Complete Worksheet: Adding and Subtracting Decimal Numbers in Grade 4

Master decimal arithmetic with 5 comprehensive exercises including step-by-step solutions, rules, and detailed summary for long-term retention.

Worksheet Solutions: Exercises 1 to 3
1 Adding decimals with tenths
Exercise 1
Add: 4.6 + 2.8
Definition:

Decimal Addition: Align decimal points vertically and add each column starting from the rightmost digit

Addition method:
  1. Align decimal points in columns
  2. Add digits in each column from right to left
  3. Carry over if sum exceeds 9
  4. Place decimal point in the answer
Expression
4.6 + 2.8
Alignment
4.6
+2.8
----
7.4
Step 1: Align decimal points

Write the numbers so that decimal points are in the same column

4.6
+2.8
----
   
Step 2: Add tenths column

6 + 8 = 14, write down 4 and carry over 1

4.6
+2.8
----
  .4
  ¹
Step 3: Add units column

4 + 2 + 1 (carry) = 7

4.6
+2.8
----
7.4
4.6 + 2.8 = 7.4
Final answer:

4.6 + 2.8 = 7.4

Applied rules:

• Decimal Alignment: Always align decimal points when adding/subtracting

• Carrying: When sum ≥ 10, carry the tens digit to the next column

• Place Value: Each column represents tenths, units, tens, etc.

Tip 1: Always write decimals in columns with decimal points aligned.
Tip 2: Remember: 10 tenths = 1 unit.
2 Subtracting decimals with borrowing
Exercise 2
Subtract: 6.2 - 3.7
Definition:

Decimal Subtraction: Align decimal points and subtract each column, borrowing when necessary

Expression
6.2 - 3.7
Alignment
6.2
-3.7
----
2.5
Step 1: Align decimal points

Write the numbers so that decimal points are in the same column

6.2
-3.7
----
   
Step 2: Subtract tenths column

2 - 7: Since 2 < 7, borrow 1 from units column (6 becomes 5, 2 becomes 12)

12 - 7 = 5

5¹²
6.2
-3.7
----
  .5
Step 3: Subtract units column

5 - 3 = 2

5¹²
6.2
-3.7
----
2.5
6.2 - 3.7 = 2.5
Final answer:

6.2 - 3.7 = 2.5

Applied rules:

• Decimal Alignment: Always align decimal points when adding/subtracting

• Borrowing: When top number < bottom number, borrow from the next higher place value

• Place Value: Each column represents tenths, units, tens, etc.

Tip 1: Borrowing: 1 unit = 10 tenths.
Tip 2: Check your answer by adding the result to the subtrahend.
3 Adding decimals with hundredths
Exercise 3
Add: 3.45 + 2.67
Definition:

Decimal Addition with Hundredths: Align decimal points and add each column including hundredths

Expression
3.45 + 2.67
Alignment
3.45
+2.67
-----
6.12
Step 1: Align decimal points

Write the numbers so that decimal points are in the same column

3.45
+2.67
-----
    
Step 2: Add hundredths column

5 + 7 = 12, write down 2 and carry over 1

3.45
+2.67
-----
   .2
   ¹
Step 3: Add tenths column

4 + 6 + 1 (carry) = 11, write down 1 and carry over 1

3.45
+2.67
-----
  .12
  ¹¹
Step 4: Add units column

3 + 2 + 1 (carry) = 6

3.45
+2.67
-----
6.12
3.45 + 2.67 = 6.12
Final answer:

3.45 + 2.67 = 6.12

Applied rules:

• Decimal Alignment: Always align decimal points when adding/subtracting

• Place Value: Columns represent hundredths, tenths, units, tens, etc.

• Carrying: When sum ≥ 10, carry the tens digit to the next column

Tip 1: 10 hundredths = 1 tenth.
Tip 2: Count decimal places in both numbers to verify answer accuracy.
Rules and Methods Summary
4.6 + 2.8 = 7.4
Decimal Addition
Rule 1
Align decimal points
Line up columns correctly
Rule 2
Add each column
Start from rightmost digit
Rule 3
Carry when needed
If sum ≥ 10, carry over
Key definitions:

Decimal Point: Separates whole numbers from fractional parts

Tenths: First digit after decimal point (1/10)

Hundredths: Second digit after decimal point (1/100)

Thousandths: Third digit after decimal point (1/1000)

Complete methodology:
  1. Align decimal points: Write numbers in columns 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 rightmost column and move left
  4. Carry or borrow: When needed, apply carrying for addition or borrowing for subtraction
Tip 1: Always align decimal points before performing operations.
Tip 2: Adding zeros at the end doesn't change the decimal value.
Tip 3: Remember: 10 tenths = 1 unit, 10 hundredths = 1 tenth.
Tip 4: Check your answer by estimating the result.
Common errors: Misaligning decimal points, forgetting to carry/borrow, mixing up addition and subtraction.
Exam preparation: Practice alignment, review carrying/borrowing, work with word problems.
Formulas to know by heart:

• Decimal Addition: Align → Add columns → Carry if needed

• Decimal Subtraction: Align → Subtract columns → Borrow if needed

• Place Values: Units, Tenths (1/10), Hundredths (1/100), Thousandths (1/1000)

• Carrying: When sum ≥ 10, carry 1 to next column

• Borrowing: When top < bottom, borrow 1 from next column

Worksheet Solutions: Exercises 4 to 5
4 Subtracting decimals with multiple borrowing
Exercise 4
Subtract: 8.02 - 3.57
Definition:

Multiple Borrowing: When subtracting decimals, sometimes you need to borrow from multiple place values

Expression
8.02 - 3.57
Alignment
8.02
-3.57
-----
4.45
Step 1: Align decimal points

Write the numbers so that decimal points are in the same column

8.02
-3.57
-----
    
Step 2: Subtract hundredths column

2 - 7: Since 2 < 7, need to borrow. But tenths column has 0, so borrow from units column first.

8 (units) becomes 7, 0 (tenths) becomes 10. Now borrow from tenths: 10 becomes 9, 2 becomes 12

12 - 7 = 5

7⁹¹²
8.02
-3.57
-----
   .5
Step 3: Subtract tenths column

9 - 5 = 4

7⁹¹²
8.02
-3.57
-----
  .45
Step 4: Subtract units column

7 - 3 = 4

7⁹¹²
8.02
-3.57
-----
4.45
8.02 - 3.57 = 4.45
Final answer:

8.02 - 3.57 = 4.45

Applied rules:

• Decimal Alignment: Always align decimal points when adding/subtracting

• Multiple Borrowing: When borrowing from zero, continue borrowing from next non-zero column

• Place Value: Each column represents hundredths, tenths, units, etc.

Tip 1: When borrowing from zero, go to the next non-zero digit.
Tip 2: Mark borrowed amounts clearly to avoid confusion.
5 Adding decimals with different decimal places
Exercise 5
Add: 5.8 + 2.346
Definition:

Different Decimal Places: Add zeros to make all numbers have the same number of decimal places

Expression
5.8 + 2.346
With Zeros
5.800 + 2.346
Result
8.146
Step 1: Equalize decimal places

Add zeros to 5.8 to match the number of decimal places in 2.346

5.8 becomes 5.800

5.800
+2.346
------
     
Step 2: Align decimal points

Write the numbers so that decimal points are in the same column

Step 3: Add thousandths column

0 + 6 = 6

5.800
+2.346
------
    .6
Step 4: Add hundredths column

0 + 4 = 4

5.800
+2.346
------
   .46
Step 5: Add tenths column

8 + 3 = 11, write down 1 and carry over 1

5.800
+2.346
------
  .146
  ¹¹
Step 6: Add units column

5 + 2 + 1 (carry) = 8

5.800
+2.346
------
8.146
5.8 + 2.346 = 8.146
Final answer:

5.8 + 2.346 = 8.146

Applied rules:

• Equalizing Decimals: Add zeros to make all numbers have same decimal places

• Decimal Alignment: Always align decimal points

• Carrying: When sum ≥ 10, carry to next column

Tip 1: Adding zeros at the end doesn't change the decimal value.
Tip 2: Always equalize decimal places before adding.

Complete Summary: Adding and Subtracting Decimal Numbers

Definitions of All Concepts Used

  • Decimal Number: A number that includes a decimal point, separating the whole number part from the fractional part (e.g., 3.75)
  • Decimal Point: The dot (.) that separates the whole number part from the fractional part in a decimal number
  • Tenths: The first digit after the decimal point, representing 1/10 of a unit (e.g., in 4.3, the 3 is in the tenths place)
  • Hundredths: The second digit after the decimal point, representing 1/100 of a unit (e.g., in 4.37, the 7 is in the hundredths place)
  • Thousandths: The third digit after the decimal point, representing 1/1000 of a unit (e.g., in 4.375, the 5 is in the thousandths place)
  • Place Value: The value of a digit based on its position in the number (units, tenths, hundredths, etc.)
  • Carrying: Moving a value of 10 from one column to the next higher column when the sum in a column is 10 or greater
  • Borrowing: Taking a value of 10 from a higher column to add to a lower column when the top number is smaller than the bottom number in subtraction

Core Rules, Laws, and Principles

  • Decimal Alignment Rule: Always align decimal points when adding or subtracting decimal numbers
  • Place Value Principle: Each column represents a specific place value (tenths, hundredths, thousandths, etc.)
  • Carrying Law: When the sum in a column is 10 or greater, carry the tens digit to the next column
  • Borrowing Law: When subtracting and the top digit is smaller than the bottom digit, borrow from the next higher place value
  • Zero Addition Principle: Adding zeros after the last non-zero digit in a decimal does not change its value (e.g., 3.5 = 3.50 = 3.500)
  • Value Relationship: 10 hundredths = 1 tenth, 10 tenths = 1 unit, 10 units = 1 ten

Step-by-Step Methods and Procedures

Decimal Addition Method:

  1. Align decimal points in columns
  2. Add zeros to equalize decimal places if needed
  3. Add digits in each column from right to left
  4. Carry over when sum ≥ 10
  5. Place decimal point in the answer

Decimal Subtraction Method:

  1. Align decimal points in columns
  2. Add zeros to equalize decimal places if needed
  3. Subtract digits in each column from right to left
  4. Borrow when top digit < bottom digit
  5. Place decimal point in the answer

Multiple Concrete Examples

Simple Examples:

  • 2.3 + 1.4 = 3.7 (no carrying needed)
  • 5.8 - 2.3 = 3.5 (no borrowing needed)
  • 0.5 + 0.7 = 1.2 (carrying needed)

Advanced Examples:

  • 4.256 + 1.789 = 6.045 (multiple carrying)
  • 9.003 - 2.457 = 6.546 (multiple borrowing)
  • 12.34 + 5.678 = 18.018 (different decimal places)

Tips, Tricks, and Common Pitfalls

Tips and Tricks:

  • Draw a vertical line under decimal points to ensure alignment
  • Use the rhyme: "Point to point, line them up tight!"
  • Think of money when adding decimals ($3.50 + $2.25)
  • Add zeros to make all numbers have the same decimal places
  • Estimate first to check if your answer makes sense

Common Pitfalls:

  • Misaligning decimal points
  • Forgetting to carry or borrow
  • Mixing up addition and subtraction
  • Placing the decimal point incorrectly
  • Not equalizing decimal places before adding

Key Notes and Takeaways for Memorization

  • Memory Aid: Remember: 10 tenths = 1 unit, 10 hundredths = 1 tenth, 10 thousandths = 1 hundredth
  • Verification: Always check your subtraction by adding the result to the subtrahend to get the minuend
  • Pattern Recognition: Look for opportunities to add zeros to make calculations easier
  • Place Value Focus: Each column represents a specific fraction of a unit
  • Process Consistency: Always work from right to left, regardless of operation

Questions & Answers

Question: I keep forgetting to align the decimal points when adding decimals. How can I remember this important rule?

Answer: Great question! Here are some helpful strategies to remember decimal alignment:

  • Visual cue: Draw a vertical line under the decimal points to ensure they're perfectly aligned
  • Rhyme to remember: "Point to point, line them up tight!"
  • Think of money: When adding $3.50 and $2.75, you naturally align the decimal points
  • Place value connection: Remember that each column represents specific place values (tenths, units, etc.)

Example: When adding 4.7 and 2.56, write it as:

4.70
+2.56
----
7.26

Notice how the decimal points are in the same column, and we added a zero to make the calculation easier.

Question: Why do I sometimes need to borrow from the units column when subtracting decimals, like in 5.3 - 2.8?

Answer: Borrowing is needed when the top digit in a column is smaller than the bottom digit. Let's break down 5.3 - 2.8:

  • In the tenths column: 3 - 8
  • Since 3 is less than 8, we need more tenths to complete the subtraction
  • We borrow 1 from the units column (5 becomes 4)
  • This 1 borrowed unit becomes 10 tenths, which we add to our original 3 tenths
  • Now we have 13 tenths - 8 tenths = 5 tenths

The key relationship: 1 unit = 10 tenths. This is why borrowing works!

4¹³
5.3
-2.8
----
2.5

Always remember: when borrowing, decrease the next higher place value by 1 and increase the current place value by 10.

Question: How do I add decimals with different numbers of decimal places, like 8.7 + 3.245?

Answer: When adding decimals with different numbers of decimal places, equalize them by adding zeros:

  1. Identify the number with the most decimal places (3.245 has 3 decimal places)
  2. Add zeros to the other number to match (8.7 becomes 8.700)
  3. Align decimal points and add normally

Important: Adding zeros after the decimal point does NOT change the value!

8.700
+3.245
------
11.945

This method ensures that tenths are added to tenths, hundredths to hundredths, etc. The mathematical principle is that 8.7 = 8.700, so we're not changing the value, just making the calculation easier.

Tip: Always count decimal places in your answer to verify it matches the pattern of the numbers you added.