Adding and Subtracting Decimals

Adding and subtracting decimals is the same as the addition and subtraction of whole numbers keeping in mind that the decimal point needs to be in place. The length of the decimal numbers can be adjusted by adding or removing zeros from the decimal part. Let us learn more about the addition and subtraction of decimals in this article.

The addition and subtraction of decimals involves the usual addition and subtraction rules. The only points to be taken care of are the decimal places after the decimal point. The numbers need to be written in columns according to their place values before and after the decimal point. The decimal place value chart shows that the place values before the decimal point start from ones tens, hundreds, and so on; whereas, the place values after the decimal point start from tenths, followed by hundredths, and so on. Let us understand this with the help of the addition of the decimal numbers explained in the following section.

Addition of Decimals

The addition of decimals is done by starting from the right-hand side and then we move on to the left adding each column. For example, let us add 12.5 + 14.9 using the following steps.

• Step 1: Write the numbers one below the other such that they are aligned as per their place values and the decimal point is placed one below the other.
• Step 2: Now add the decimal numbers to get the sum. In this case, 12.5 + 14.9 = 27.4

Now let us understand the subtraction of decimals in the following section.

Subtraction of Decimals

The subtraction of decimals is done in the same way as the subtraction of whole numbers. We just need to write the numbers correctly according to their place values. Let us understand this with the help of the example given below.

Example: Subtract the given decimals: 15.8 - 2.7

Solution: Let us subtract these decimals using the following steps.

• Step 1: Write the numbers one below the other such that the larger number is on top and the smaller number is written below it.
• Step 2: Now subtract the decimal numbers starting from the tenths column, moving on to the ones column, and then the tens column. Copy the decimal as it comes. In this case, 15.8 - 2.7 = 13.1

Adding and Subtracting Unlike Decimals

'Unlike decimals' are those decimal numbers that do not have the same number of digits after the decimal point. For example, 3.45 and 7.831 are 'unlike decimals' because 3.45 has two numbers after the decimal point and 7.831 has three numbers after the decimal point. In other words, unlike decimals are said to be of different lengths. The operation of addition and subtraction can be conveniently performed even with these unlike decimals. We just need to convert the 'unlike decimals' to 'like decimals' by writing zeros in the places wherever the length of decimal numbers is not the same. In this way, the decimal digits in each of the numbers becomes equal and it is easier to add or subtract the numbers. Let us understand this with the help of the following example.

Example: Add the decimal numbers 24, 32.1, 0.08, 0.5, and 4.003

Solution: Let us add these numbers using the following steps.

• Step 1: Here, each of the numbers needs to have an equal number of decimal digits.
• Step 2: For this, we rewrite the numbers as follows: 24.000, 32.100, 0.080, 0.500, and 4.003. Therefore, the sum of the given decimal numbers is 60.683

For adding or subtracting a decimal and a 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 zeros after the decimal point. For example, the whole number 5 is written in the decimal form as 5.0. Let us understand this with the help of the following examples.

Example: Add 15 + 12.56

• Step 1: Refer to the figure given above and place a decimal after 15 and write two zeros after it so that both the numbers become like decimals.
• Step 2: Now add the decimal numbers and find the sum using the usual rules of addition. Therefore, the 15 + 12.56 = 27.56

Let us understand this using subtraction.

Example: Subtract 6 - 2.25

• Step 1: Refer to the figure given above and place a decimal after 6 and write two zeros after it so that both the numbers become like decimals.
• Step 2: Now subtract the decimal numbers and find the difference using the usual rules of subtraction. Therefore, 6 - 2.25 = 3.75

Important Points on Addition and Subtraction of Decimals

• The value of a decimal does not change on placing a zero after the decimal digits. For example, 5 can be written as 5.00
• Even though the time and angle measure is represented in decimal format, they cannot be added or subtracted as decimals.

☛ Related Topics

• Adding and Subtracting Decimals Worksheets
• Adding and Subtracting Decimals Worksheets 6th grade
• Adding and Subtracting Decimals Worksheets 5th grade
• Dividing Decimals
• Multiplying Decimals

How to Add and Subtract Decimals?

The addition and subtraction of decimals is done using the usual addition and subtraction rules. The only thing to be kept in mind is the number of digits after the decimal point and that the decimal point needs to be placed appropriately in the sum or the difference. The numbers need to be written in columns according to their place values before and after the decimal point and then they are added or subtracted.

What is the Rule for Adding and Subtracting Decimals?

The rule for adding and subtracting decimals is related to the decimal point. For example, in order to add 56.12 + 10.14, we need to align these numbers one below the other such that the decimal point falls in place and all the numbers are written according to the place values. This will result in 66.26. In case if they are unlike decimals, we need to convert them to like decimals by writing the appropriate number of zeros after the decimal so that the decimal places become equal. For example, 34.25 + 12.986 can be written as 34.250 + 12.986 and the sum will be 34.250 + 12.986 = 47.236

How to Add and Subtract Decimals with Whole Numbers?

In order to add and subtract decimals with whole numbers, we need to change the whole number into a decimal number. This is done by placing a decimal after the whole number and then writing the required number of zeros after the decimal point. For example, if we need to add 8 + 4.321, then we can write the whole number 8 in the decimal form as 8.000 and then add it to 4.321. After this, the numbers can be added and written as, 8.000 + 4.321 = 12.321

How to Add Decimal Numbers?

For adding any two decimal numbers, we use the following steps. Let us understand this using an example. For example, let us add 23.12 + 4.23

• Step 1: Write the numbers one below the other such that they are aligned as per their place values and the decimal point is placed one below the other.
• Step 2: Now add the decimal numbers to get the sum. In this case, it will be 23.12 + 4.23 = 27.35

How to Subtract Decimal Numbers?

In order to subtract any two decimal numbers, we use the following steps. Let us understand this using an example. For example, let us subtract 44.32 - 3.6

• Step 1: Write the numbers one below the other such that they are aligned as per their place values and the decimal point is placed one below the other.
• Step 2: Now subtract the decimal numbers to get the difference. In this case, it will be 44.32 - 03.60 = 40.72

How to Add a Decimal Number and a Whole Number?

In order to add a decimal number to a whole number, the whole number needs to be changed to a decimal. For example, let us add 5 and 3.236. Here, we change 5 to 5.000 and we have 5.000 + 3.326 = 8.326

How to Multiply Two Decimals?

The multiplication of decimals with whole numbers is similar to the multiplication of whole numbers. The only difference is 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 the given decimal numbers. Suppose the multiplicand has 2 numbers after the decimal point and the multiplier has 1 number after the decimal point, then we will add these 2 + 1 = 3. So, we will place the decimal in the product after 3 places from the right. For example, 0.04 × 0.2 = 0.008

How to Divide a Decimal by Another Decimal?

In order to divide a decimal number by a decimal number, we need to convert the divisor into a whole number and then continue the division. For example, if we need to divide 13.8 ÷ 0.6, we will use the following steps.

• Step 1: The dividend is 13.8 and the divisor is 0.6. We need to change the divisor to a whole number and so we will multiply it by 10 so that the decimal point shifts to the right and it becomes a whole number. This means, 0.6 × 10 = 6
• Step 2: We need to treat the dividend in the same way as we had treated the divisor. So, we will multiply the dividend by 10 as well. This means it will be 13.8 × 10 = 138. In other words, we need to move both the decimal points to the right until the divisor becomes a whole number. Therefore, 138 ÷ 6 = 23.