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Mental Arithmetic with Time

Doing calculations with time is very important when we need to do many things in a day. To make time for all the stuff you want to do, you need to be able to do mental arithmetic with time.

When you calculate time, it’s important to remember that there are $60$ minutes in an hour. The place value system changes a bit, but not a lot. You just have to make sure that when you change hours into minutes, one hour is $60$ minutes. If you want to change from minutes to hours, remember that $60$ minutes goes into one hour. Let’s check out some examples.

Example 1

Which time is longer? 1 hour and 50 minutes or 100 minutes?

You need to find out how many minutes there are in $1$ hour and $50$ minutes. You know that

\begin{array}{l} 1 hour & = 60 minutes \\ 1 hour and 50 minutes & = 60 minutes + 50 minutes \\ = 110 minutes \end{array}

As $110$ minutes are more than $100$ minutes, you know that $1$ hour and $50$ minutes is longer than $100$ minutes.

Example 2

What’s the time in $2$ hours and $15$ minutes? Draw the clock to the right on a piece of paper and fill in the hands in the correct positions.

Two analog clocks. The right clock is missing its minute and hour hands

Example 3

Which time is longer? 130 minutes or 2 hours?

This time we’ll calculate the other way, and find out how many hours $130$ minutes are. Remember that $60$ minutes are $1$ hour.

\begin{array}{l} 130 minutes \\ = 60 minutes + 60 minutes + 10 minutes \\ = 1 hour + 1 hour + 10 minutes \\ = 2 hours and 10 minutes \end{array}

Because $2$ hours and $10$ minutes is longer than $2$ hours, you know that $130$ minutes is longer than $2$ hours.

Example 4

What’s the time 2 hours and 15 minutes after it was 16:50?

In problems like this, it’s usually smart to look at the minutes first and the hours afterwards. From the given time you can see that you are in the 50th minute. Because you need to find the time in $15$ minutes, you get

50 minutes + 15 minutes = 65 minutes

There are $60$ minutes in $1$ hour, giving you

65 minutes = 1 hour and 5 minutes

From the given time, you can see that you’re in hour $16$ . Because you want to find the time in $2$ hours, you get

16 hours + 2 hours = 18 hours

You also need to add the hour you got from the minutes. That gives you

18 hours + 1 hour = 19 hours

You have $5$ minutes left over. That makes it so the new time is 19:05.

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Learning About the Clock (Five To and Five Past)

Calculations with the Clock

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