Addition and Subtraction of Decimal Numbers

🏆Practice addition and subtraction of decimal fractions

Simple Operations with Decimal Numbers

We will solve addition and subtraction operations of decimal numbers in vertical form, always keeping in mind the following rules:
• All the rules that are applicable to the addition and subtraction of whole numbers also apply to decimal numbers.
• The decimal points must always be aligned one under the other.
• Numbers must be written in an orderly manner - both to the right of the decimal point and to its left (tenths under tenths, hundredths under hundredths, and so on)

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Test yourself on addition and subtraction of decimal fractions!


\( 0.75+0.35= \)

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How to Add and Subtract Decimal Numbers

In this article, we will learn how to add and subtract decimal numbers in a simple, easy, and quick way.
In fact, adding and subtracting decimal numbers is very similar to operations with whole and common numbers that we already know and can even solve in our heads without needing to write them down.
Let's remember how to add or subtract whole numbers:
When we have an exercise like 678+879 678+879 
Our intuition naturally prompts us to solve it vertically, so we will write:

Excellent! After having remembered how to solve addition and subtraction exercises with whole numbers and having paid attention to critical issues such as:

Writing the numbers clearly by placing the corresponding digits on top of each other (hundreds over hundreds, tens over hundreds, and units over units)
and the correct carry over: noting part of the number above in an orderly manner ("remember that I carry one over..."), let's move on to the addition and subtraction of decimal numbers.

We will always solve the addition and subtraction of decimal numbers vertically!

What we need to pay attention to in the addition and subtraction of decimal numbers:

  • Write the decimal points one under the other.
  • Strictly comply with orderly writing - both in the part of the whole numbers and in the decimals
    Hundreds under the hundreds, tens under the hundreds, units under the units,
    tenths under the tenths, hundredths under the hundredths, and thousandths under the thousandths.
  • Be methodical with the correct carry over - in the same way we do in the addition and subtraction of whole numbers, we will proceed according to the general rules of vertical addition and subtraction.

Suggestion: To make the exercise look more organized we can add the figure 0 0 at the end of the decimal number, to the right, without changing its value.

Now, let's practice

Exercise 1 (addition of decimal numbers)

Solve the exercise: 134.12+56.76=134.12+56.76=


Let's write the exercise in vertical form and pay attention to the rules and the important points we have emphasized before.
Notice, the decimal point is under the other decimal point.
In the result, we will also copy the decimal point to the exact place it originally occupied.

Notice that we have correctly carried over when we added 4+6 4+6 and got 10 10 .

A notation like this, for example

Would be a mistake!

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Exercise 2 (addition of decimal numbers)

Let's move on to the next exercise:


Let's write it in vertical form, clearly and correctly:

Note: It is extremely important to write in an orderly and clear manner, both the side of the whole numbers and the decimals, to obtain a correct result.
If you do not see the exercise in a very orderly way you can add a 0 that will not affect the numerical value (marked in pink), and thus, get a clearer view of the exercise.

Exercise 3 (addition of decimal numbers)

Now we will see an exercise with carrying over to the part after the decimal point:
Solve the exercise
185.28+76.9= 185.28+76.9= 

Let's write it correctly:

We can see that the number we carried over passed to the other side of the decimal point, this is totally correct.

Do you know what the answer is?

Now let's move on to a subtraction exercise.

Exercise 1 (Subtraction of Decimal Numbers)


Let's write it in an organized way:

Notice that we need to borrow, we will do it according to the same rules of adding and subtracting whole numbers.

Exercise 2 (Subtraction of Decimal Numbers)

Example of an advanced exercise: 

In this exercise, we will need to borrow twice.

Infallible recommendation:
To always know how to write the exercises correctly, it is advisable that, after noting the first decimal number, you place the decimal point of the second fraction directly below the decimal point of the first fraction, and only after doing this, write the remaining numbers.

Check your understanding

When can sums and subtractions of decimal numbers be solved without using the vertical form?

In general, we recommend solving additions and subtractions of decimal numbers only in vertical form.
In case the exercises are very simple (without carrying and without too many digits) they can be solved without arranging them in vertical form. Clearly, everything depends on the instructions noted in the exam.
Example of solution: 3.32+1.12=3.32+1.12=
Let's add the units and we will get 55
Let's add the tenths and we will get 44
Let's add the hundredths and we will get 44
The solution is 5.445.44

Do you think you will be able to solve it?
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