Introduction
In a day there are 24 hours. Each hour has 60 minutes in total and each minute has 60 seconds in it. To multiply and divide the time you should remember this basic information. The extra seconds, minutes, and hours should be converted into the next bigger unit, if there are more than 60 seconds in your answer you will convert it into minutes and so on. We will learn the concept by the example of multiplication and division of time.
Multiplication of Time
Time can be added and subtracted as well as multiplied easily. In order to multiply time, you need to remember some rules which will help you in calculating the answer.
If after multiplication you have more than 59 seconds, then divide the number by 60. The remainder you will get is the number of seconds and the quotient would change into the number of minutes.
The same is for the minutes, here if you have more than 59 minutes then divide it by 60 and the remainder is your required minutes and the quotient you got is the number of hours.
For hours, if there are more than 23 hours then divide the number by 24 and the remainder you got will be the hours and the quotient will be the number of days.
Division of Time
The division of time can be done like it was multiplied. Here we will change the time from the largest to the smallest unit. The rules which will help you to divide time are given below.
After dividing time if you get the quotient as the decimal number then, the whole number should be counted as the number of days and the decimal point should be multiplied by 24 to get the number of hours.
If dividing the hour's quotient comes out as a decimal number then, the whole number part is counted as the number of hours, and the decimal part is multiplied by 60 to get the number of minutes.
The same needs to be done for minutes where the whole number part of the quotient will be the number of minutes and the decimal part of the number will be multiplied by 60 to get the number of seconds.
Example of Multiplication of Time
If a person travels for 6 days and takes 15 hours 40 minutes 22 seconds in a day. Then how much time did he spend traveling for 5 days?
In order to find the total time he spent on traveling for 5, we need to multiply 6 by 15 hours 40 minutes, and 22 seconds.
As there are 60 seconds which will make a minute. The result we got is 110 seconds, which means that 110 needs to be divided by 60. We will get quotient 1 and the remainder as 50. So the quotient 1 needs to be carried over to the minutes and the total number of seconds we get is 50 seconds.
Now, 200 minutes need to be divided by 60 as in an hour there are only 60 minutes. After dividing 200 by 60 we will get the quotient as 3 and the remainder will be 20. 3 would be carried over in the hour's column and 20 would be added to the extra 1 minute that we got from the second column. The total number of minutes we now have is 21 minutes.
75 hours need to be changed by dividing it by 24. The quotient we get is 3 and the remainder is also 3. So the quotient will be changed into the number of days (3 days) and the remainder obtained is our number of hours (3 hours)
So the total time he spent traveling for 5 days is 3 days 6 hours 21 minutes 50 seconds.
How Do We Divide Time in Order to Understand It?
To understand how to divide time we can take an example. Divide 20 hours 14 minutes by 5.
The division of the time is done in a way that is similar to the division of normal numbers. First, divide 20 hours 14 minutes by 5 the answer we get is 4 hours 2.8 minutes. As the minutes are in decimal numbers and we need to change them to whole numbers. The number before the decimal is considered as the whole number of minutes and the number after the decimal is the fraction part of the minute which needs to be changed into seconds.
So, we need to multiply 0.8 by 60 which will result in 48. Now we got 2 minutes and 48 seconds as the answer. So we got the final answer as 4 hours 2 minutes and 48 seconds.
Conclusion
The time can be added, subtracted, multiplied, and divided using some basic rules. There are 24 hours in a day, 60 minutes in an hour, and 60 seconds in a minute. In order to convert a large quantity (hours) to a smaller quantity (minutes or seconds) we need to divide and if we need to convert a small quantity (seconds) to a larger one (hours) then we need to multiply. This conversion help will help you to calculate the time correctly.
Sample Questions
1. How many minutes are there in 320 seconds?
4
5
6
7
Ans: 5
Explanation: there are 5 minutes and 20 seconds in 320 seconds. To calculate we just need to divide 320 by 60 and the quotient will be our minutes and the remainder will be our seconds.
2. How many days are there in 54 hours?
2
3
4
5
Ans: 2
Explanation: to find the number of days 54 hours divide it by 24. The quotient obtained is the number of days and the remainder is the number of hours. So, in 54 hours there are 2 days and 6 hours.
3. How many minutes are there in a day?
1220
1330
1440
1550
Ans: 1440
Explanation: To find the total number of minutes in a day we need to multiply 24 and 60. This will result in 1440.
FAQs on Time Multiply
1. How do you multiply units of time like hours, minutes, and seconds?
To multiply time, you handle each unit separately and then convert any excess. Here are the steps:
- Multiply Each Unit: First, multiply the seconds, then the minutes, and then the hours by the given number.
- Convert Seconds: If the total seconds are 60 or more, divide the number by 60. The remainder is your new seconds, and the quotient is carried over to the minutes column.
- Convert Minutes: Add the carried-over value to your minutes total. If the new total is 60 or more, divide it by 60. The remainder is your final minutes, and the quotient is carried over to the hours column.
- Finalise Hours: Add the carried-over value to your hours total. This gives you the final answer.
2. Can you provide a simple example of multiplying time in a real-life situation?
Certainly. Imagine you practice playing the guitar for 45 minutes every day. To find out the total practice time over 3 days, you multiply:
45 minutes × 3 = 135 minutes.
Since there are 60 minutes in an hour, we convert this. 135 minutes is more than one hour. We divide 135 by 60, which gives us 2 with a remainder of 15. Therefore, you practiced for a total of 2 hours and 15 minutes over the 3 days.
3. Why is it necessary to convert minutes and seconds after multiplying time?
It is necessary to convert minutes and seconds because our time system is not based on 10s like regular numbers. We use a sexagesimal (base-60) system for seconds and minutes. This means a unit 'rolls over' when it reaches 60, not 100. For example, getting a result of 90 minutes is mathematically correct but not how we express time. We convert it to 1 hour and 30 minutes to make it understandable and standard.
4. What is the most common mistake students make when multiplying time?
The most common mistake is forgetting to carry over and convert the units. For example, after multiplying and getting a result like '5 hours and 70 minutes', a student might leave the answer like that. The correct final step is to convert the 70 minutes into 1 hour and 10 minutes, and then add that to the hours, for a final, correct answer of 6 hours and 10 minutes.
5. How is multiplying time different from multiplying regular numbers?
The main difference lies in the base system used for calculations. Regular numbers use the decimal or base-10 system, where you carry over to the next place value every time you reach 10. However, time uses a mixed-base system:
- Seconds and minutes are base-60 (they roll over to the next unit at 60).
- Hours are base-24 (they roll over to days at 24).
This is why multiplying time requires the extra step of division and conversion, which is not needed for multiplying regular numbers.
6. How can you calculate the total seconds in a full day using multiplication?
To find the total seconds in a day, you perform a series of multiplications based on time conversions:
- First, find seconds in an hour: 60 seconds/minute × 60 minutes/hour = 3,600 seconds per hour.
- Next, find seconds in a day: 3,600 seconds/hour × 24 hours/day = 86,400 seconds per day.
So, a full day has 86,400 seconds.
7. A movie is 2 hours and 20 minutes long. If you watch it 4 times, what is the total viewing time?
To solve this, multiply each unit of time by 4:
- Minutes: 20 minutes × 4 = 80 minutes.
- Hours: 2 hours × 4 = 8 hours.
Now, convert the minutes. Since 80 minutes is more than 60, we convert it to hours. 80 minutes = 1 hour and 20 minutes.
Finally, add this to the hours you calculated: 8 hours + 1 hour and 20 minutes = 9 hours and 20 minutes. The total viewing time is 9 hours and 20 minutes.
