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Time Math


Solving times in Math means to calculate amount of time spent by doing addition and subtraction or converting time from one unit to another using multiplication and Division Operations. For doing conversions we need to learn converting factors of several units. Problems like time math include questions based on clock timings.

Once you know basic units of time and their conversions it becomes easy to handle such problems. There are certain basics which are used in problems involving days, months, weeks, years, hours, minutes and seconds. In 365 days we have 52 weeks. In one month we have 4 weeks. A year with 366 days makes a leap year. In 1 hour there are 60 minutes and 60 * 60 = 3600 seconds. That is there are 60 seconds per minute.

To solve such problems, first note down the given units and check out the conversion table to get the resultant unit. In case of addition or subtraction operations we need to have common units. In time maths problems a particular reference has to be defined: like in a clock we define 12, 6, 3 and 9 as reference points in many problems. For instance, when small hand of clock completes two cycles from 12 to 12, 24 hours of a day are formed.

Calendar Time

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Calendar in general is used to keep a record of days, years, weeks and months. Calendar time usually tells us the exact date for some happening. In daily routine we refer to calendar time and date to prepare our schedule accordingly. If we talk about the date that we see in the calendar, it is referred to by day, month and year. There can be several formats to mention a date. Out of days, months and years, year is usually written in numeric form.
Days can named specifically from the 7 days of a week from Sunday to Saturday and its numeric form is chosen from total Numbers of days in a month. Similarly, we have 12 months in a year, which signifies either writing the name of month or its corresponding serial number. Now we may have 366 days in a year making it a leap year (otherwise it would have 365 days in general).
Using calendar to calculate time is done by performing operations with dates. Dates cannot be added or subtracted directly. But the number of days or years or months or weeks can be obtained by operating on days, months and years of dates separately.

Clocks Word Problems

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Clocks word problems in mathematics involves resolving value of time from different perspectives like time spent being calculated by doing addition or subtraction. Clock problems may also include questions related to conversion of one unit of time to another by doing multiplication or Division Operations. There are some general formulae that we use for conversions in time Math. Units of time that can be found in clocks word problems are hours, minutes, seconds or milliseconds. Basic and standard information that we all must know to solve such word problems includes: Use of number of days, months, weeks, years, hours, minutes and seconds. Standard says: There are 365 days in a year making 52 weeks. Every month has 4 weeks. A year that has 366 days is called as leap year. Coming to clock timings particularly:

In 1 hour there are 60 minutes and 3600 seconds. That is there are 60 seconds per minute. So, conversion formulae can be derived as follows:

1 hr = 60 minutes.......... equation 1

1 hr = 3600 seconds = 60 * 60.............. seconds equation 2

Using equations 1 and 2 we can write a new equation in minutes and seconds as follows:

1 minute = 60 seconds,

1 sec = 103 milliseconds,

When we solve such word problems, we first write down the available information in form of mathematical expressions, like we used to do in other word problems. In clock word problems this information will be present in form of units of time. If conversions are required, perform the necessary conversions. For instance, 'A' worked for 1 hour and 'B' worked for 20 minutes. How much time they spent in total?

Solution: A’s time is given in hours. So, we need to convert the unit of 'B' matching that of 'A' or vice – versa. So, our total time here will be: 4/3 hr or 80 minutes.

Clocks - Telling Time to Hours

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Clock can be both analogue or digital, clock is used to tell time. A clock usually tells time in hours and minutes. Clock has actually three hands, they are hour hand, minute hand and second hand. Hour hand is smaller and minute hand is larger in size. Seconds hand is longest hand among all three hands. This variation is done only to distinguish them. Hour hand rotates forward by one clock number after every hour, we can say that when minute hand completes one cycle around the clock then it indicates that an hour has passed away. When we read a clock, first we look at hour hand and then at minute hand and finally decide what is the time. Time may be represented in form of A.M. and P.M.
Let’s try to find how the Clocks Telling Time To Hours?

A clock can tell the time to hours or half an hour or hour and minutes etc. If we want time to hours then first of all Set hour hand. Then in second step, look at that clock number on which the hours hand is indicating. This clock number will be used as hour. For instance, if hand hour is at 1 and minute hand is at 12 clock number then we will say that it is 1 o’clock. Sometimes when the hand hour doesn’t points exactly on clock number then it will be pronounced in some other way. For instance if hour hand is half way the 5 and 6, we will read 5 as hour number.
It is shown below in following figure.

Here in first watch, the hour hand is at clock number 1 and minute hand is at 12 which indicates that the time is 1 o’clock. In second figure, hour hand is between clock Numbers 5 and 6 where five will be treated as hour hand and will be read as five and thirty o’clock.

Time, Money, and Estimating

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Time, money, and estimating are also type of problems in Math that would need knowledge of Money Counting, time math and estimation of values. So, to solve these problems we discuss them as follows:

Money counting is usually dealt with respect to currencies. As money seems to be an essential thing that we deal with almost daily, it becomes easy for us to learn its counting techniques. We have following categorization of money counting:
First and foremost job is to discuss the fundamental operations like to add, subtract, multiply and divide. These all techniques are used when we imitate money counting. For example, suppose we have $ 50 in a bag, out of which $ 10 is given to a shopkeeper. How much quantity of cash we are left with in bag? Need of subtraction operation is being seen here as after giving $ 10 to shopkeeper the amount of money in bag gets reduced and so our resultant amount is $ 50 - $ 10 = $ 40.

We may also face some money problems that contain percentages like problems based on Profit and Loss or discounts. Such problems are generally expressed as statements and we need to understand the way data has been expressed. This will let us grab important numerical data and put them in specified formulae to get desired value. Here also basic operations of that we discussed as fundamentals would be needed to solve problems.

Next we discuss time. What is time? It is what keeps your daily schedule run. Solving problems related to time in math means solving the times that are expressed as hours, minutes, seconds, days, year, weeks, months etc. Estimating values in math problems help us move in a correct direction to find solution of the problem. Estimating power depends on way you take the problem and also on what type of problem we are dealing with.

Clocks - Telling Time to Half-Hours

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Smallest unit of time is second. If we start looking from smallest unit of time to larger ones, we observe that 60 seconds makes 1 minute. Similarly 60 minutes makes one hour. A day means 24 hours. Similarly we have collection of 7 days which we call as one week, 30 or 31 days makes 1 month. Similarly we say that 12 months forms one year.

Now in order to keep track of time, we have a clock. A clock has 3 hands. It has Numbers from 1 to 12 in form of Circle. Longest hand of clock is of seconds, which completes one rotation in one minute. Then next hand is of minute, which moves only one step in one minute and it takes one hour to complete one rotation. Now we will look at smallest hand of clock, which is the hour hand. It takes one hour to move from 1 number to another. So we say that seconds hand moves fastest and seconds hand moves slowest. Let us look at Clocks Telling Time to Half Hours.

If we say that time in clock is 5 O’clock, it means that hour hand is pointing at number 5 and minute hand is at number 6. In same way, we say that if we find the minute hand at number 6 and hour hand is at the middle of any two numbers, then time is half past of number which it has crossed. So if hour hand is between 4 and 5, and minute hand is at 6, then we say that time is half past 4 in the clock.