Adding and Subtracting Decimals

For Elementary Students

The Golden Rule: Line Up the Decimal Points!

When adding or subtracting decimals, the most important rule is to line up the decimal points!

Think about it like this: The decimal point is like a fence — everything on the left is whole numbers, everything on the right is parts. Keep the fence in the same place!

Adding Decimals

Example: 3.25 + 1.4 = ?

Step 1: Write one number above the other and line up the decimal points

  3.25
+ 1.4
-----

Step 2: Add zeros to make both numbers the same length (optional but helpful!)

  3.25
+ 1.40
-----

Step 3: Add like normal, starting from the right

• Hundredths: 5 + 0 = 5
• Tenths: 2 + 4 = 6
• Ones: 3 + 1 = 4

  3.25
+ 1.40
-----
  4.65

Answer: 4.65

Step 4: Don't forget the decimal point in your answer!

Another Adding Example

Example: 5.6 + 2.83 = ?

Step 1: Line up the decimal points

  5.6
+ 2.83
------

Step 2: Add zeros to make them the same length

  5.60
+ 2.83
------

Step 3: Add column by column

• Hundredths: 0 + 3 = 3
• Tenths: 6 + 8 = 14 → Write 4, carry 1
• Ones: 5 + 2 + 1 = 8

    ¹
  5.60
+ 2.83
------
  8.43

Answer: 8.43

Subtracting Decimals

Subtracting decimals is the same — line up the decimal points!

Example: 5.3 − 2.17 = ?

Step 1: Line up the decimal points

  5.3
− 2.17
------

Step 2: Add zeros to make them the same length

  5.30
− 2.17
------

Step 3: Subtract column by column

• Hundredths: 0 − 7 → Can't do it! Need to borrow
• Borrow from tenths: 10 − 7 = 3
• Tenths: 2 − 1 = 1 (it became 2 after we borrowed)
• Ones: 5 − 2 = 3

  5.²3¹0
− 2.17
------
  3.13

Answer: 3.13

Money Is Decimals!

When you add or subtract money, you're adding decimals!

Example: You have $4.50. Your friend gives you $3.75. How much do you have now?

  $4.50
+ $3.75
-------
  $8.25

Answer: $8.25

Remember!

✓ Always line up the decimal points

✓ Add zeros to make numbers the same length

✓ Put the decimal point in your answer directly below the others

For Junior High Students

The Golden Rule

When adding or subtracting decimals, always line up the decimal points. Then add or subtract just like whole numbers, keeping the decimal point in the same position.

Why it works: Lining up decimal points ensures you're adding tenths to tenths, hundredths to hundredths, etc. — just like lining up place values with whole numbers.

Adding Decimals

Example: 3.25 + 1.4

Step 1: Line up the decimal points and pad with zeros

  3.25
+ 1.40
------

Step 2: Add column by column from right to left

• Hundredths: 5 + 0 = 5
• Tenths: 2 + 4 = 6
• Ones: 3 + 1 = 4

  3.25
+ 1.40
------
  4.65

Step 3: Place decimal point directly below the other decimal points

Answer: 4.65

Adding with Carrying (Regrouping)

Example: 2.78 + 3.65

  2.78
+ 3.65
------

Step 1: Hundredths: 8 + 5 = 13 → write 3, carry 1

Step 2: Tenths: 7 + 6 + 1 = 14 → write 4, carry 1

Step 3: Ones: 2 + 3 + 1 = 6

  ¹ ¹
  2.78
+ 3.65
------
  6.43

Answer: 6.43

Key insight: Carrying works the same as with whole numbers — you're just regrouping 10 hundredths into 1 tenth, or 10 tenths into 1 one.

Adding Three or More Decimals

Example: 1.5 + 2.34 + 0.876 = ?

Step 1: Line up decimal points and add zeros

  1.500
  2.340
+ 0.876
-------

Step 2: Add column by column

  ¹ ¹
  1.500
  2.340
+ 0.876
-------
  4.716

Answer: 4.716

Subtracting Decimals

The same rule applies: line up the decimal points, pad with zeros, then subtract.

Example: 5.3 − 2.17

Step 1: Line up and pad

  5.30
− 2.17
------

Step 2: Subtract column by column with borrowing

• Hundredths: 0 − 7 → need to borrow → 10 − 7 = 3
• Tenths: 2 − 1 = 1 (the 3 became 2 after borrowing)
• Ones: 5 − 2 = 3

  5.²3¹0
− 2.17
------
  3.13

Answer: 3.13

Subtracting from a Whole Number

Example: 7 − 3.45

Step 1: Write 7 as a decimal: 7.00

  7.00
− 3.45
------

Step 2: Subtract with borrowing

  6.⁹9¹0
− 3.45
------
  3.55

Answer: 3.55

Why pad with zeros? It makes borrowing easier and helps visualize place values.

Checking Your Work

Method 1: Addition checks subtraction

If 5.3 − 2.17 = 3.13, then 3.13 + 2.17 should equal 5.3

  3.13
+ 2.17
------
  5.30 ✓

Method 2: Estimation

Before calculating, estimate to check if your answer is reasonable.

Example: 5.3 − 2.17

Estimate: 5 − 2 = 3

Actual answer: 3.13 (close to 3!) ✓

Example: 8.91 + 4.56

Estimate: 9 + 5 = 14

Actual answer should be around 14.

Tips for Success

Tip 1: Always write the decimal point in your answer directly below the other decimal points

Tip 2: Pad with trailing zeros so both numbers have the same number of decimal places

Tip 3: Double-check by estimating: 5.3 − 2.17 should be roughly 5 − 2 = 3 — and 3.13 is close to 3 ✓

Tip 4: Line up the decimal points FIRST, before you start calculating

When adding money, you are adding decimals! $4.50 + $3.75 = $8.25

Real-Life Applications

Shopping: "Item 1 costs $3.49, item 2 costs $2.75. What's the total?"

  $3.49
+ $2.75
-------
  $6.24

Sports: "First jump: 5.82 meters. Second jump: 6.15 meters. Total distance?"

  5.82
+ 6.15
------
 12.97 meters

Measurements: "You need 7.5 cups of flour. You have 3.25 cups. How much more?"

  7.50
− 3.25
------
  4.25 cups

Temperature: "Morning: 18.3°C. Evening: 24.7°C. How much warmer?"

  24.7
− 18.3
------
   6.4°C warmer

Common Mistakes

Mistake 1: Not lining up decimal points

❌ WRONG:

  3.25
+  1.4
-----

(Ones digits lined up instead of decimal points)

✓ CORRECT:

  3.25
+ 1.4
-----

(Decimal points lined up)

Mistake 2: Forgetting the decimal in the answer

3.25 + 1.40 = 465 ❌ (should be 4.65)

Mistake 3: Not adding zeros before borrowing

Makes borrowing harder to visualize!

Mental Math Strategies

Add/subtract whole parts separately from decimal parts:

3.6 + 2.8 = ?

• Whole parts: 3 + 2 = 5
• Decimal parts: 0.6 + 0.8 = 1.4
• Total: 5 + 1.4 = 6.4

Round, calculate, adjust:

7.89 + 3.12 = ?

• Round: 8 + 3 = 11
• Adjust: Added 0.11 too much, added 0.12 too little → Close to 11
• Actual: 11.01

Practice