Learn all about adding decimals and subtracting decimals in this free basic math lesson.

### Adding and subtracting with decimals

**Adding** and **subtracting** decimals happens a lot in real life. You may find that you need to add up the cost of your groceries to see if you have enough money to pay for them. Or perhaps you need to subtract the cost of a bill from your bank account.

When you're adding or subtracting decimal numbers, it's important to set up the expression **correctly**. The **numbers** need to be in a certain place, and so do the **decimals**.

Click through the slideshow below to learn how to set up these expressions.

First, let's set up an addition expression: 21.4 plus 6.82.

Just like with any addition example, we're going to **stack** one number on top of the other.

But instead of lining our numbers up on the right...

But instead of lining our numbers up on the right...we're going to line up the **decimal points**.

No matter how many numbers are on either side of the decimal point, we'll always line up the decimal points before adding.

Once we have the decimal points lined up, our decimals are ready to be added.

When we subtract decimals, we'll set up the decimals in the same way. Let's set up this example.

Instead of lining up our two numbers on the right, we'll line up the two decimal points.

And now our decimals are ready to be subtracted.

#### Adding decimal numbers

Now that we know how to set up problems with decimals, let's practice by solving a few. First, we'll work on **adding**. If you feel comfortable adding larger numbers, you're ready to add decimal numbers.

Click through the slideshow to learn how to add decimals.

Let's try solving this problem: 1.9 + 2.15.

First, we'll make sure the decimals are lined up.

We'll start by adding the digits farthest to the **right**. In this case, we have nothing on top and 5 on the bottom.

Nothing plus 5 equals 5. We'll write 5 beneath the line.

Now we'll add the next set of digits to the** left**: 9 and 1.

9 + 1 equals 10, but there's no room to write both digits in 10 underneath the 9 and 1. We'll have to **carry**.

We learned how to carry numbers in the lesson on Adding Two- and Three-Digit Numbers.

We'll write the right digit, 0, **under** the line...

We'll write the right digit, 0, **under** the line...then we'll carry the left digit, 1, up to the **next** set of digits in the problem.

Now we'll write the decimal point. We'll place it directly **beneath** the other two decimal points.

Next, we'll move **left** to add the next set of digits: 1 and 2. Since we carried the 1, we'll add it too.

1 + 1 + 2 equals 4. We'll write 4 below the line.

We're done. 1.9 + 2.15 = 4.05. We can read this answer as **four and five-hundredths**.

Let's try it with a money problem: $51.99 + $25.32.

We'll make sure our decimal points are lined up properly.

As always, we'll start by adding the digits on the right. Here, that's 9 and 2.

9 + 2 equals 11, so it looks like we'll have to** carry**.

The 1 on the **right** stays underneath the 9 and the 2.

We'll carry the 1 on the** left** and place it above the **next** set of digits to the left.

Now we'll move **left** to add the next set of digits. Since we carried the 1, we'll add it too.

1 + 9 + 3 = 13.

We'll put the 3 **under** the digits we added.

We'll carry the 1 and place it **above** the next column to the left.

Now it's time to write the decimal point. Remember to place it directly **beneath** the other two decimal points.

Next, we'll move **left** and add the next set of digits. We'll make sure to add the 1 we carried.

1 + 1 + 5 = 7. We'll write 7 beneath the line.

To finish, we'll add the next column to the **left:** 5 and 2.

5 + 2 equals 7. We'll write 7 underneath the 2.

We'll finish by writing the **dollar sign** ($).

We're done. $51.99 + $25.32 = $77.31. We can read this answer as **seventy-seven dollars and thirty-one cents**.

#### Try This!

Try solving these problems to practice adding decimal numbers.

#### Subtracting Decimal Numbers

On the previous page, you saw that **adding** numbers with decimals is a lot like adding other numbers. The same is true for **subtracting** numbers with decimals. If you can subtract large numbers, you can subtract numbers with decimals too!

Click through the slideshow to learn how to subtract decimals.

Let's try to solve this problem: 41.2 - 3.09.

First, we'll make sure the expression is set up correctly. Here, 41.2 is the larger number, so we'll put it on top.

The decimal points are lined up.

As always, we’ll begin with the digits farthest to the **right**. Here, we have nothing on top and 9 on the bottom.

We can’t take 9 away from nothing. We'll need to place a digit **after** 41.2 so we can subtract from it.

The value of our number won't change if we use the digit that means nothing: 0. We'll place a 0 after 41.2.

Now we can subtract the digits on the right. 0 is smaller than 9, so we’ll need to **borrow** to make 0 larger.

We learned how to borrow in the lesson on Subtracting Two- and Three-Digit Numbers.

We'll borrow from the digit to the **left** of 0. Here, it's 2. We'll take **1** from it.

2 - 1 = 1. To help us remember we subtracted 1, we'll cross out the 2 and write 1 **above** it.

Then we'll place the 1 we took next to the 0.

0 becomes 10.

10 is larger than 9, which means we can subtract. We'll solve for 10 - 9.

10 - 9 = 1. We'll write 1 beneath the line.

Now we'll move **left** to subtract the next set of digits: 1 - 0.

1 - 0 = 1. We'll write 1 beneath the line.

Now it's time to write the **decimal point**. We'll place it directly **beneath** the other two decimal points.

Now we'll find the **difference** of the next set of digits to the left: 1 - 3.

Because 1 is smaller than 3, it looks like we'll need to borrow again. We need to make the 1 larger.

We'll borrow from the digit to the **left** of 1. Here, we'll borrow 1 from the 4.

4 - 1 = 3. We'll write 3 above the 4.

Then we'll place the 1 we took **next** to the 1.

1 becomes 11.

11 is larger than 3, which means we can subtract. We'll solve for 11 - 3.

11 - 3 = 8. We'll write 8 beneath the line.

Finally, we'll move to the **left** to subtract the last set of digits. The top digit is 3, but there's nothing beneath it.

3 minus nothing equals 3, so we'll write 3 beneath the line.

41.2 - 3.09 = 38.11. We can read this as **thirty-eight and eleven-hundredths**.

Let's try subtracting money. Let's see if we can solve $14.76 - $3.86.

First, let's make sure the expression is set up correctly. The larger number is on** top**, and the decimal points are** lined up**.

As always, let's start by finding the **difference** of the digits on the right. Here, that's 6 - 6.

6 - 6 = 0. We'll write 0 beneath the line.

We'll move** left** to the next set of digits: 7 and 8. 7 is smaller than 8, so we'll borrow to make 7 larger.

Let's look at the digit to the **left** of 7. Here, it's 4. We'll take 1 from it.

4 - 1 = 3. We'll cross out the 4 and write 3 **above** it.

Then we'll place the 1 we took **next** to the 7.

7 becomes 17.

Now it's time to subtract. We'll solve for 17 - 8.

17 - 8 = 9. We'll write 9 beneath the line.

We'll put a **decimal point** directly **beneath** the other two decimal points.

Next, we'll move **left** to find the **difference** of the next set of digits. Here, that's 3 - 3.

3 - 3 = 0. We'll write 0 below the line.

Finally, we'll move** left** to **subtract** the last set of digits. The top digit is 1, but there's nothing beneath it.

1 minus nothing equals 1. We'll write 1 beneath the line.

Next, we'll write a **dollar sign** ($) to the left of the 1.

$14.76 - $3.86 = $10.90. We can read this as **ten dollars and ninety cents**.

#### Try This!

Try solving these problems to practice subtracting decimal numbers.

### Assessment

Want even more practice? Try out a short assessment to test your skills by clicking the link below:

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