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Multiply: \( 3-8 \) hours 15 minutes 25 seconds by 5 . \( \frac{4}{4} 5 \) years 8 months 15 days by 6. 9 years 5 months 24 days by 5 .

Ask by Watson Garza. in Nepal
Nov 14,2024

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Tutor-Verified Answer

Answer

1. -23 hours 54 minutes 0 seconds 2. 8 years 8 months 15 days 3. 47 years 4 months 26 days

Solution

Let's perform the multiplications step by step. ### 1. Multiply \( 3 - 8 \) hours 15 minutes 25 seconds by 5. First, we need to convert \( 3 - 8 \) hours into a single unit. - \( 3 - 8 \) hours = \( -5 \) hours. - Now, convert everything to seconds: - \( -5 \) hours = \( -5 \times 3600 = -18000 \) seconds. - \( 15 \) minutes = \( 15 \times 60 = 900 \) seconds. - \( 25 \) seconds = \( 25 \) seconds. Now, combine these: \[ -18000 + 900 + 25 = -17175 \text{ seconds}. \] Now, multiply by 5: \[ -17175 \times 5 = -85875 \text{ seconds}. \] Convert back to hours, minutes, and seconds: - \( -85875 \) seconds = \( -85875 \div 3600 = -23.9 \) hours, which is \( -23 \) hours and \( -0.9 \times 3600 = -3240 \) seconds. - \( -3240 \) seconds = \( -54 \) minutes and \( -0 \) seconds. So, the result is: \[ -23 \text{ hours } 54 \text{ minutes } 0 \text{ seconds}. \] ### 2. Multiply \( \frac{4}{4} 5 \) years 8 months 15 days by 6. First, simplify \( \frac{4}{4} = 1 \), so we have \( 1 \) year \( 5 \) months \( 15 \) days. Now, convert everything to days: - \( 1 \) year = \( 365 \) days (ignoring leap years for simplicity). - \( 5 \) months = \( 5 \times 30 = 150 \) days (assuming an average month length). - \( 15 \) days = \( 15 \) days. Total days: \[ 365 + 150 + 15 = 530 \text{ days}. \] Now, multiply by 6: \[ 530 \times 6 = 3180 \text{ days}. \] Convert back to years, months, and days: - \( 3180 \div 365 = 8.7 \) years, which is \( 8 \) years and \( 0.7 \times 365 \approx 255.5 \) days. - \( 255.5 \) days = \( 8 \) months and \( 15.5 \) days (assuming an average month length). So, the result is: \[ 8 \text{ years } 8 \text{ months } 15 \text{ days}. \] ### 3. Multiply \( 9 \) years \( 5 \) months \( 24 \) days by \( 5 \). Convert everything to days: - \( 9 \) years = \( 9 \times 365 = 3285 \) days. - \( 5 \) months = \( 5 \times 30 = 150 \) days (assuming an average month length). - \( 24 \) days = \( 24 \) days. Total days: \[ 3285 + 150 + 24 = 3459 \text{ days}. \] Now, multiply by 5: \[ 3459 \times 5 = 17295 \text{ days}. \] Convert back to years, months, and days: - \( 17295 \div 365 = 47.4 \) years, which is \( 47 \) years and \( 0.4 \times 365 \approx 146 \) days. - \( 146 \) days = \( 4 \) months and \( 26 \) days (assuming an average month length). So, the result is: \[ 47 \text{ years } 4 \text{ months } 26 \text{ days}. \] ### Final Results: 1. \( -23 \text{ hours } 54 \text{ minutes } 0 \text{ seconds} \) 2. \( 8 \text{ years } 8 \text{ months } 15 \text{ days} \) 3. \( 47 \text{ years } 4 \text{ months } 26 \text{ days} \)

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The Deep Dive

To multiply the time quantities, let's break down each case. First calculation: \( (3 \text{ hours} - 8 \text{ hours}) + 15 \text{ minutes} + 25 \text{ seconds} = (-5 \text{ hours}) + 15 \text{ minutes} + 25 \text{ seconds} \). Converting to seconds for multiplication: \(-5 \text{ hours} = -18,000 \text{ seconds}\), so: Total = \(-18,000 + 15 \times 60 + 25 = -17,025 \text{ seconds}\). Now multiplying by 5: \(-17,025 \times 5 = -85,125 \text{ seconds}\) or \(-23 \text{ hours} 40 \text{ minutes} 25 \text{ seconds}\). Second calculation: \(\frac{4}{4} = 1\), so multiply \( 1 \text{ year} 8 \text{ months} 15 \text{ days} \) by 6: Using standard time conversions: \(6 \text{ years}, 48 \text{ months}, 90 \text{ days} = 6 \text{ years} + 4 \text{ months} + 0 \text{ days} = 6 \text{ years} 4 \text{ months}\). Third calculation: \(9 \text{ years} 5 \text{ months} 24 \text{ days} \times 5 = 45 \text{ years} + 25 \text{ months} + 120 \text{ days}\) translates to: \(45 \text{ years} + 2 \text{ years} + 1 \text{ month} + 30 \text{ days} = 47 \text{ years} 1 \text{ month} 30 \text{ days}\). So the results are: 1. \(-23 \text{ hours} 40 \text{ minutes} 25 \text{ seconds}\) 2. \(6 \text{ years} 4 \text{ months}\) 3. \(47 \text{ years} 1 \text{ month} 30 \text{ days}\)

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