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ExplainerMathGrades 3–5

Adding and Subtracting Decimals

What Is This?

Adding and subtracting decimals works exactly like adding and subtracting whole numbers — with one critical rule: you must line up the decimal points before you calculate. Once the decimal points are aligned, every digit is in its correct place value column and you can add or subtract just as you normally would.

Why Does It Matter?

Any time you work with money, measurements, or data you will be adding and subtracting decimals. Adding up a grocery bill, finding how much change you should get, comparing race times, or calculating rainfall totals all require this skill. It also builds directly toward multiplying and dividing decimals.

The Golden Rule — Line Up the Decimal Points

Before you add or subtract any decimals, rewrite the problem vertically so the decimal points form a straight column. Every tenths digit lines up with every tenths digit; every hundredths digit lines up with every hundredths digit.

Wrong — not aligned:

  3.4 5
+  2.1

Correct — aligned:

  3.45
+ 2.10
------

Using Placeholder Zeros

When two decimals have a different number of decimal places, fill the shorter one with placeholder zeros so both numbers have the same number of decimal places. This makes column addition safe and clear.

Example: 5.3 + 2.47

Write 5.3 as 5.30:

  5.30
+ 2.47
------
  7.77

The placeholder zero shows there are zero hundredths in 5.3 — it does not change the value, but it prevents column errors.

Adding Decimals — Step by Step

Example: 6.48 + 3.75

Step 1: Write vertically, decimal points aligned.

  6.48
+ 3.75
------

Step 2: Add from right to left, just like whole numbers.

  • Hundredths: 8 + 5 = 13 → write 3, carry 1
  • Tenths: 4 + 7 + 1 (carried) = 12 → write 2, carry 1
  • Ones: 6 + 3 + 1 (carried) = 10 → write 0, carry 1
  • Tens: 0 + 0 + 1 = 1

Step 3: Bring down the decimal point.

  6.48
+ 3.75
------
 10.23

Answer: 10.23 ✓

Subtracting Decimals — Step by Step

Example: 8.52 − 3.76

Step 1: Write vertically, decimal points aligned.

  8.52
- 3.76
------

Step 2: Subtract from right to left, borrowing when needed.

  • Hundredths: 2 − 6, can't do it → borrow from tenths: 12 − 6 = 6
  • Tenths: 4 (after borrowing) − 7, can't do it → borrow from ones: 14 − 7 = 7 (tenths column was 5, became 4 after lending, then borrowed from ones to get 14)
  • Ones: 7 (after borrowing) − 3 = 4

Step 3: Bring down the decimal point.

  8.52
- 3.76
------
  4.76

Answer: 4.76 ✓

Subtracting From a Whole Number

When subtracting a decimal from a whole number, add a decimal point and placeholder zeros to the whole number first.

Example: 7 − 2.34

Write 7 as 7.00:

  7.00
- 2.34
------

Now subtract normally:

  • Hundredths: 0 − 4, borrow → 10 − 4 = 6
  • Tenths: 9 (after borrowing) − 3 = 6 (the 0 became 10 after borrowing, gave 1 to hundredths, leaving 9... wait — let's track carefully)

Careful working:

  6.9 10
  7. 0  0
- 2. 3  4
---------
  4. 6  6

Answer: 4.66 ✓

Worked Examples

Worked Example 1: 14.6 + 8.75

Add a placeholder zero to 14.6:

  14.60
+  8.75
-------
  23.35
  • Hundredths: 0 + 5 = 5
  • Tenths: 6 + 7 = 13 → write 3, carry 1
  • Ones: 4 + 8 + 1 = 13 → write 3, carry 1
  • Tens: 1 + 0 + 1 = 2

Answer: 23.35

Worked Example 2: 10.00 − 4.37

  10.00
-  4.37
-------
   5.63
  • Hundredths: 0 − 7, borrow chain → 10 − 7 = 3
  • Tenths: 9 − 3 = 6 (after borrowing)
  • Ones: 9 − 4 = 5 (after borrowing)
  • Tens: 0

Answer: 5.63

Worked Example 3: 0.9 + 0.45 + 1.3

Align all three numbers (add placeholder zeros):

  0.90
  0.45
+ 1.30
------
  2.65
  • Hundredths: 0 + 5 + 0 = 5
  • Tenths: 9 + 4 + 3 = 16 → write 6, carry 1
  • Ones: 0 + 0 + 1 + 1 = 2

Answer: 2.65

Worked Example 4 (Word Problem): Maya had $12.50. She spent $4.75 on lunch. How much does she have left?

  12.50
-  4.75
-------
   7.75

Answer: $7.75

Estimating to Check Your Answer

Before or after calculating, round each decimal to the nearest whole number and add or subtract mentally. If your exact answer is far from your estimate, recheck your work.

Example: 6.48 + 3.75

  • Estimate: 6 + 4 = 10
  • Exact: 10.23 ✓ (close to 10 — reasonable)

Example: 8.52 − 3.76

  • Estimate: 9 − 4 = 5
  • Exact: 4.76 ✓ (close to 5 — reasonable)

Common Mistakes

Mistake 1: Not aligning decimal points Adding 3.4 + 2.15 as if they were whole numbers (34 + 215) gives a completely wrong answer. Always rewrite vertically with decimal points in a column first.

Mistake 2: Forgetting placeholder zeros Subtracting 5.3 − 2.47 without writing 5.3 as 5.30 can cause column errors. Always make both numbers the same length before calculating.

Mistake 3: Dropping the decimal point in the answer After you calculate, the decimal point must come straight down into the answer. 6.48 + 3.75 = 10.23, not 1023.

Mistake 4: Borrowing errors when subtracting Borrowing across zeros (e.g. 10.00 − 4.37) requires a chain of borrowing. Work carefully one column at a time, updating each digit as you borrow.

Key Takeaways

  • Always line up the decimal points before adding or subtracting
  • Use placeholder zeros to make both numbers the same length
  • Add or subtract column by column from right to left, carrying or borrowing as needed
  • Bring the decimal point straight down into the answer
  • Estimate first to check your answer is reasonable
  • When subtracting from a whole number, add ".00" before you start

Practice and Resources

Ready to practise? Try our Grade 3-5 Adding and Subtracting Decimals Worksheet with problems covering column addition, borrowing, money, and measurement. Test yourself with the Grade 3-5 Math Practice Test.

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