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Addition and Subtraction of Decimals


When it comes to addition of decimals and subtraction of decimals in Math, tackling such sums follows the same process as when dealing with addition and subtraction sums involving whole numbers.


One does have to pay attention to the position of the decimal point.

When setting up the sum the point gets placed in the appropriate position in the answer section, aligned with the original sum.




Addition and Subtraction of Decimals
Sums


(1.1) 

What is   2.412 + 3.536 ?

Solution   

\begin{array}{r} \space\space\space{\bf{2.412}}\space\space\\ +\space\space{\bf{3.536}}\space\space\\ \hline \space\space\space\space\space\space{\bf{5.948}}\space\space \end{array}

2.412 + 3.536  =  5.948



(1.2) 

What is   1.37 + 5.252 ?

Solution   

We don’t need to worry about the decimal numbers not initially having the same amount of digits after the decimal point.
We can just expand  1.37  appropriately.

\begin{array}{r} \space\space\space{\bf{1.370}}\space\space\\ +\space\space{\bf{5.252}}\space\space\\ \hline \space\space\space\space\space\space{\bf{6.622}}\space\space\\ ^{\tiny{1}} \space\space\space\space\space\space\space \end{array}
1.37 + 5.252  =  6.622



(1.3) 

What is   3 + 1.2 + 3.43 ?

Solution   

\begin{array}{r} \space\space\space{\bf{3.00}}\space\space\\ \space\space{\bf{1.20}}\space\space\\ +\space\space{\bf{3.43}}\space\space\\ \hline \space\space\space\space\space\space{\bf{7.63}}\space\space \end{array}

3 + 1.2 + 3.43  =  5.948



(1.4) 

What is   6.3781.24 ?

Solution   

\begin{array}{r} \space\space\space{\bf{6.378}}\space\space\\ -\space\space{\bf{1.240}}\space\space\\ \hline \space\space\space\space\space\space{\bf{5.138}}\space\space \end{array}

6.3781.24  =  5.138







Addition and subtraction of Decimals
Word Problems


Below is a selection of the type of word problems involving addition of decimals and subtraction that can be encountered.



(2.1) 

One week a TV in an electronics shop costs  $120.60.

The following week the price of the TV is reduced by  $15.30.

What is the price of the TV in the second week?

Solution   
\begin{array}{r} \space\space\space{\bf{120.60}}\space\space\\ {\text{--}}\space\space\space{\bf{15.30}}\space\space\\ \hline {\bf{.}}\space\space\space\space\space\space \end{array}       =>       \begin{array}{r} {\color{darkred}\scriptsize{1}} \space\space\space\space\space\space\space\space\space\space\space\space\\ \space\space\space{\bf{1{\cancel{2}}^{\tiny{1}}0.60}}\space\space\\ {\text{--}}\space\space\space{\bf{1\space5.30}}\space\space\\ \hline {\bf{10\space5.30}}\space\space \end{array}

The TV in the electronics shop was priced at  $105.30  in the second week.




(2.2) 

A man who weighs  85.78 Kg  decides to go on a diet for a month to try and lose some weight.

At then end of the month after losing some weight on the diet he weighs  83.62 Kg,  having lost  2.16 Kg.

But over the next month he puts back on  0.57 Kg.
How much did he weigh after the 2 months had passed?

Solution   
\begin{array}{r} \space\space\space{\bf{85.78}}\space\space\\ {\text{--}}\space\space\space{\bf{2.16}}\space\space\\ +\space\space\space{\bf{0.57}}\space\space\\ \hline \space{\bf{.}}\space\space\space\space\space\space \end{array}     =>     \begin{array}{r} \space\space\space{\bf{85.78}}\space\space\\ {\text{--}}\space\space\space{\bf{2.16}}\space\space\\ +\space\space\space{\bf{0.57}}\space\space\\ \hline \space\space{\bf{84.19}}\space\space\\ ^{\tiny{1}} \space\space\space\space\space\space\space\space \end{array}

After the 2 months were up, the man weighted  88.19 Kg.




(2.3) 

The temperature in a house is  17.043°C  when the owner decides to turn up the heating a bit.

After the heating is turned on, the temperature in the house rises by  2.5076°C.

What was the temperature in the house after the heating was turned up?

Solution   

\begin{array}{r} \space\space\space{\bf{17.0430}}\space\space\\ +\space\space\space{\bf{2.5076}}\space\space\\ \hline {\bf{.}}\space\space\space\space\space\space\space\space\space\space\space \end{array}     =>     \begin{array}{r} \space\space\space{\bf{17.0430}}\space\space\\ +\space\space\space{\bf{2.5076}}\space\space\\ \hline {\bf{19.5506}}\space\space\\ ^{\tiny{1}} \space\space\space\space\space\space\space \end{array}

After the heating was turned up the temperature in the house reached  19.5506°C.





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