Addition and Subtraction of Decimal Fractions

Decimal Fractions

Decimals are a fraction with any power of ten as the denominator. For example, the decimal representation of the fraction 6/10 is 0.6. The decimal point is the dot at the end of a number. The fraction’s numerator, or fractional component, is represented by the number to the right of the decimal point. The fraction’s whole number is represented by the number to the left of the decimal point, 4310, for example, is written as 4.3, with 4 being the whole number and 0.3 being the fractional part. The decimal point divides the whole integer and fractional parts of the equation.

Addition of Decimals

Follow the steps below to do a decimal addition operation:

Step 1: Write the numbers in a way that the decimals are exactly lined up.

Step 2: Insert zeroes whenever the length of decimal numbers differs.

Step 3: Now add the decimal values and discover the output to addition.

Solved Example on Decimal Addition

We add 14.02, 198.3 and 394.051.

We convert the given decimals into like decimals so that they can be arranged together vertically. So 14.02 becomes 14.020, 198.3 becomes 198.300 and 394.051 remains the same. 

14.020 + 198.300 + 394.051

We then write the decimals in columns in such a way that the decimal points are arranged one below the other. Add the numbers like usual to get the final answer.

    14.020

  198.300

+ 394.051

___________

    606.371

Therefore we get 606.371 as our answer.

When one has to perform subtraction of decimal numbers, they have to follow the rule of carrying over the balance digit to the right side, just like it is done in whole numbers. 

First, one has to properly align and write the decimal numbers in a way that the decimals are lined together.

Second, if the length of the decimal numbers are not the same, simply add zeroes to make the number of digits after the decimal same in both the numbers. 

Finally, perform subtraction like you normally would, and find the result. 

Solved Example on Decimal Subtraction

We have to subtract 3.456 from 7.1.

We first make the given decimal like and then align the decimals vertically in such a way that the decimal point is aligned vertically.

So, 7.1 becomes 7.100 and 3.456 remains the same. Aligning the decimals and subtracting as usual to get the answer.

  7.100

– 3.456

_______

   3.644

Hence, we get 3.644 as our answer.

Important points on Addition and Subtraction of Decimals

A few key aspects are listed below to assist you in better comprehending this topic.

• Placing a zero after the decimal digits has no effect on the decimal value.
• In addition or subtraction of decimal numbers, the decimal for the solution is the maximum of the decimals of the individual integers.
• Despite the fact that the time and angle measurements are in decimal format, they cannot be added or subtracted using decimals.

Word Problems Including Addition and Subtraction of Decimals

Problem1 : Kylie had 25m of ribbon. She uses 8m and 13 cm to decorate a skirt. How much length of ribbon is left with Kylie?

Solution

Length of ribbon Kylie had = 25m = 25.00

Length of the ribbon used by Kylie = 8m 13 cm = 8.13

Therefore the remaining length of the ribbon will be calculated by subtracting the whole length of the ribbon by the length of ribbon used.

 25.00

– 8.13

______

16.87

Hence, the remaining length of the ribbon is 16m and 87cm.

Problem 2: We have purchased a bicycle for $389.98 and a helmet for $23.64. What is the total cost of the bill?

Solution 

Since we have to find the total cost we add the amounts given.

398.98

+23.64

_________

422.62

So the total bill amount comes out to be $422.62.

Decimals in Real Life

In everyday life, we deal with decimal addition and subtraction while dealing with:

• Money
• Observations (Length, Mass, Capacity, Volume)
• Temperature

Conclusion

We learned how we carry out operations like addition and subtraction on decimals. When adding and subtracting decimals, the numbers should be aligned vertically based on their place values to perform the addition and subtraction correctly and properly. Once aligned correctly, they can be added and subtracted like normal numbers, irrespective of the decimal point. We just have to carry down the decimal point when doing the sums.