Introduction

In this lesson, you will learn how to add and subtract with decimal numbers. Addition and subtraction with decimals are the same as addition and subtraction with whole numbers. You’ll stack the numbers and line them up according to place values; when dealing with decimals, this means you line up the decimals.

There may be instances when there aren’t the same number of digits after the decimal place in both numbers. You can fill in any places to the right of the decimal with a zero. In numbers, this could look like the following example:

\begin{align*}
3.15 = 3.150 = 3.150000000 \\
\end{align*}

These videos illustrate the lesson material below. Watching the videos is optional.

• Addition with Decimals (06:14 mins) | Transcript
• Subtraction with Decimals (05:30 mins) | Transcript

Steps for Addition: Combining Two Positive or Two Negative Numbers

1. Stack the numbers according to place value. This will line up the decimals.
2. Add the numbers in the columns starting with the column on the right.
3. Carry numbers into the next place value to the left as needed.
4. Repeat this pattern for each remaining column.
5. Bring the decimal down.
6. Check the sign. If both numbers were positive, the answer is positive. If both numbers were negative, the answer is negative.

Addition with Decimals

The steps for addition with decimals are exactly the same as the steps for addition with whole numbers, except that you have to keep track of the decimal point.

Example 1
\(1.3+2.8\)

Start with 1.3, which is shown on the number line below, and add 2.8.

Figure 1

The only difference between adding whole numbers and adding decimal numbers is bringing the decimal down. When you put the numbers into their columns according to place value, the decimals automatically line up. In this example, the answer is 4.1.

Bringing the decimal down just means that you put the decimal in the answer in the same column as the other decimals. In the figure below, the other decimals go between the ones place and the tenths place, so that is where the decimal in the answer will go.

Figure 2

Example 2
\(-12.91 + (-3.82)\)

The figure below shows an addition problem where both numbers are negative. When you add them together, you will put negative signs in front of both of them to remind you that the answer will be negative. Follow the steps above and the answer is -16.73.

Figure 3

Steps for Subtraction: Combining Both a Positive and a Negative Number

These are the steps for subtraction with both a positive and a negative number:

1. Place the biggest number on top.
2. Stack in columns according to place value. This will line up the decimals.
3. Regroup as needed.
4. Subtract in columns by place value starting on the right and going left.
5. Bring the decimal down.
6. The strongest number wins, meaning if the bigger number was negative then the answer is negative. If the bigger number was positive, then the answer is positive.

Subtraction with Decimal Numbers

Example 3
\(3.4-7.8\)

Imagine that these numbers don’t have a decimal in them. If there were no decimal, you would simply subtract the smaller number from the larger number. You would figure out if the remaining number was negative or positive, and that would be the answer. Thankfully, the steps for subtraction with decimal numbers are exactly the same as the steps for subtraction with whole numbers. The only difference is that you have to keep track of the decimal point.

Figure 4

There are two ways to go about solving this problem. The first is converting it into an addition problem, because subtraction is the same as adding a negative number. This method is shown in the figure above, and the answer is -4.4.

\begin{align*}3.4-7.8 &=-4.4\\\\\text{OR}\\\\3.4+(-7.8) &=-4.4\end{align*}

The figure below shows the subtraction algorithm. Put the biggest number on top and the smaller number on the bottom and line up the place values, then subtract. Since the bigger number had a negative sign in front of it, the answer is negative. This method gives the same answer: -4.4.

Figure 5

Steps for Subtraction

Example 4
\(3.4 + (-2.1)\) or \(3.4 - 2.1\)

By following the steps, you will determine the answer is 1.3.

\begin{align*} &3.4\\ - &2.1\\ \hline &1.3 \end{align*}

Things to Remember

• In addition, if both numbers are positive, the answer is positive.
• In addition, if both numbers are negative, the answer is negative.
• In subtraction, if the bigger number is positive, the answer is positive.
• In subtraction, if the bigger number is negative, the answer is negative.

Practice Problems

1. \(2.4 + 8.8 = ?\) (
   Solution

   x

   Solution: 11.2
   Details:
   Using place values, add 2.4 and 8.8.
   Line up the numbers in their corresponding places.
   
   
   
   Next, add the numbers in the tenth column. Since \(4 + 8 = 12\), place the 2 below the tenths place and the 1 in the ones place.
   
   
   Finally, add the numbers in the ones place. Include the 1 carried over from the tenths place.
   \(1 + 2 + 8 = 11\)
   
   
   The final answer: 11.2
   Be sure to include the decimal point between the tenths place and the ones place.
   )
2. \(8.12 + 9.81 = ?\) (
   Solution

   x

   Solution: 17.93
   Details:
   Using place values, add 8.12 and 9.81.
   Line up the numbers in their corresponding place values.
   
   
   Next, add the numbers in the hundredths column. Since \(2 + 1 = 3\), place the 3 below the hundredths place.
   
   
   Next, add the numbers in the tenths column. Since \(1 + 8 = 9\), place the 9 below the tenths place.
   
   
   Finally, add the numbers in the ones column. Since \(8 + 9 = 17\), put a 7 in the ones place and the 1 in the tens place.
   
   
   The final answer: 17.93
   Be sure to include the decimal point between the tenths place and the ones place.
   )
3. \(5.92 + 3.22 = ?\) (
   Video Solution

   x

   Solution: 9.14
   Details:
   

   
   
   Transcript )
4. \(7.2 - 1.5 = ?\) (
   Solution

   x

   Solution:
   5.7
   )
5. \(5.2 - 5.4 = ?\) (
   Solution

   x

   Solution:
   -0.2
   )
6. \(39.6 - 88.88 = ?\) (
   Video Solution

   x

   Solution: -49.28
   Details:
   

   
   
   | Transcript)