{ years}} = \frac{20}{10} \text{ decades} = 2 \text{ decades}
$$

    13. 200 years = 2\boxed{\text{2}} centuries

  14. Convert years to centuries using the conversion factor 1 century=100 years1 \text{ century} = 100 \text{ years}.

    $$
200 \text{ years} \times \frac{1 \text{ century}}{100 \text{ years}} = \frac{200}{100} \text{ centuries} = 2 \text{ centuries}
$$

    14. How many minutes are there in 1121\frac{1}{2} hours?

  15. Convert the mixed number to a decimal.

    $$
1\frac{1}{2} \text{ hours} = 1.5 \text{ hours}
$$

  16. Convert hours to minutes using the conversion factor 1 hour=60 minutes1 \text{ hour} = 60 \text{ minutes}.

    $$
1.5 \text{ hours} \times \frac{60 \text{ minutes}}{1 \text{ hour}} = 1.5 \times 60 \text{ minutes} = \boxed{\text{90 minutes}}
$$

    15. If a movie lasts 2 hours and 45 minutes, how many minutes long is it?

  17. Convert the hours to minutes.

    $$
2 \text{ hours} \times \frac{60 \text{ minutes}}{1 \text{ hour}} = 120 \text{ minutes}
$$

  18. Add the remaining minutes to the converted hours.

    $$
120 \text{ minutes} + 45 \text{ minutes} = \boxed{\text{165 minutes}}
$$
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