Free Decimal Worksheets: Adding and Subtracting Decimals in Grade 4

Master decimal operations with our free worksheets: place value alignment, decimal point handling, and precision checking.

Solution: Exercises 1 to 3
1 Basic decimal addition
Exercise 1
Calculate:
\(4.37 + 2.58\)
Definition:

Decimal addition: Align decimal points and add column by column, carrying over when needed

Addition method:
  1. Align decimal points vertically
  2. Add zeros if necessary to make columns equal
  3. Add column by column from right to left
  4. Carry over when sum exceeds 9
Numbers aligned
4.37
Units: 4
Tenths: 3
Hundredths: 7
2.58
Units: 2
Tenths: 5
Hundredths: 8
Result
\(6.95\)
Step 1: Align decimal points

\(4.37 + 2.58\) becomes:

\(\begin{array}{r} 4.37 \\ + 2.58 \\ \hline \end{array}\)

Step 2: Add hundredths column

\(7 + 8 = 15\), write down 5, carry over 1

Step 3: Add tenths column

\(3 + 5 + 1 = 9\)

Step 4: Add units column

\(4 + 2 = 6\)

\(4.37 + 2.58 = 6.95\)
Final answer:

\(4.37 + 2.58 = 6.95\)

Applied rules:

• Decimal alignment: Always align decimal points before adding

• Place value: Add digits in the same place value columns

• Carrying: When sum exceeds 9, carry the extra to the next column

2 Decimal subtraction
Exercise 2
Calculate:
\(7.84 - 3.29\)
Definition:

Decimal subtraction: Align decimal points and subtract column by column, borrowing when needed

Numbers aligned
7.84
Units: 7
Tenths: 8
Hundredths: 4
3.29
Units: 3
Tenths: 2
Hundredths: 9
Result
\(4.55\)
Step 1: Align decimal points

\(7.84 - 3.29\) becomes:

\(\begin{array}{r} 7.84 \\ - 3.29 \\ \hline \end{array}\)

Step 2: Subtract hundredths column

\(4 < 9\), so borrow from tenths: \(14 - 9 = 5\)

Step 3: Subtract tenths column

After borrowing: \(7 - 2 = 5\)

Step 4: Subtract units column

\(7 - 3 = 4\)

\(7.84 - 3.29 = 4.55\)
Final answer:

\(7.84 - 3.29 = 4.55\)

Applied rules:

• Decimal alignment: Always align decimal points before subtracting

• Borrowing: When top digit is smaller, borrow from the next higher place value

• Place value: Subtract digits in the same place value columns

3 Mixed operations
Exercise 3
Calculate:
\(8.63 - 4.17 + 2.59\)
Definition:

Mixed operations: Perform operations from left to right following order of operations

First operation
\(8.63 - 4.17\)
Second operation
\(result + 2.59\)
Final result
\(7.05\)
Step 1: Align decimal points for subtraction

\(8.63 - 4.17\):

\(\begin{array}{r} 8.63 \\ - 4.17 \\ \hline \end{array}\)

Step 2: Subtract hundredths column

\(3 - 7\), so borrow: \(13 - 7 = 6\)

Step 3: Subtract tenths column

After borrowing: \(5 - 1 = 4\)

Step 4: Subtract units column

\(8 - 4 = 4\)

Step 5: Add the result to 2.59

\(4.46 + 2.59 = 7.05\)

\(8.63 - 4.17 + 2.59 = 7.05\)
Final answer:

\(8.63 - 4.17 + 2.59 = 7.05\)

Applied rules:

• Order of operations: Perform operations from left to right

• Decimal alignment: Align decimal points for each operation

• Sequential calculation: Solve one operation at a time

Decimal Worksheet Summary
Key Concepts & Definitions
Core Definitions:

• Decimal number: A number that contains a decimal point separating the whole number part from the fractional part

• Decimal point: The dot that separates the whole number from the fractional part

• Place value: The value of a digit based on its position relative to the decimal point

• Tenths: The first digit to the right of the decimal point (1/10 of a unit)

• Hundredths: The second digit to the right of the decimal point (1/100 of a unit)

Step-by-Step Methods
Addition Method:
  1. Align decimal points: Write numbers vertically with decimal points lined up
  2. Add zeros if needed: Make all numbers have the same number of decimal places
  3. Add column by column: Start from the rightmost column (hundredths)
  4. Carry over: When sum ≥ 10, carry the extra to the next column
  5. Place decimal point: Put the decimal point in the answer directly below others
Subtraction Method:
  1. Align decimal points: Write numbers vertically with decimal points lined up
  2. Add zeros if needed: Make all numbers have the same number of decimal places
  3. Subtract column by column: Start from the rightmost column (hundredths)
  4. Borrow when needed: When top digit is smaller, borrow from next column
  5. Place decimal point: Put the decimal point in the answer directly below others
Examples & Practice
Simple Example: 3.2 + 1.4 = 4.6 (no carrying needed)
With Carrying: 2.8 + 1.7 = 4.5 (carry 1 from tenths to units)
With Borrowing: 6.3 - 2.8 = 3.5 (borrow from units to tenths)
Advanced: 9.54 - 4.28 + 1.76 = 7.02 (mixed operations)
Tips & Common Mistakes
Always align decimal points! This is the most important step.
Add zeros when needed: 3.2 = 3.20 to match 1.45 decimal places.
Don't forget to carry/borrow: This is where many mistakes happen.
Watch the decimal point: It must align in your answer.
Free Decimal Worksheets
Worksheet Collection
📋
Addition
20 problems
Subtraction
20 problems
Mixed Ops
15 problems
Word Problems
10 problems
Download Addition Worksheet
Download Subtraction Worksheet
Download Mixed Operations
Download Word Problems
Worksheet Features
✅ Aligned Decimals
Vertical format
✅ Step-by-step
Guided practice
✅ Answer Keys
Complete solutions
✅ Progressive
Easy to hard
Practice Problems
Level 1
1.2 + 3.4
5.6 - 2.1
4.3 + 1.7
Level 2
2.45 + 1.78
6.32 - 2.89
4.76 + 2.54
Level 3
8.46 - 3.29 + 1.54
7.23 + 2.87 - 4.15
9.65 - 2.48 - 1.73
Level 4
12.34 + 5.67 - 8.91
15.78 - 9.23 + 4.56
20.01 - 12.34 + 7.89
Decimal Operations: In-Depth Concepts
\(a.bc + d.ef = (a+d).(b+e)(c+f)\)
Decimal Addition Rule
Key definitions:

Decimal system: A base-10 number system where each position represents a power of 10

Place value: The value of a digit based on its position relative to the decimal point

Decimal alignment: Positioning decimal points directly above each other in vertical calculations

Complete methodology:
  1. Identify decimal places: Count digits after the decimal point in each number
  2. Align decimal points: Write numbers vertically with decimal points lined up
  3. Add zeros if needed: Make all numbers have the same number of decimal places
  4. Perform operation: Add or subtract column by column from right to left
  5. Place decimal point: Put the decimal point in the answer directly below others
  6. Verify result: Check if the answer makes sense with estimation
Tip 1: Always align decimal points, even if numbers have different decimal places.
Tip 2: Add zeros to the right of the last decimal digit to make calculation easier.
Tip 3: Estimate first: round decimals to whole numbers to predict the approximate answer.
Tip 4: Always check your work by performing the inverse operation.
Common errors: Misaligning decimal points, forgetting to carry/borrow, placing decimal point incorrectly in answer.
Key insight: Each place value to the right of the decimal point is 1/10 the value of the place to its left.
Essential rules for decimal operations:

• Alignment rule: Always align decimal points vertically before calculating

• Zero padding: Add zeros to match decimal places if necessary

• Carrying rule: When sum in a column is ≥10, carry the excess to the next column

• Borrowing rule: When subtracting and top digit is smaller, borrow from next column

• Decimal placement: Decimal point in answer aligns with those in the problem

Questions & Answers

Question: Are these decimal worksheets really free? Do I need to pay anything to download them?

Answer: Yes, all our decimal worksheets are completely free to download and use! We believe quality education resources should be accessible to everyone.

Our worksheets include:

  • Step-by-step guided practice problems
  • Answer keys with detailed solutions
  • Progressive difficulty levels
  • Various problem types (addition, subtraction, mixed operations)

Simply click the download button and save the PDF to your device. No registration or payment required!

Question: I'm having trouble with borrowing in decimal subtraction. How can I practice this skill more?

Answer: Borrowing in decimal subtraction happens when the top digit is smaller than the bottom digit in a column. Our worksheets have dedicated sections for borrowing practice!

Here's the process:

  1. Look at the column where the top number is smaller than the bottom
  2. Go to the next column to the left and decrease its value by 1
  3. Add 10 to the current column's top number
  4. Now subtract normally

Example: 5.23 - 1.78
In hundredths: 3 < 8, so borrow from tenths: 13 - 8 = 5
In tenths: 1 < 7 (after borrowing), so borrow from units: 11 - 7 = 4
Answer: 3.45

Practice with our worksheets - they have plenty of borrowing problems!

Question: How can I check if my decimal worksheet answers are correct? Sometimes I'm not sure if I made a mistake.

Answer: Each of our worksheets comes with a complete answer key so you can check your work! Additionally, here are verification methods:

Estimation is your best friend:

  • For 4.56 + 2.34, estimate 5 + 2 = 7
  • Your actual answer should be close to 7
  • If you got 69.90, that's way off from 7, so you made a mistake

Other verification methods:

  • Add the result back to the subtracted number (for subtraction problems)
  • Subtract one of the original numbers from the sum (for addition problems)
  • Check if the decimal point is in the right place

Always ask yourself: "Does this answer make sense?" Our answer keys provide step-by-step solutions so you can see where you went wrong!