Free Math Guide

Decimal Addition and Subtraction Explained

Learn how to line up place values, add placeholder zeros, carry or borrow when needed, and check decimal answers for reasonableness.

Practice Decimal Operations Read the Guide

Adding and subtracting decimals uses the same column methods as whole-number arithmetic. The difference is that each digit must stay in its correct place-value column. Once decimal points are aligned, ones combine with ones, tenths with tenths, hundredths with hundredths, and so on. Placeholder zeros make missing places visible without changing either number's value.

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The Central Rule

Align Decimal Points Before Calculating

Write one number above the other so their decimal points form a vertical line. This automatically aligns digits that have the same place value. Do not line up the last digits unless doing so also aligns the decimal points.

Addition

Combine Matching Places

Add from right to left. When a column totals 10 or more, write its ones digit and carry to the next place-value column.

Decimal under decimal
Subtraction

Compare Matching Places

Subtract from right to left. When a top digit is too small, regroup one unit from the place-value column immediately to its left.

Decimal under decimal

Bring the Decimal Point Straight Down

Once the decimal points in the problem are aligned, the decimal point in the answer belongs directly beneath them. Addition and subtraction do not move a decimal point left or right.

Keep Every Digit in Its Column

Decimal Place-Value Columns

Each move to the left makes a place value ten times greater. Each move to the right makes it one tenth as great. A digit's location determines its value, so mixing columns changes the number being calculated.

Hundreds Tens Ones Decimal Tenths Hundredths Thousandths
0 1 8 . 7 0 0
0 0 6 . 4 5 0

Read the Columns, Not Just the Digits

In 18.7, the 7 means seven tenths. In 6.45, the 4 means four tenths and the 5 means five hundredths. Aligning decimals places the 7 above the 4 because both digits occupy the tenths column.

Show Missing Decimal Places

Use Placeholder Zeros When Decimal Lengths Differ

You may write zeros to the right of a decimal number's last digit without changing its value. These zeros make empty place-value columns visible and give each column a digit to add or subtract.

18.7 = 18.70 = 18.700

For Addition

Rewrite 4.8 + 0.37 as 4.80 + 0.37 so the hundredths column is 0 + 7.

For Subtraction

Rewrite 20 − 6.825 as 20.000 − 6.825 so every decimal place can be regrouped correctly.

Add Zeros Only Where They Preserve Value

A trailing zero after the decimal portion does not change a number: 3.5 = 3.50. Inserting a zero between existing digits does change the value: 3.5 is not equal to 3.05.

Addition Method

How to Add Decimals

Align the decimal points, make the decimal portions the same length with zeros if needed, and add from the smallest place value on the right toward the left.

Example: Add 18.7 + 6.45

  1. Align the decimal points.
  2. Write 18.7 as 18.70 to show the hundredths place.
  3. Add hundredths: 0 + 5 = 5.
  4. Add tenths: 7 + 4 = 11. Write 1 and carry 1 to the ones column.
  5. Add ones and tens, including the carried 1.
18.70 +6.45 25.15

Carrying Crosses Place Values

Ten hundredths equal one tenth, and ten tenths equal one whole. Carrying records that exchange in the next column to the left; it is not an extra number added without a place-value reason.

Subtraction Method

How to Subtract Decimals

Place the greater number on top unless the problem is intended to have a negative answer. Align the decimal points, add placeholder zeros, and subtract from right to left, regrouping when necessary.

Example: Subtract 12.4 − 3.75

  1. Rewrite the problem as 12.40 − 3.75.
  2. In the hundredths column, regroup one tenth so 10 − 5 = 5.
  3. After regrouping, the tenths column becomes 3 − 7, so regroup one whole.
  4. Subtract the tenths, ones, and tens columns.
  5. Bring the decimal point straight down.
12.40 −3.75 8.65

Borrow From the Next Column to the Left

One whole becomes 10 tenths, one tenth becomes 10 hundredths, and one hundredth becomes 10 thousandths. If a zero blocks the regrouping path, continue left until you reach a nonzero digit.

Apply the Methods

Worked Decimal Addition and Subtraction Examples

Addition

Different Decimal Lengths

Add 4.8 + 0.37.

  1. Rewrite 4.8 as 4.80.
  2. Add hundredths: 0 + 7 = 7.
  3. Add tenths: 8 + 3 = 11; write 1 and carry 1.
  4. Add ones: 4 + 0 + 1 = 5.
4.80 + 0.37 = 5.17
Subtraction

Subtract From a Whole Number

Subtract 20 − 6.825.

  1. Rewrite 20 as 20.000.
  2. Regroup through the zeros to reach the thousandths.
  3. Subtract each column from right to left.
  4. Keep the decimal point aligned.
20.000 − 6.825 = 13.175
Money

Find a Total Cost

A notebook costs $3.75 and a folder costs $2.40. Find the total.

  1. Both amounts already show hundredths.
  2. Add: 3.75 + 2.40 = 6.15.
  3. State the answer as money using two decimal places.
The total cost is $6.15.
Measurement

Find a Difference

One board is 8.2 feet long and another is 5.68 feet long. How much longer is the first?

  1. Rewrite 8.2 as 8.20.
  2. Subtract 8.20 − 5.68.
  3. Include the measurement unit.
The first board is 2.52 feet longer.
Addition

Add Thousandths

Add 7.056 + 2.9.

  1. Rewrite 2.9 as 2.900.
  2. Add from thousandths through ones.
  3. Bring down the aligned decimal point.
7.056 + 2.900 = 9.956
Subtraction

Regroup Across a Zero

Subtract 10.02 − 4.786.

  1. Rewrite 10.02 as 10.020.
  2. Regroup as each smaller top digit requires.
  3. Subtract and keep three decimal places in the work.
10.020 − 4.786 = 5.234

Check for Reasonableness

Estimate Before or After Calculating

Rounding the original numbers gives a nearby result to compare with the exact answer. Estimation will not prove every digit is correct, but it quickly exposes many misplaced decimal points and operation errors.

Addition estimate
18.7 + 6.45 is about 19 + 6 = 25, so the exact answer 25.15 is reasonable.
Subtraction estimate
12.4 − 3.75 is about 12 − 4 = 8, so the exact answer 8.65 is reasonable.
Operation check
A positive addition result should exceed each addend. A positive subtraction result should be less than the starting amount.
Inverse-operation check
Check 12.40 − 3.75 = 8.65 by adding 8.65 + 3.75 and confirming that the sum is 12.40.
Estimate with rounded numbers, but calculate the exact problem with the original values.

Watch for These Errors

Common Decimal Addition and Subtraction Mistakes

Aligning the Last Digits

Line up decimal points, not the rightmost printed digits. In 4.8 + 0.37, the 8 belongs above the 3 because both are tenths.

Skipping Placeholder Zeros

An empty place is worth zero, but writing the zero helps prevent a digit from being placed or regrouped in the wrong column.

Moving the Decimal Point

For addition and subtraction, place the answer's decimal point directly below the aligned decimal points. Do not count decimal places as in multiplication.

Forgetting a Carry

When a column total is 10 or greater, record the carried amount above the next column and include it in that column's sum.

Subtracting the Smaller Digit From the Larger Digit

Subtraction keeps its direction. If the top digit is smaller, regroup; do not reverse only that column.

Forgetting to Reduce the Donor Column

When one unit is regrouped from a column, that column loses one. Record both parts of the exchange.

Rounding Before the Exact Calculation

Use rounding to estimate or when the question requests it. Replacing the original values too early changes the exact answer.

A Reliable Process

How to Add or Subtract Decimals Step by Step

1. Identify the operation
Determine whether the problem asks you to combine quantities or find a difference.
2. Align the decimals
Write the numbers vertically with decimal point directly under decimal point.
3. Add placeholder zeros
Extend shorter decimal portions with trailing zeros until both numbers show the same places.
4. Calculate right to left
Add or subtract one place-value column at a time, carrying or borrowing when needed.
5. Place the decimal
Bring the aligned decimal point straight down into the answer.
6. Check the result
Compare with an estimate and use the inverse operation when a full check is helpful.

Practice Decimal Addition and Subtraction

Solve randomized problems on an interactive place-value board. Fill in the answer one digit at a time, request a targeted hint, and receive immediate feedback on carrying, borrowing, and decimal alignment.

Open the Decimal Practice Tool

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