Exercise 1

Convert the following units into sexagesimal form:

12,413 seconds.

7,950 seconds.

2.32 hours.

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Exercise 2

Convert the following units into decimal form.

3h 26 min 53 s.

2 h 48min 30 s.

3 h 36 min 42 s.

Exercise 3

Calculate:

6 h 13 min 24 s − 2 h 24 nin 36 s.

Exercise 4

Calculate:

5 h 48min 50 s + 6 h 45 min 30 s + 7 h 58 min 13 s

6 h 13 min 45 s + 7 h 12 min 43 s + 6 h 33 min 50 s

Exercise 5

Calculate:

(15 h 13 min 42 s) × 7.

 

Solution of exercise 1

Convert the following units into sexagesimal form:

12,413 seconds

\begin{array}{ccccccccccc} & & 206&\\ \cline{3-10} \multicolumn{2}{r}{60 \surd} & 12413&& \\ & &12360& & & & \\ \cline{3-7} \cline{6-10} & &53&&\\ \end{array}

The quotient 206 will be further divided by 60 to get hours or degree like this:

\begin{array}{ccccccccccc} & & 3&\\ \cline{3-10} \multicolumn{2}{r}{60 \surd} & 206&& \\ & &180& & & & \\ \cline{3-7} \cline{6-10} & &26&&\\ \end{array}

12413 s = 3h 26 min 53 sec

 

7,950 seconds

\begin{array}{ccccccccccc} & & 132&\\ \cline{3-10} \multicolumn{2}{r}{60 \surd} & 7950&& \\ & &7920& & & & \\ \cline{3-7} \cline{6-10} & &30&&\\ \end{array}

The quotient 206 will be further divided by 60 to get hours or degree like this:

\begin{array}{ccccccccccc} & & 2&\\ \cline{3-10} \multicolumn{2}{r}{60 \surd} & 132&& \\ & &120& & & & \\ \cline{3-7} \cline{6-10} & &12&&\\ \end{array}

7950 s = 2h 12 min 30 sec

2.32 hours

0.32 x 60 = 19.2 min

0.2 x 60 = 12 = 12 sec

2h 19 min 12 s

 

 

Solution of exercise 2

Convert the following units into decimal form.

3h 26 min 53 s

3h                =   3 x 3600 s       = 10, 800 s

26 min        = 26 x 60 s           = 1560 s

53 s             =                                      53 s

3h  26 min 53 s                        = 12413 s

2h 48 min 30 s

2h            =    2 x 3600 s         =    7200 s

48 min    =  48 x 60 s             = 2880 s

30 s         =                                       30 s

2h 48 min 30 s                       = 10110 s

3h 36 min 42 s

3h              =  3 x 3600s        = 10800 s

36 min      = 36 x 60 s           = 2160 s

42 s           =                                     42 s

3h   36 min 42 s                    = 13,002 s

 

Solution of exercise 3

Calculate:

6 h 13 min 24 s − 2 h 24 nin 36 s.

\begin{document} \begin{tabular}{cccc}    & 6h  &  13min  &  24s\\ -& 2h  & 24min  & 56 s \\ \hline     &4h  & -11min & -32s \\ \end{tabular}

Add 60 seconds section of the first number and subtract 1 from the minutes part like this:

\begin{document} \begin{tabular}{cccc}    & 6h  &  12min  &  84s\\ -& 2h  & 24min  & 56 s \\ \hline     &4h  & -12min & 28s \\ \end{tabular}

Repeat the same process for minutes:

\begin{document} \begin{tabular}{cccc}    & 5h  &  72min  &  84s\\ -& 2h  & 24min  & 56 s \\ \hline     &3h  & 48min & 28s \\ \end{tabular}

 

Solution of exercise 4

Calculate:

15 h 48min 50 s + 6 h 45 min 30 s + 7 h 58 min 13 s.

\begin{document} \begin{tabular}{cccc}    & 5h  &  48min  &  50s\\ +& 6h  & 45min  & 30 s \\ & 7h  & 58min  & 13 s \\ \hline     &18h  & 151min & 93s \\ \end{tabular}

Divide 93 by 60:

\begin{array}{ccccccccccc} & & 1&\\ \cline{3-10} \multicolumn{2}{r}{60 \surd} & 93&& \\ & &60& & & & \\ \cline{3-7} \cline{6-10} & &33&&\\ \end{array}

The remainder reflects seconds and add the quotient to minutes to make it 152 and divide it by 60 like this:

\begin{array}{ccccccccccc} & & 2&\\ \cline{3-10} \multicolumn{2}{r}{60 \surd} & 152&& \\ & &120& & & & \\ \cline{3-7} \cline{6-10} & &32&&\\ \end{array}

Add the quotient 2 to hours to get 18 + 2 = 20 h and the remainder is minutes. The final answer is:

20 h 32 min 33 sec

 

6 h 13 min 45 s + 7 h 12 min 43 s + 6 h 33 min 50 s

\begin{document} \begin{tabular}{cccc}    & 6h  &  13min  &  45s\\ +& 7h  & 12min  & 43s \\ & 6h  & 33min  & 50 s \\ \hline     &19h  & 58min & 138s \\ \end{tabular}

Divide 138 by 60:

\begin{array}{ccccccccccc} & & 2&\\ \cline{3-10} \multicolumn{2}{r}{60 \surd} & 138&& \\ & &120& & & & \\ \cline{3-7} \cline{6-10} & &18&&\\ \end{array}

Add the quotient 2 to minutes to make is 58 + 2 = 60 and divide it by 60 like this:

\begin{array}{ccccccccccc} & & 1&\\ \cline{3-10} \multicolumn{2}{r}{60 \surd} & 60&& \\ & &60& & & & \\ \cline{3-7} \cline{6-10} & &0&&\\ \end{array}

Add the quotient 1 to hours to make it 19h + 1 = 20 h. the final answer will be:

20h 18 s

 

Solution of exercise 5

Calculate:

(15 h 13 min 42 s) × 7

(15 h 13 min 42 s) × 7 = 105h   91 min       294 s

Divide 294 by 60:

\begin{array}{ccccccccccc} & & 4&\\ \cline{3-10} \multicolumn{2}{r}{60 \surd} & 294&& \\ & &240& & & & \\ \cline{3-7} \cline{6-10} & &54&&\\ \end{array}

The number in the remainder is the seconds and add the quotient 4 to minutes to make is 91 + 4 = 95 and divide it by 60 like this:

\begin{array}{ccccccccccc} & & 1&\\ \cline{3-10} \multicolumn{2}{r}{60 \surd} & 95&& \\ & &60& & & & \\ \cline{3-7} \cline{6-10} & &35&&\\ \end{array}

The remainder 35 is minutes and add the quotient 1 to hours. The final answer is:

106 h 35 min 54 sec

 

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Emma

I am passionate about travelling and currently live and work in Paris. I like to spend my time reading, gardening, running, learning languages and exploring new places.