Adding and Subtracting Decimals

Adding and subtracting decimals works exactly like adding and subtracting whole numbers. The one critical rule: line up the decimal points vertically so that digits in the same place value are aligned. Then add or subtract column by column, just as you would with whole numbers.

Adding Decimals

Steps:

1. Write the numbers vertically, lining up the decimal points
2. Fill in trailing zeros so both numbers have the same number of decimal places
3. Add column by column from right to left, carrying as needed
4. Bring the decimal point straight down into the answer

Example 1: Add $12.6 + 3.47$

Line up and fill in a trailing zero:

$\begin{array}{r} 12.60 \\ +\;\; 3.47 \\ \hline 16.07 \end{array}$

Answer: $16.07$

Example 2: Add $0.045 + 1.3 + 0.72$

Equalize decimal places (thousandths):

$\begin{array}{r} 0.045 \\ 1.300 \\ +\; 0.720 \\ \hline 2.065 \end{array}$

Answer: $2.065$

Example 3: Add $156.8 + 47.95$

$\begin{array}{r} 156.80 \\ +\;\; 47.95 \\ \hline 204.75 \end{array}$

Answer: $204.75$

Subtracting Decimals

The same principle applies — line up the decimal points, fill in zeros, and subtract with borrowing as needed.

Example 4: Subtract $50.00 - 23.85$

$\begin{array}{r} 50.00 \\ -\; 23.85 \\ \hline 26.15 \end{array}$

Answer: $26.15$

Example 5: Subtract $8.3 - 2.175$

Equalize decimal places:

$\begin{array}{r} 8.300 \\ -\; 2.175 \\ \hline 6.125 \end{array}$

Answer: $6.125$

Example 6: Subtract $15 - 7.63$

Write 15 as 15.00:

$\begin{array}{r} 15.00 \\ -\;\; 7.63 \\ \hline \;\;7.37 \end{array}$

Answer: $7.37$

Common Mistake: Forgetting to Line Up

If you forget to line up the decimal points and instead right-align like whole numbers, you will get the wrong answer:

Wrong (right-aligned like whole numbers — $3.5 + 2.14$ misread as $35 + 214$):

$\begin{array}{r} 3.5 \\ +\; 2.14 \\ \end{array} \quad \rightarrow \quad \text{wrong answer}$

Correct (decimal points aligned, trailing zero added):

$\begin{array}{r} 3.50 \\ +\; 2.14 \\ \hline 5.64 \end{array}$

Always line up the decimal points first, then fill in trailing zeros so each number has the same number of decimal places.

Real-World Application: Making Change

You buy items costing $4.79, $12.50, and $3.25. You pay with two $20 bills. How much change?

Step 1: Add the prices:

$\begin{array}{r} 4.79 \\ 12.50 \\ +\;\; 3.25 \\ \hline 20.54 \end{array}$

Step 2: Subtract from amount paid:

$40.00 - 20.54 = 19.46$

Answer: $19.46 in change.

Practice Problems

Test your understanding with these problems. Click to reveal each answer.

Key Takeaways

• Line up decimal points — this is the most important step
• Fill in trailing zeros to make all numbers the same length
• Then add or subtract exactly as you would with whole numbers
• Carry and borrow work the same way as with whole numbers
• Bring the decimal point straight down into your answer

Return to Arithmetic for more foundational math topics.