Subtraction of Minutes and Seconds

7/27/2019 Subtraction of Minutes and Seconds

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Subtraction of Hours and MinutesHow to subtract hours and minutes.

If the number of minutes being subtracted is more than the original

minutes, do the following:o Subtract 1 from the original number of hours.

o Increase the number of original minutes by 60.

Subtract the minutes.

Subtract the hours.

Example: What is 4 hours 11 minutes minus 2 hours 47 minutes.

The original number of minutes (11) is less than the 47 minutesbeing subtracted so:

o Subtract 1 from the original number of hours. (4 hours - 1hour = 3 hours)

o Increase the number of minutes by 60. (11 minutes + 60minutes = 71 minutes)

Subtract the minutes. (71 minutes - 47 minutes = 24 minutes)

Subtract the hours. (3 hours - 2 hours = 1 hour)

Answer: 1 hour 24 minutes

Subtraction of Minutes and SecondsHow to subtract minutes and seconds

If the number of seconds being subtracted is more than the originalseconds, do the following:

o Subtract 1 from the original number of minutes.

o Increase the number of original seconds by 60.

Subtract the seconds.

Subtract the minutes.

Example: What is 4 minutes 11 seconds minus 2 minutes 47 seconds.

The original number of seconds (11) is less than the 47 secondsbeing subtracted so:


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o Subtract 1 from the original number of minutes. (4 minutes -1 minute = 3 minutes)

o Increase the number of seconds by 60. (11 seconds + 60seconds = 71 seconds)

Subtract the seconds. (71 seconds - 47 seconds = 24 seconds)

Subtract the minutes. (3 minutes - 2 minutes = 1 minute)

Answer: 1 minute 24 seconds

Subtraction rules for DATE, TIME, and TIMESTAMP

The only arithmetic operation that can be performed on datetime values issubtraction. The subtraction operator can be used with datetime values only

when both operands are dates, or both operands are times, or both operands aretimestamps.

DATE

The result of subtracting one date (DATE2) from another (DATE1) is a dateduration that specifies the number of years, months, and days between the twodates. The data type of the result is DECIMAL(8,0). For example, the result ofDATE('3/15/2000') DATE('12/31/1999') is 00000215 (a duration of 0 years, 2months, and 15 days).

If DATE1 is greater than or equal to DATE2, DATE2 is subtracted from DATE1. IfDATE1 is less than DATE2, however, DATE1 is subtracted from DATE2, and thesign of the result is made negative. The following procedural description clarifiesthe steps involved in the operation result = DATE1 - DATE2.

If DAY(DATE2) DAY(DATE1)

then DAY(RESULT) = N + DAY(DATE1) - DAY(DATE2)

where N = the last day of MONTH(DATE2).

MONTH(DATE2) is then incremented by 1.

If MONTH(DATE2) MONTH(DATE1)

then MONTH(RESULT) = 12 + MONTH(DATE1) - MONTH(DATE2).


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YEAR(DATE2) is then incremented by 1.

YEAR(RESULT) = YEAR(DATE1) - YEAR(DATE2).

TIME

The result of subtracting one time (TIME2) from another (TIME1) is a timeduration that specifies the number of hours, minutes, and seconds between thetwo times. The data type of the result is DECIMAL(6,0). For example, the result of

TIME(11:02:26) TIME(00:32:56) is 102930 (a duration of 10 hours, 29minutes, and 30 seconds).

If TIME1 is greater than or equal to TIME2, TIME2 is subtracted from TIME1. IfTIME1 is less than TIME2, however, TIME1 is subtracted from TIME2, and the signof the result is made negative. The following procedural description clarifies thesteps involved in the operation result = TIME1 - TIME2.

If SECOND(TIME2) SECOND(TIME1)

then SECOND(RESULT) = 60 + SECOND(TIME1) - SECOND(TIME2).

MINUTE(TIME2) is then incremented by 1.

If MINUTE(TIME2) MINUTE(TIME1)

then MINUTE(RESULT) = 60 + MINUTE(TIME1) - MINUTE(TIME2).

HOUR(TIME2) is then incremented by 1.

HOUR(RESULT) = HOUR(TIME1) - HOUR(TIME2).

TIMESTAMP

The result of subtracting one timestamp (TS2) from another (TS1) is a timestampduration that specifies the number of years, months, days, hours, minutes,seconds, and microseconds between the two timestamps. The data type of theresult is DECIMAL(20,6).

If TS1 is greater than or equal to TS2, TS2 is subtracted from TS1. If TS1 is lessthan TS2, however, TS1 is subtracted from TS2 and the sign of the result is madenegative. The following procedural description clarifies the steps involved in theoperation result = TS1 - TS2:

If MICROSECOND(TS2)


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If MICROSECOND(TS2) > MICROSECOND(TS1)

then MICROSECOND(RESULT) = 1000000 + MICROSECOND(TS1) -MICROSECOND(TS2)

and SECOND(TS2) is incremented by 1.

The seconds and minutes part of the timestamps are subtracted as specified inthe rules for subtracting times. The date part of the timestamps is subtracted asspecified in the rules for subtracting dates.

9. Comparison and Subtraction of Time Intervals

The Easy Case - Conversions not needed

Here are two time intervals in cosmetic normal formal

T1 = 6 hours 35 minutes and 15 seconds


The second time interval T2 has more hours, more minutes and seconds than the first T1. So

it is larger.

The subtraction


T1 = 6 hours 35 minutes and 15 seconds __

T2 - T1 = 2 hours 10 minutes and 15 seconds

suggests T2 is 2 hours 10 minutes and 15 seconds more than T1.

Let us check that by an addition:

2 hours 10 minutes and 15 seconds

T1 = 6 hours 35 minutes and 15 seconds +

8 hours 45 minutes and 30 seconds = T2

Harder Cases - Conversions Needed

Here are two more time intervals



The first time interval T1 has 2 more hours than the second T2. Just one of those extra hours

by itself is larger than the minute and second part of the other time interval T2. So in this

case, the first time interval is more than (larger than) the second. Subtraction will say howmuch more.


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The first time interval T1 in its minutes and second portion has fewer minutes and fewer

seconds than the other time interval T2 . So the first column method for subtraction

introduced above would have us write:

The subtraction



T2 - T1 = 2 hours ?? minutes and ?? seconds

If we avoid negative numbers or counts, we will have difficulty with the seconds and minute

entries in this subtraction. But the first time interval T1 has 2 more hours than the second T2.

Just one of those extra hours by itself is larger than the minute and second part of the other

time interval T2. That suggests a conversion:

1 hour = 59 minutes and 60 seconds and so 7 hours = 6 hours, 59 minutes and 60 seconds.

Now T1 = 7 hours 35 minutes and 15 seconds

= 6 hours, 59 minutes and 60 seconds + 35 minutes and 15 seconds

We want to subtract T2 = 5 hours 45 minutes and 30 seconds from the latter.

T1 = 6 hours, 59 minutes and 60 seconds + 35 minutes and 15 seconds


T1 - T2 = 1 hour 14 minutes and 30 seconds + 35 minutes and 15 seconds

That latter gives

T1 - T2 = 1 hour 49 minutes and 45 seconds

The latter gives how much, the first time length T1 is more than the other time interval T2.

Let us check that:

1 hour 49 minutes and 45 seconds

T2 = 5 hours 45 minutes and 30 seconds +

7 hours, 35 minutes and 15 seconds = T11 1

Observe the presence of carries in the minute and hours columns.

The foregoing calculations suggest a column method for subtraction when conversions are

needed.

First, write



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as before, but with an extra line. The extra line is needed.

We will cross-out the 7 hours on the top line, and replace its by 6 hours, 59 minutes and 60seconds

on the second line. That gives


6 hours, 59 minutes and 60 seconds


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Example B.

50 hours 23 minutes 17 seconds versus 34 hours 25 minutes 25 seconds.

Solution: The first time interval is larger as it has more hours than than first. The difference

isgive by first writing

hours mins secs

50 23 17

23 25 25 -

with an extra line since conversions will be needed in the minute and seconds column. Now

in place, cross-out the 50 and replace it by an entry of 49 hours, 59 minutes and 60 seconds in

line 2. That should give you

hours mins secs

50 23 17

49 59 60

23 25 25 -

Now continue the calculation in place to obtain the following:

hours mins secs

50 23 17 (line 1)

49 59 60 (line 2)

23 25 25 - (line 3)

26 57 52 (line 4)

Work: 17 + 60 - 25 = 17 + 35 = 52

23+ 59 - 25 = 23 + 37 = 57

49 - 26 = 23

The longer time interval should be 26 hours, 57 minutes and 52 seconds more than the

first. Finally, check that in place by verifying the original line 1 (no cross-out) is the sume oflines 3 and 4

Example C.


Solution: Again, the first time interval is larger as it has more minutes than than first. The

difference is calculated by first writing

hours mins secs

30 35 13


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30 20 25 -

with an extra line since conversions will be needed in the minute and seconds column. Now

in place, cross-out the 35 in the minute column and replace it by an entry of 34 minutes and

60 seconds in line 2. That should give you

hours mins secs

30 35 13

34 60

30 20 25 -


hours mins secs

30 35 13 (line 1)34 60 (line 2)

30 20 25 - (line 3)

14 48 (line 4)

Work: 13 + 60 - 25 = 13 + 35 = 48

34 - 20 = 14

The longer time interval should be 14 minutes and 48 seconds more than the first. Finally,

check that in place by verifying the original line 1 (no cross-out) is the sum of lines 3 and 4

Example D.


Solution: Again, the first time interval is larger as it has more hours than than first. The


hours mins secs

55 43 35

35 13 55 -

with an extra line since conversions will be needed in the seconds column. No conversions

are needed elsewhere. The first line has more minutes than the last line. Now in place,

cross-out the 43 in the minute column and replace it by an entry of 42 minutes and 60

seconds in line 2. That should give you

hours mins secs

55 43 35

42 6035 13 55 -


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hours mins secs

55 43 3542 60

35 13 55 -

20 29 40

Work: 35 + 60 - 55 = 35 + 5 = 40

42 - 13 = 29


first. Finally, check that in place by verifying the original line 1 (no cross-out) is the sum of

the last two lines.

Example D - Revisited


Solution: Again, the first time interval is larger as it has more hours than than first. The


hours mins secs

55 43 35

35 13 55 -

with an extra line since conversions will be needed in the seconds column. No

conversions are needed elsewhere.

In this second version of Example D, we will convert 55 hours into 54 hours, 59 minutes

and 60 seconds. That is not necessary because 43 minutes and 35 seconds is longer than

13 minutes and 55 seconds, and hence conversion of 43 minutes into 42 minutes and 60

seconds was good enough (and quicker). We doing this to compare and contrast the tworoutes for obtaining a solution. You need the experience.

The first line has more hours than the last line. Now in place, cross-out the 55 in the hour

column and replace it by an entry of 54 hours, 59 minutes and 60 seconds in line 2. That

should give you

hours mins secs

55 43 35

54 59 60

35 13 55 -


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hours mins secs

55 43 3554 59 60

35 13 55 -

20 29 40

1

Work: 35 + 60 - 55 = 35 + 5 = 40 as before

43 + 59 -13 = 43 + 46 = 89 or 1 hour and 29 minutes

(that gives a carry of 1 hour to add into the hours column

1+ 54 - 35 = 1 + 19 = 20

Again, the time interval should be 20 hours, 29 minutes and 40 seconds more than the

first.

In this second approach, the conversion of 55 hours into 54 hours, 59 minutes and 60

seconds was not wrong, but it the effect of introducing the conversion of 89 minutes into

the answer.

Without the conversion of 89 minutes into 1 hour and 29 minutes, the above calculation

would have given

hours mins secs

55 43 35

54 59 60

35 13 55 -

19 89 40

or 19 hours, 89 minutes and 40 seconds as a result, correct except it is not in cosmetic

normal form.

Example E.

25 hours 45 minutes 10 seconds versus 40 hours 18 minutes 55 seconds versus .

Solution: The second time interval has more hours than the first. So it is larger.

The difference is calculated by first writing

hours mins secs

40 18 55

25 45 10 -


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with an extra line since conversions will be needed. Now in place, 55 secs - 10 secs gives 45

secs.

In place that gives

hours mins secs

40 18 55

25 45 10 -

45

Now in place, cross-out the 40 in the hour column and replace it by an entry of 39 hours and

60 minutes in the extra line.

hours mins secs

40 18 5539 60

25 45 10 -

45


hours mins secs

40 18 55

39 60

25 45 10 -

14 33 45

Work: 18 + 60 - 45 = 18 + 15 = 33

39 - 25 = 14


other. Finally, check that in place by verifying the original line 1 (no cross-out) is the sum of

the last two.

Remark: We could use negative numbers here.

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Subtraction of Minutes and Seconds