Addition and Subtraction of Decimals
Counting numbers was easy. But it became difficult once the numbers changed to decimals, isn't it? We will try making it simple. Did you know, we can add and subtract decimals also, with the help of our ten fingers? In this minilesson, we shall explore the world of addition and subtraction 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.
1.  What is Addition and Subtraction of Decimals? 
2.  How to Add or Subtract Decimals of Varying Lengths? 
3.  How to Add and Subtract Decimals and Whole Numbers? 
What is Addition and Subtraction of 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. For example, let's see how the numbers 2.357 and 6.14 are added up in the image given below:
Addition of Decimals
For the operation of addition in decimals, follow the steps given below:
 Step 1: Write the numbers, such that the decimals are lined perfectly.
 Step 2: Write zeroes in the places wherever the length of decimal numbers is not the same.
 Step 3: Now add the decimal numbers and find the output to addition.
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. 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. Here, the addition of 0.5 + 0.9 is the same as the addition of 5 + 9 = 14. And the decimal is placed in the answer 1.4.
Subtraction of Decimals
For the operation of subtraction in decimals, the rule of carryover is followed as in the normal whole numbers.
 Step 1: Write the numbers, such that the decimals are lined perfectly.
 Step 2: Write zeroes in the places wherever the length of decimal numbers is not the same.
 Step 3: Now subtract the decimal numbers and find the output to subtraction.
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. 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. 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.
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
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
How to 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. For example, the whole number 5 is written in decimal form as 5.0. Below given is a stepbystep method to Add and Subtract Decimals and Whole Numbers:
 Step 1: Write the numbers, such that the decimals are lined perfectly.
 Step 2: Put zeroes equal to the other decimal number length, which makes it a decimal number.
 Step 3: Now add the decimal numbers and find the output to addition.
Let us add the number 15 to 12.56. Here the number 15 is changed to 15.00.
15.00 + 12.56 = 15 + 0.00 + 12 + 0.56 = 15 + 12 + 0.00 + 0.56 = 17 + 0.56 = 27.56
Important Points on Addition and Subtraction of Decimals
Given below are a few important points that will help you in understanding this concept better.
 The value of a decimal does not change on placing a zero after the decimal digits.
 The decimal for the answer in the addition or subtraction of decimal numbers is the maximum of the decimals of the individual numbers.
 Even though the time and angle measure is represented in decimal format, they cannot be added or subtracted as decimals.
Solved Examples on Addition and Subtraction of Decimals

Example 1: James has been asked by his teacher to add 0.2 + 0.22 + 0.222 + 0.2222. 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.
∴ The sum is 0.8642

Example 2: Ron has to calculate the difference between 7847 and 78.47. Help Ron to calculate!
Solution:
The number 7847 is written in decimal form as 7847.00. Now the subtraction can be performed in the following step.
Thus, the value is 7768.53.
Practice Questions on Addition and Subtraction of Decimals
FAQs on Addition and Subtraction of Decimals
How Do You Add Two Decimal Numbers?
For adding two decimals, we can use the following steps:
 Step 1: Write the numbers, such that the decimals are lined perfectly.
 Step 2: Write zeroes in the places wherever the length of decimal numbers is not the same.
 Step 3: Now add the decimal numbers and find the output to addition.
Let us understand this with the help of a simple example: 23.1+ 4.23 = 23.10 + 4.23 = 27.33
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.
 Step 1: Write the numbers, such that the decimals are lined perfectly.
 Step 2: Write zeroes in the places wherever the length of decimal numbers is not the same.
 Step 3: Now subtract the decimal numbers and find the output to subtraction.
For example, 44.32  3.6 = 44.32  03.60 = 40.72
How Do You Line Up Decimals When Adding and Subtracting?
For adding or subtracting decimals, the total number of digits after the decimal point in the two numbers should be similar. Then, we align both the numbers by taking the decimal point as the common intersection. You will notice that the numbers have been aligned now.
How Do You Subtract Decimals With Regrouping?
In order to solve subtraction of decimals with regrouping, follow the given steps:
 Step 1: Keep all positive numbers (addition) and negative numbers (subtraction) on different sides
 Step 2: Make a bracket around all negative numbers, take out the common subtraction sign, and make all the positive numbers inside the bracket.
 Step 3: Write the numbers, such that the decimals are lined perfectly.
 Step 4: Write zeroes in the places wherever the length of decimal numbers is not the same.
 Step 5: Now add/subtract the decimal numbers and find the output to subtraction.
For example, 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
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
How Do You Multiply Two Decimals?
Multiplication of decimals with whole numbers is similar to the multiplication of whole numbers, the only difference being in the placement of the decimal point. The following steps can be followed to multiply decimals with whole numbers:
 Step 1: Initially, Ignore the decimal point and multiply the two numbers normally.
 Step 2: After multiplication, count the number of decimal places in decimal numbers. The product obtained after multiplication will have the same number of decimal places.
 Step 3: Place the decimal point in the obtained product following Step 2.
For example, 0.2 × 0.04 = 0.008
How Do You Divide One Decimal With Another Decimal Number?
To divide a decimal number by a decimal number, multiply the divisor by as many tens as necessary until we get a whole number, and remember to multiply the dividend by the same number of tens. For example, 13.8 ÷ 0.6 becomes 138 ÷ 6 = 23.