Addition and Subtraction of Decimals

Addition and Subtraction of Decimals
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Counting numbers was easy. But it became difficult once the numbers changed to decimals, isn't it? We will try making it simple. 

Addition of Numbers

Did you know, we can add and subtract decimals also, with the help of our ten fingers?  

In this mini-lesson, we shall explore the world of decimals, by finding answers to questions like how to add or subtract decimals, how to add or subtract decimals of varying lengths, and other similar questions related to decimals. 

Lesson Plan

How to Add or Subtract Decimals?

The operations of addition or subtraction of decimals are the same as the normal numbers. 

But, the place values of the digits in the numbers should be rightly matched.

Addition of Decimals

Addition of Decimals

This addition of decimals can be understood with the help of a simple example: \[ 12.5 + 4.9 \] 

We can separate the decimals from the whole numbers.   \[  \begin{align}12.5 + 4.9 &=12 + 0.5 + 4 + 0.9 \\&= 12 + 4 + 0.5 + 0.9 \\ &= 16 + 1.4 \\&= 16 + 1 + 0.4 \\&= 17.4 \end{align}\]

Here, the addition of \(0.5 + 0.9 \) is the same as the addition \( 5 + 9 = 14 \). And the decimal is placed in the answer \(1.4 \)

\[\begin{align}12.5& \\ +4.9 \\ \hline  \\ 17.4 \\ \hline \end{align} \]

Subtraction of Decimals

Subtraction of decimals

For the operation of subtraction in decimals the rule of rule of carry over is followed as in the normal whole numbers.

Let us understand this with an example: \[ 14.5 - 8.7 \]

Here, we segregate the decimals and whole numbers and separately conduct the operation of subtraction.

 \[  \begin{align} 14.5 - 8.7 &= 14 + 0.5 -(8 + 0.7) \\&= 14 + 0.5 - 8 - 0.7 \\ &=14 - 8 + 0.5 - 0.7 \\ &= 6 -0.2 \\ &= 5 + 1.0 - 0.2 \\ &= 5 + 0.8 \\ &= 5.8\end{align}\]

Here the number 1 is taken from 6, to help for further subtraction.

Also the subtraction \(1 .0 - 0.2 \) is same as the subtraction \(10 - 2  = 8\). And a decimal is placed in the answer \(0.8 \) 

 \[  \begin{align} 14.5\\ - 8.7\\ \hline\\5.8 \\ \hline \end{align}\]


How to Add or Subtract Decimals of Varying Lengths?

The operation of addition and subtraction can be conveniently performed, even with decimals of varying lengths.

The decimal digits in each of the numbers should be made equal.

To understand this, let us add the decimal numbers 24, 32.1, 0.08, 0.5, and 4.003

Here each of the numbers needs to have an equal number of decimal digits.

For this, we change the numbers as 24.000, 32.100, 0.080, 0.500, and 4.003

\(\begin{align}24.000+ 32.100+ 0.080+0.500+ 4.003 &= 24 + 32 + 4 + 0.000 + 0.100 + 0.080 + 0.500 + 0.003 \\&=60 + 0.683 \\&=60.683 \end{align}\)

\[\begin{align}24.000\\ 32.100\\ 0.080\\0.500\\+ 4.003 \\ \hline \\60.683 \\\hline \end{align}\]

 
important notes to remember
Important Notes
  1. The value of a decimal does not change on placing a zero after the decimal digits.
  2. The decimal for the answer in the addition or subtraction of decimal numbers is the maximum of the decimals of the individual numbers. 
  3. Even though the time and angle measure is represented in decimal format, they cannot be added or subtracted as decimals. 

How do You Add and Subtract Decimals and Whole Numbers?

For adding or subtracting a decimal and whole number, the whole number is changed into a decimal number. This is done by placing a decimal after the whole number and then writing the required number of zeroes after the decimal point.

The whole number 5 is written in decimal form as 5.0

Let us add the number 15 to 12.56. Here the number 15 is changed to 15.00

\[  \begin{align} 15.00 + 12.56 &= 15 + 0.00 + 12 + 0.56 \\ &=15 + 12 + 0.00 + 0.56 \\&=17 + 0.56 \\&= 27.56 \end{align}\]

 \[  \begin{align} 15.00 \\+ 12.56 \\ \hline  \\ 27.56 \\ \hline \end{align}\]

 
Challenge your math skills
Challenging Question

Find the sum of the fractions after converting them into decimals.  \[\dfrac{1}{2} +\dfrac{1}{4} + \dfrac{1}{8} + \dfrac{1}{16} +\dfrac{1}{32} + \dfrac{1}{64} \]

Solved Examples

Example 1

 

 

James has been asked by his teacher to add .2 + .22 + .222 + .2222.  How can we help James with his addition of these decimal numbers?

Solution

The numbers are altered by placing a few zeros after the decimals, such that each of the numbers has an equal number of decimals.

\[  \begin{align}0.2 = 0.2000 \\0.22 = 0.2200 \\0.222 = 0.2220 \\ 0.2222 = 0.2222 \end{align} \] 

\[  \begin{align}.2000 \\ .2200\\.2220 \\+.2222 \\ \hline  \\ 0.8642 \\ \hline\end{align}\]

\(\therefore \text{The sum is } 0.8642 \)
Example 2

 

 

Diya is trying to simplify 11.89 – 14.32 + 20.87. Can you help Diya in simplifying the given numbers?

Solution

Let us first add the numbers 11.89, 20.87, and then subtract 14.32 from the result.

 \[  \begin{align} 11.89\\+20.87 \\ \hline  \\ 32.76 \\ \hline\end{align}\]

 \[  \begin{align} 32.76 \\-14.32 \\ \hline  \\ 18.44 \\ \hline\end{align}\]

\(\therefore \text{The answer is } 18.44 \)
Example 3

 

 

Find the answer for 987.62 + 0.08 + 43.5

Solution

The number of decimals in each of the numbers to be added should be equal.

43.5 is changed to 43.50 and now we have equal number of decimal digits in all the numbers.

 \[  \begin{align} 987.62\\  0.08& \\+ 43.50 \\ \hline  \\ 1031.20 \\ \hline\end{align}\]

\(\therefore \text{The answer is } 1031.20 \)
Example 4

 

 

Find the value for 328.7 + 443.035

Solution

Before adding the numbers the number of decimals in each of the numbers, needs to be equal.

328.7 is changed to 328.700. Now, both the numbers 328.700 and 443.035 have an equal number of decimals.

 \[  \begin{align} 328.700 \\+ 443.035 \\ \hline  \\ 771.735\\ \hline\end{align}\]

\(\therefore \text{The value is } 771.735 \)
Example 5

 

 

Ron has to calculate 7847 – 78.47. Please help Ron with his calculation.

Solution

The number 7847 is written in decimal form as 7847.00. Now the subtraction can be performed in the following step.

\[  \begin{align} 7847.00 \\– 78.47 \\ \hline  \\ 7768.53\\ \hline\end{align}\]

\(\therefore \text{The value is } 7768.53 \

Interactive Questions on Addition and Subtraction of Decimals

Here are a few activities for you to practice. Select/Type your answer and click the "Check Answer" button to see the result.

 

 
 
 
 
 
 

Let's Summarize

The mini-lesson targeted the fascinating concept of addition and subtraction of decimals. The math journey around addition and subtraction of decimals started with what a student already knew about numbers and went on to creatively crafting a fresh concept in the young minds. Done in a way that not only it is relatable and easy to grasp, but also will stay with them forever. 

About Cuemath

At Cuemath, our team of math experts is dedicated to making learning fun for our favorite readers, the students!

Through an interactive and engaging learning-teaching-learning approach, the teachers explore all angles of a topic.

Be it worksheets, online classes, doubt sessions, or any other form of relation, it’s the logical thinking and smart learning approach that we, at Cuemath, believe in.


FAQs on Addition and Subtraction of Decimals

1. How do you add two decimal numbers?

For adding two decimals we first align the numbers as per decimal places and the digit value and then add it similar to the normal addition.  Let us understand this with the help of a simple example.

\[ 23.1+ 4.23 = 23.10 + 4.23 = 27.33\]

2. How do you subtract two decimal numbers?

The subtraction of decimal numbers follow similar to the usual numbers.  Here also the decimal numbers and the respective digits should be aligned before subtraction.

\[ 44.32 - 3.6 = 44.32 - 03.60 = 40.72\]

3. How do you line up decimals when adding and subtracting?

For adding or subtracting decimals, the number of decimals digits in each of the numbers should be equal and then the decimals can be easily lined up. 

4. How do you subtract decimals with regrouping?

For subtraction of decimals, all the positive numbers and the negative numbers should be grouped and added separately. Then the operation of the subtraction can be performed on the sum of the grouped numbers.

\(4.3 - 12.1 + 15.2 - 2.7 - 1.5 \)= \((4.3 + 15.2) - (12.1 + 2.7 + 1.5) \)= \(19.5 - 16.3 = 3.2 \)

5. How do you add a decimal and whole number?

To add a decimal and a whole number, the whole number should be changed to a decimal. Let us add 5 and 3.236.

Here we change 5 to 5.000 and we have  5.000 + 3.326 = 8.326

6. How do you multiply two decimals?

On multiplying two decimal numbers the number of decimal add up in the resultant answer.  \[ 0.2 \times 0.04 = 0.008\]

7. How do you divide one decimal with another decimal number?

The process of division of two decimal numbers is the same as the normal division.  Here the number of decimal places in the answer is a subtraction of the decimal places of the individual numbers.  \[ \dfrac{0.008}{0.2} = 0.04\]

  
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