Solved Exercises on Adding Decimals in Grade 4

Master adding decimals: aligning decimal points, carrying over, and solving decimal addition problems through these 5 detailed exercises.

Solution: Exercises 1 to 3
1 Adding decimals without carrying
Exercise 1
Add: 0.23 + 0.15
Definition:

Decimal addition: Adding decimal numbers by aligning decimal points and adding each place value separately

Addition method:
  1. Align the decimal points vertically
  2. Add each column from right to left
  3. Write the decimal point in the answer aligned with the others
  4. Carry over if necessary
Problem
0.23 + 0.15
Sum
0.38
Step 1: Align decimal points
0
.
2
3

+
.
1
5
Step 2: Add hundredths

3 + 5 = 8 (write 8 in hundredths place)

Step 3: Add tenths

2 + 1 = 3 (write 3 in tenths place)

Step 4: Add ones

0 + 0 = 0 (write 0 in ones place)

0
.
2
3

+
.
1
5

-
-
-
-
-

0
.
3
8
0.23
0 ones, 2 tenths, 3 hundredths
0.15
0 ones, 1 tenth, 5 hundredths
0.38
0 ones, 3 tenths, 8 hundredths
0.23 + 0.15 = 0.38
Final answer:

0.23 + 0.15 = 0.38

Applied rules:

• Decimal Alignment: Always align decimal points

• Place Value Addition: Add digits in the same place value

• Right-to-Left: Add columns from right to left

2 Adding decimals with carrying
Exercise 2
Add: 0.47 + 0.36
Definition:

Carrying: When the sum of a column is 10 or more, write the ones digit and carry the tens digit to the next column

Problem
0.47 + 0.36
Sum
0.83
Step 1: Align decimal points
0
.
4
7

+
.
3
6
Step 2: Add hundredths

7 + 6 = 13 (write 3 in hundredths place, carry 1 to tenths)

Step 3: Add tenths

4 + 3 + 1 (carried) = 8 (write 8 in tenths place)

Step 4: Add ones

0 + 0 = 0 (write 0 in ones place)

0
.
4
7

+
.
3
6

-
-
-
-
-

0
.
8
3

↑
Carry 1
Step 5: Verify the answer

0.47 + 0.36 = 0.83 ✓

0.47 + 0.36 = 0.83
Final answer:

0.47 + 0.36 = 0.83

Applied rules:

• Carrying Rule: When sum ≥ 10, carry the tens digit

• Decimal Alignment: Keep decimal points aligned

• Sequential Addition: Add each column separately

3 Adding decimals with different place values
Exercise 3
Add: 1.2 + 0.45
Definition:

Different place values: When decimals have different numbers of digits, add zeros to make them equal length

Problem
1.2 + 0.45
Sum
1.65
Step 1: Equalize decimal places

1.2 = 1.20 (add a zero to match 0.45's two decimal places)

Step 2: Align decimal points
1
.
2
0

+
.
4
5
Step 3: Add hundredths

0 + 5 = 5 (write 5 in hundredths place)

Step 4: Add tenths

2 + 4 = 6 (write 6 in tenths place)

Step 5: Add ones

1 + 0 = 1 (write 1 in ones place)

1
.
2
0

+
.
4
5

-
-
-
-
-

1
.
6
5
Step 6: Verify the answer

1.2 + 0.45 = 1.65 ✓

1.2 + 0.45 = 1.65
Final answer:

1.2 + 0.45 = 1.65

Applied rules:

• Place Value Equalization: Add zeros to match decimal places

• Decimal Alignment: Always align decimal points

• Column Addition: Add each place value separately

Rules and methods, laws,...
a.bc + d.ef = (a+d).(b+e)(c+f) \text{ (with carrying as needed)}
Decimal Addition Formula
Key definitions:

Decimal: A number that contains a decimal point separating the whole and fractional parts

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

Place value: The value of a digit based on its position (ones, tenths, hundredths, etc.)

Carrying: Moving a digit to the next column when the sum is 10 or more

Alignment: Keeping decimal points in the same vertical line

Complete methodology:
  1. Align decimal points: Write numbers so decimal points are in the same column
  2. Equalize decimal places: Add zeros if needed to make decimal places equal
  3. Add column by column: Start from the rightmost column (smallest place value)
  4. Carry over when needed: If sum ≥ 10, write the ones digit and carry the tens digit
  5. Keep decimal point aligned: Place the decimal point in the answer aligned with the others
  6. Verify the answer: Check by estimating or subtracting
Tip 1: Always align decimal points before adding.
Tip 2: Add zeros to make decimal places equal for easier alignment.
Tip 3: Add from right to left, just like with whole numbers.
Tip 4: Check your answer by estimating (round numbers and add).
Common errors: Misaligning decimal points, forgetting to carry, adding decimal places incorrectly.
Key concepts: Place value, decimal alignment, carrying, column addition.
Rules to remember:

• Decimal Point Alignment: Always align decimal points vertically

• Right-to-Left Addition: Start adding from the rightmost column

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

• Place Value Addition: Only add digits in the same place value

• Zero Padding: Add zeros to equalize decimal places if needed

\text{If } a.bc + d.ef \text{ and } c+f \geq 10, \text{ then carry 1 to the tenths column}
Carrying Condition
Key Notes to Remember:

• Decimal points must be in the same column

• Add each place value separately

• Carry over when the sum is 10 or more

• Estimate to check reasonableness of answer

Solution: Exercises 4 to 5
4 Adding multiple decimals
Exercise 4
Add: 0.25 + 0.17 + 0.38
Definition:

Multiple decimal addition: Adding three or more decimal numbers by aligning decimal points and adding column by column

Problem
0.25 + 0.17 + 0.38
Sum
0.80
Step 1: Align all decimal points
0
.
2
5

+
.
1
7

+
.
3
8
Step 2: Add hundredths

5 + 7 + 8 = 20 (write 0 in hundredths place, carry 2 to tenths)

Step 3: Add tenths

2 + 1 + 3 + 2 (carried) = 8 (write 8 in tenths place)

Step 4: Add ones

0 + 0 + 0 = 0 (write 0 in ones place)

0
.
2
5

+
.
1
7

+
.
3
8

-
-
-
-
-

0
.
8
0

↑
Carry 2
Step 5: Verify the answer

0.25 + 0.17 + 0.38 = 0.80 ✓

Number Ones Tenths Hundredths 0.25 0 2 5 0.17 0 1 7 0.38 0 3 8 Sum 0 8 0
0.25 + 0.17 + 0.38 = 0.80
Final answer:

0.25 + 0.17 + 0.38 = 0.80

Applied rules:

• Multiple Alignment: Align all decimal points

• Column Addition: Add all digits in each column

• Carrying Rule: Carry when sum ≥ 10

5 Word problem with decimal addition
Exercise 5
Sarah bought 2.5 kg of apples, 1.75 kg of oranges, and 0.8 kg of grapes. How much fruit did she buy in total?
Definition:

Word problem: A real-world scenario requiring mathematical operations to solve

Problem
2.5 + 1.75 + 0.8
Total
5.05 kg
Step 1: Identify the numbers to add

Apples: 2.5 kg, Oranges: 1.75 kg, Grapes: 0.8 kg

Step 2: Equalize decimal places

2.50 + 1.75 + 0.80 (add zeros to make all have 2 decimal places)

Step 3: Align decimal points
2
.
5
0

+
.
7
5

+
.
8
0
Step 4: Add hundredths

0 + 5 + 0 = 5 (write 5 in hundredths place)

Step 5: Add tenths

5 + 7 + 8 = 20 (write 0 in tenths place, carry 2 to ones)

Step 6: Add ones

2 + 1 + 0 + 2 (carried) = 5 (write 5 in ones place)

2
.
5
0

+
.
7
5

+
.
8
0

-
-
-
-
-

5
.
0
5

↑
Carry 2
Step 7: State the final answer

Sarah bought 5.05 kg of fruit in total

Sarah bought 5.05 kg of fruit in total
Final answer:

Sarah bought 5.05 kg of fruit in total

Applied rules:

• Problem Analysis: Identify numbers to add

• Decimal Alignment: Align all decimal points

• Real-world Context: Include units in final answer

Decimal Addition Fundamentals and Practice
a.bc + d.ef = (a+d).(b+e)(c+f) \text{ (with carrying as needed)}
Decimal Addition Formula
Key definitions:

Decimal: A number that contains a decimal point separating the whole and fractional parts

Decimal Addition: The process of adding decimal numbers together

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

Place Value: The value of a digit based on its position (ones, tenths, hundredths, etc.)

Carrying: Moving a digit to the next column when the sum is 10 or more

Alignment: Keeping decimal points in the same vertical line

Estimation: Approximating the answer to check reasonableness

Complete methodology:
  1. Read the problem: Identify the decimal numbers to add
  2. Align decimal points: Write numbers vertically with decimal points aligned
  3. Equalize decimal places: Add zeros if needed to make all numbers have the same number of decimal places
  4. Add column by column: Start from the rightmost column (smallest place value)
  5. Carry over when needed: If sum ≥ 10, write the ones digit and carry the tens digit
  6. Place the decimal point: Keep it aligned with the original numbers
  7. Verify the answer: Check by estimating or using inverse operations
Tip 1: Always align decimal points before adding, regardless of the number of decimal places.
Tip 2: Add zeros to make decimal places equal for easier alignment and fewer mistakes.
Tip 3: Add from right to left, just like with whole numbers, paying attention to carrying.
Tip 4: Estimate the answer first to check if your final answer is reasonable.
Tip 5: In word problems, always include the appropriate units in your final answer.
Common errors: Misaligning decimal points, forgetting to carry, adding decimal places incorrectly, not including units in word problems.
Success strategies: Careful alignment, systematic addition, checking work, using estimation.
Essential formulas and rules:

• Decimal Point Alignment: Always align decimal points vertically

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

• Place Value Addition: Add digits in the same place value column

• Zero Padding: Add zeros to equalize decimal places when needed

• Verification: Estimate to check reasonableness of answer

\text{If } c+f \geq 10 \text{ in } a.bc + d.ef, \text{ carry 1 to the tenths column}
Carrying Condition
Memory Aids:

• "Decimal Points Must Align": Always line up the dots

• "Carry When 10+": If sum is 10 or more, carry to next column

• "Right to Left": Add columns starting from the right

• "Estimate First": Check if your answer makes sense

Decimal Addition Process
1
Align
2
Equalize
3
Add
4
Carry
5
Verify

Questions & Answers

Question: Why do I need to line up the decimal points when adding decimals? Can't I just add them like regular numbers?

Answer: Great question! Lining up decimal points ensures you're adding the same place values together:

  • Ones with ones
  • Tenths with tenths
  • Hundredths with hundredths

If you don't align them, you might add tenths to hundredths or ones to tenths, which would give you the wrong answer.

Example: 0.2 + 0.03

  • Correct: 0.20 + 0.03 = 0.23
  • Wrong: 0.2 + 0.03 = 0.23 (but if misaligned, you might get 0.05)

Think of it like lining up apples with apples and oranges with oranges!

Question: When do I need to carry in decimal addition? Is it the same as with whole numbers?

Answer: Yes, carrying in decimal addition works exactly the same way as with whole numbers!

You carry when the sum of a column is 10 or more:

  • If the hundredths column adds to 10 or more, carry 1 to the tenths column
  • If the tenths column adds to 10 or more, carry 1 to the ones column
  • If the ones column adds to 10 or more, carry 1 to the tens column

Example: 0.7 + 0.5 = 1.2

  • 7 tenths + 5 tenths = 12 tenths = 1 whole + 2 tenths
  • Write 2 in tenths place, carry 1 to ones place
  • 0 + 0 + 1 (carried) = 1 in ones place

The decimal point stays in the same position - it doesn't get carried!

Question: What if one decimal has more digits than another? Do I need to add zeros?

Answer: Yes! Adding zeros helps you align the decimal points and makes the addition clearer.

Example: 1.5 + 0.234

  • 1.500 (added two zeros to match 0.234's three decimal places)
  • + 0.234
  • -------
  • 1.734

Remember: adding zeros after the decimal point doesn't change the value!

  • 1.5 = 1.50 = 1.500 = 1.5000
  • All represent the same value

The zeros just help you keep track of place values and prevent mistakes during addition.

It's especially helpful when adding multiple decimals with different numbers of digits.