Adding and Subtracting Decimals

Adding and subtracting decimals is just like adding and subtracting whole numbers but with an additional twist: we have to make sure we line up our decimal points!

Check out our Adding and Subtracting Decimals Calculator below for examples of how to add and subtract decimals. And if you want to learn more about adding and subtracting decimals, explore the lesson below!

Adding and Subtracting Decimals Calculator

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First, let’s line up our numbers. We want our decimal points to be lined up, so our question will look like this

Since and have a different number of digits after the decimal point, we can add trailing zeros as placeholders:

How Do I Add and Subtract Decimals?

Think of adding decimals like adding beads to a necklace. We can have all sorts of wacky beads or charms, but no matter what, their bead holes have to line up or we won’t be able to string them together! Our decimal points are like the bead holes. We might have decimals of different lengths, but as long as we make sure to line up our decimal points, we’ll be able to add them up with no problem!

Beads being lined up

Let’s check out an example!

Example 1

What is ? Drag the second number to lineup the decimal points.

Fantastic work! After we line up our decimal points, our problem will look like this:

Now that we have our numbers lined up correctly, there’s just one thing we need to do before we add our numbers.

Trailing Zeros

In our problem, has two digits after the decimal point while only has one. Before we add our two numbers, we want them to have the same number of digits after the decimal point. We can do this by adding a trailing zero to .

Trailing zeros are zeros that we can add to the end of a decimal without changing its value. If we added a trailing zero to the number , it would become which is equivalent to . When adding and subtracting decimals, we often use trailing zeros as placeholders so that our two numbers have the same number of digits after the decimal point.

Polite Zeros 🚶🏿🚶🏼🚶🏾

We can only add trailing zeros to the end of numbers. Consider what would happen if we added a zero in the middle of the number and made it . That would change the number’s value!

It’s also important to note that we can only add trailing zeros after the decimal point. For example, if we added a trailing zero to the number , it would become instead of . Think of your digits like people waiting in line. The trailing zero can never cut in the middle. It always has to go to the end!

Stanley Hudson from the Office shaking his head no

Before we add and , we want to add a trailing zero to so that our two numbers have the same number of digits after the decimal.

Which of the following correctly shows with a trailing zero?

Awesome job! If we add a trailing zero to , it’ll become . Our problem now becomes , which we can solve by adding normally:

Notice that our answer has the same number of digits after the decimal point as and . When we add or subtract decimals, we want the decimal point in our answer to line up as well!

Let’s look at another example.

Example 2

What is ?

Let’s line up our numbers! Slide until the two decimals are lined up correctly.

Wow! Amazing!

Let’s add trailing zeros so that our two numbers have the same number of digits after the decimal point. Which of the following shows our problem after we’ve added the correct number of trailing zeros?

Splendid! Now we can subtract! When we subtract from , we'll get   .

That’s exactly right! Since and both have digits after the decimal point, our answer must as well.

Now that you know how to add and subtract decimals, it’s time to show off your skills in the Quick Practice below!

Quick Practice

Question 1

Slide your numbers until they line up correctly:

Superb! Now select the option that adds the correct number of trailing zeroes:

Amazing work! Now when we add and , we'll get 

That’s exactly right! We want the decimal point in our answer to line up with the decimal points in our problem, so we will get as our final answer.

Amazing work! You’ve completed this lesson!

Dancing Homer