Solved Exercises on Adding and Subtracting Decimal Numbers in Grade 4

Master decimal arithmetic: alignment, carrying, borrowing, and place value through these 5 detailed exercises.

Solution: Exercises 1 to 3
1 Adding decimals with tenths
Exercise 1
Add: 3.7 + 2.5
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
3.7 + 2.5
Alignment
3.7
+2.5
----
6.2
Step 1: Align decimal points

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

3.7
+2.5
----
   
Step 2: Add tenths column

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

3.7
+2.5
----
  .2
  ¹
Step 3: Add units column

3 + 2 + 1 (carry) = 6

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

3.7 + 2.5 = 6.2

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: 5.3 - 2.8
Definition:

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

Expression
5.3 - 2.8
Alignment
5.3
-2.8
----
2.5
Step 1: Align decimal points

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

5.3
-2.8
----
   
Step 2: Subtract tenths column

3 - 8: Since 3 < 8, borrow 1 from units column (5 becomes 4, 3 becomes 13)

13 - 8 = 5

4¹³
5.3
-2.8
----
  .5
Step 3: Subtract units column

4 - 2 = 2

4¹³
5.3
-2.8
----
2.5
5.3 - 2.8 = 2.5
Final answer:

5.3 - 2.8 = 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: 4.25 + 1.68
Definition:

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

Expression
4.25 + 1.68
Alignment
4.25
+1.68
-----
5.93
Step 1: Align decimal points

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

4.25
+1.68
-----
    
Step 2: Add hundredths column

5 + 8 = 13, write down 3 and carry over 1

4.25
+1.68
-----
   .3
   ¹
Step 3: Add tenths column

2 + 6 + 1 (carry) = 9

4.25
+1.68
-----
  .93
Step 4: Add units column

4 + 1 = 5

4.25
+1.68
-----
5.93
4.25 + 1.68 = 5.93
Final answer:

4.25 + 1.68 = 5.93

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, laws,...
3.7 + 2.5 = 6.2
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)

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

Solution: Exercises 4 to 5
4 Subtracting decimals with multiple borrowing
Exercise 4
Subtract: 7.03 - 2.47
Definition:

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

Expression
7.03 - 2.47
Alignment
7.03
-2.47
-----
4.56
Step 1: Align decimal points

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

7.03
-2.47
-----
    
Step 2: Subtract hundredths column

3 - 7: Since 3 < 7, need to borrow. But tenths column has 0, so borrow from units column first.

7 (units) becomes 6, 0 (tenths) becomes 10. Now borrow from tenths: 10 becomes 9, 3 becomes 13

13 - 7 = 6

6⁹¹³
7.03
-2.47
-----
   .6
Step 3: Subtract tenths column

9 - 4 = 5

6⁹¹³
7.03
-2.47
-----
  .56
Step 4: Subtract units column

6 - 2 = 4

6⁹¹³
7.03
-2.47
-----
4.56
7.03 - 2.47 = 4.56
Final answer:

7.03 - 2.47 = 4.56

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: 8.7 + 3.245
Definition:

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

Expression
8.7 + 3.245
With Zeros
8.700 + 3.245
Result
11.945
Step 1: Equalize decimal places

Add zeros to 8.7 to match the number of decimal places in 3.245

8.7 becomes 8.700

8.700
+3.245
------
     
Step 2: Align decimal points

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

Step 3: Add thousandths column

0 + 5 = 5

8.700
+3.245
------
    .5
Step 4: Add hundredths column

0 + 4 = 4

8.700
+3.245
------
   .45
Step 5: Add tenths column

7 + 2 = 9

8.700
+3.245
------
  .945
Step 6: Add units column

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

8.700
+3.245
------
1¹.945
Step 7: Add tens column

0 + 0 + 1 (carry) = 1

8.700
+3.245
------
11.945
8.7 + 3.245 = 11.945
Final answer:

8.7 + 3.245 = 11.945

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.
Decimal Arithmetic Laws, Methods, Rules, Definitions
3.7 + 2.5 = 6.2
Decimal Addition
Key definitions:

Decimal Number: A number with a decimal point separating the whole number part from the fractional part

Place Value: The value of a digit based on its position in the number

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

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

Thousandths Place: Third digit after the 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
  5. Place decimal point: In the answer, place the decimal point directly below the aligned decimal points
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.
Tip 5: When borrowing from zero, go to the next non-zero digit.
Common errors: Misaligning decimal points, forgetting to carry/borrow, mixing up addition and subtraction.
Key relationships: 10 hundredths = 1 tenth, 10 tenths = 1 unit, 10 units = 1 ten.
Verification: Add result to subtrahend to check subtraction, or estimate to check addition.
Formulas to know by heart:

• Decimal Addition: Align → Add columns → Carry if needed → Place decimal point

• Decimal Subtraction: Align → Subtract columns → Borrow if needed → Place decimal point

• Place Values: ..., Ten Thousands, Thousands, Hundreds, Tens, Units, Tenths, Hundredths, Thousandths, ...

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

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

• Zero Addition: Adding zeros after decimal doesn't change value (3.5 = 3.50 = 3.500)

Relationship 1
10 tenths = 1 unit
Basic conversion rule
Relationship 2
10 hundredths = 1 tenth
Decimal place conversion
Relationship 3
10 thousandths = 1 hundredth
Higher precision conversion
5.3 - 2.8 = 2.5
Decimal Subtraction

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.