Decimal Worksheets with Answers: Adding and Subtracting Decimals in Grade 4

Master decimal operations with our comprehensive worksheets featuring detailed solutions and answer keys.

Solution: Exercises 1 to 3
1 Basic decimal addition
Exercise 1
Calculate:
\(6.35 + 2.79\)
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
6.35
Units: 6
Tenths: 3
Hundredths: 5
2.79
Units: 2
Tenths: 7
Hundredths: 9
Result
\(9.14\)
Step 1: Align decimal points

\(6.35 + 2.79\) becomes:

\(\begin{array}{r} 6.35 \\ + 2.79 \\ \hline \end{array}\)

Step 2: Add hundredths column

\(5 + 9 = 14\), write down 4, carry over 1

Step 3: Add tenths column

\(3 + 7 + 1 = 11\), write down 1, carry over 1

Step 4: Add units column

\(6 + 2 + 1 = 9\)

\(6.35 + 2.79 = 9.14\)
Final answer:

\(6.35 + 2.79 = 9.14\)

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:
\(7.84 - 3.57\)
Definition:

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

Numbers aligned
7.84
Units: 7
Tenths: 8
Hundredths: 4
3.57
Units: 3
Tenths: 5
Hundredths: 7
Result
\(4.27\)
Step 1: Align decimal points

\(7.84 - 3.57\) becomes:

\(\begin{array}{r} 7.84 \\ - 3.57 \\ \hline \end{array}\)

Step 2: Subtract hundredths column

\(4 < 7\), so borrow from tenths: \(14 - 7 = 7\)

Step 3: Subtract tenths column

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

Step 4: Subtract units column

\(7 - 3 = 4\)

\(7.84 - 3.57 = 4.27\)
Final answer:

\(7.84 - 3.57 = 4.27\)

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:
\(8.63 - 4.27 + 3.58\)
Definition:

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

First operation
\(8.63 - 4.27\)
Second operation
\(result + 3.58\)
Final result
\(7.94\)
Step 1: Align decimal points for subtraction

\(8.63 - 4.27\):

\(\begin{array}{r} 8.63 \\ - 4.27 \\ \hline \end{array}\)

Step 2: Subtract hundredths column

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

Step 3: Subtract tenths column

After borrowing: \(5 - 2 = 3\)

Step 4: Subtract units column

\(8 - 4 = 4\)

Step 5: Add the result to 3.58

\(4.36 + 3.58 = 7.94\)

\(8.63 - 4.27 + 3.58 = 7.94\)
Final answer:

\(8.63 - 4.27 + 3.58 = 7.94\)

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: 5.2 + 1.6 = 6.8 (no carrying needed)
With Carrying: 4.8 + 2.7 = 7.5 (carry 1 from tenths to units)
With Borrowing: 8.3 - 4.9 = 3.4 (borrow from units to tenths)
Advanced: 11.45 - 6.28 + 3.76 = 8.93 (mixed operations)
Tips & Common Mistakes
Always align decimal points! This is the most important step.
Add zeros when needed: 5.3 = 5.30 to match 1.67 decimal places.
Don't forget to carry/borrow: This is where many mistakes happen.
Watch the decimal point: It must align in your answer.
Worksheets with Detailed Answers
Answer Key Features
✅
Complete Solutions
Step-by-step process
Correct Answers
Exact solutions
Error Analysis
Common mistakes
Tips & Tricks
Helpful strategies
View Addition Worksheet Solutions
View Subtraction Worksheet Solutions
View Mixed Operations Solutions
View Word Problems Solutions
How to Use Answer Keys
1. Try First
Solve problems independently
2. Check Answers
Compare with solutions
3. Review Errors
Learn from mistakes
4. Practice More
Reinforce skills
Sample Problem with Solution
Problem: 4.56 + 2.78 = _____
Solution:

Step 1: Align decimal points

\(\begin{array}{r} 4.56 \\ + 2.78 \\ \hline \end{array}\)

Step 2: Add hundredths: 6 + 8 = 14, write down 4, carry over 1

Step 3: Add tenths: 5 + 7 + 1 = 13, write down 3, carry over 1

Step 4: Add units: 4 + 2 + 1 = 7

Answer: 7.34

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: How do I use the answer keys effectively? Should I look at the answers while solving problems?

Answer: For effective learning, follow this process:

  1. Attempt first: Try to solve each problem on your own without looking at the answers
  2. Check after: Once you've completed a problem, compare your answer with the solution
  3. Analyze errors: If your answer is wrong, study the step-by-step solution to understand where you went wrong
  4. Learn from solutions: Pay attention to the method shown in the answer key

The answer keys provide:

  • The correct final answer
  • Step-by-step solution process
  • Explanation of carrying/borrowing steps
  • Alternative methods for solving problems

Never peek at answers during problem-solving - this prevents you from developing your own problem-solving skills!

Question: What if I understand the answer but still get the problem wrong? How can I improve?

Answer: This is very common! Even when you understand the solution, small mistakes can cause errors. Here's how to improve:

Common causes of errors despite understanding:

  • Misaligned decimal points - double-check vertical alignment
  • Calculation errors - practice basic addition/subtraction facts
  • Carrying/borrowing mistakes - write small numbers above columns to remind yourself
  • Place value confusion - label tenths, hundredths clearly

Strategies to improve accuracy:

  1. Slow down and be methodical
  2. Write neatly with clear place value columns
  3. Check your work by doing the inverse operation
  4. Practice similar problems repeatedly

Remember: Understanding the method is just the first step - accuracy comes with practice!

Question: Do the answer keys show alternative methods for solving problems? Sometimes I solve problems differently.

Answer: Yes, our answer keys often include multiple solution approaches! Mathematics allows for flexibility in problem-solving methods.

Common alternative methods for decimal operations:

  • Compensation method: Adjust numbers to make mental math easier (e.g., 4.98 + 2.5 becomes 5.00 + 2.5 - 0.02)
  • Partial sums: Add whole numbers and decimals separately
  • Number line approach: Visual representation of decimal operations
  • Standard algorithm: Traditional column method (shown in answer keys)

As long as your method is mathematically sound and leads to the correct answer, it's perfectly acceptable. However, the standard algorithms shown in our answer keys are:

  • Most efficient for complex problems
  • Easiest to check for teachers
  • Prepares you for higher-level math

Feel free to explore different methods, but ensure you master the standard approach too!