Solved Exercises on Decimal Addition and Subtraction in Grade 4

Master decimal operations: aligning decimals, place value understanding, and carrying/borrowing techniques through these 3 detailed exercises.

Solution: Exercises 1 to 3
1 Adding decimals
Exercise 1
Calculate:
\(2.45 + 1.37\)
Definition:

Decimals: Numbers that contain a decimal point representing fractions of whole numbers

Addition method:
  1. Align decimal points vertically
  2. Add zeros if needed to make decimal places equal
  3. Add digits column by column from right to left
  4. Place decimal point in the answer aligned with others
Expression
\(2.45 + 1.37\)
Setup
2.45
+1.37
----
3.82
Step 1: Align decimal points

\(2.45\)
+\(1.37\)
----

Step 2: Add hundredths column

\(5 + 7 = 12\), write 2, carry 1

Step 3: Add tenths column

\(4 + 3 + 1 = 8\)

Step 4: Add units column

\(2 + 1 = 3\)

\(2.45 + 1.37 = 3.82\)
Final answer:

\(2.45 + 1.37 = 3.82\)

Applied rules:

• Decimal alignment: Always line up decimal points

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

• Carrying: When sum is 10 or more, carry the extra digit

2 Subtracting decimals
Exercise 2
Calculate:
\(5.28 - 2.15\)
Definition:

Decimal subtraction: Finding the difference between two decimal numbers

Expression
\({5.28 - 2.15}\)
Setup
5.28
-2.15
----
3.13
Step 1: Align decimal points

\(5.28\)
-\(2.15\)
----

Step 2: Subtract hundredths column

\(8 - 5 = 3\)

Step 3: Subtract tenths column

\(2 - 1 = 1\)

Step 4: Subtract units column

\(5 - 2 = 3\)

\(5.28 - 2.15 = 3.13\)
Final answer:

\(5.28 - 2.15 = 3.13\)

Applied rules:

• Decimal alignment: Always line up decimal points

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

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

3 Mixed operations
Exercise 3
Calculate:
\(7.50 - 3.25 + 1.75\)
Definition:

Order of operations: Perform operations from left to right when only addition and subtraction

Expression
\({7.50 - 3.25 + 1.75}\)
First operation
\(4.25 + 1.75\)
Final result
\(6.00\)
Step 1: Perform first operation (left to right)

\(7.50 - 3.25\)
Setup: \(7.50\)
-\(3.25\)
----
\(4.25\)

Step 2: Perform second operation

\(4.25 + 1.75\)
Setup: \(4.25\)
+\(1.75\)
----
\(6.00\)

Step 3: Verify the calculation

Check: \(7.50 - 3.25 = 4.25\) and \(4.25 + 1.75 = 6.00\)

\(7.50 - 3.25 + 1.75 = 6.00\)
Final answer:

\(7.50 - 3.25 + 1.75 = 6.00\)

Applied rules:

• Order of operations: Left to right for same precedence

• Decimal alignment: Always line up decimal points

• Verification: Check each step to avoid errors

Decimal Operations Rules and Methods
\(2.45 + 1.37 = 3.82\)
Decimal Addition
Addition
\(a.b + c.d = e.f\)
Align decimal points
Subtraction
\(a.b - c.d = e.f\)
Align decimal points
Place Value
Units.Tenths.Hundredths
Each position matters
Key definitions:

Decimal: A number system based on 10, with digits to the right of the decimal point representing fractions

Tenths: The first digit after the decimal point represents 1/10

Hundredths: The second digit after the decimal point represents 1/100

Complete methodology:
  1. Align decimals: Write numbers with decimal points lined up vertically
  2. Add zeros if needed: Make all numbers have the same number of decimal places
  3. Perform operation: Add or subtract column by column from right to left
  4. Place decimal point: In the answer, align with the numbers being operated
  5. Check your work: Estimate to verify the answer makes sense
Tip 1: Always align decimal points before adding or subtracting.
Tip 2: Add zeros to make decimal places equal (e.g., 3.5 = 3.50).
Tip 3: Estimate first to check if your answer is reasonable.
Tip 4: Remember that 0.50 is the same as 0.5, just written differently.
Common errors: Misaligning decimal points, forgetting to carry/borrow, mixing up place values.
Key concept: The decimal point separates whole numbers from fractional parts.
Essential rules to remember:

• Alignment: Always line up decimal points vertically

• Place value: Work from right to left, column by column

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

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

• Verification: Always estimate to check if answer is reasonable

Decimal Place Values and Concepts
Units.Tenths.Hundredths
Decimal Place Value
Decimal Place Values:

Ones place: The digit to the left of the decimal point

Tenths place: The first digit to the right of the decimal point

Hundredths place: The second digit to the right of the decimal point

Understanding decimal notation:
  1. Identify place values: Know the value of each position
  2. Compare decimals: Start from the leftmost digit
  3. Convert to fractions: Understand the relationship between decimals and fractions
  4. Estimate values: Develop number sense for decimal amounts
Tip 1: Think of money to understand decimals (cents are hundredths of a dollar).
Tip 2: Use a place value chart to organize decimal numbers.
Tip 3: Practice reading decimals aloud (e.g., 2.45 is "two and forty-five hundredths").
Tip 4: When comparing decimals, add zeros to make comparison easier.
Decimal equivalency: 0.5 = 0.50 = 0.500 (adding zeros doesn't change value).
Real-world application: Decimals are used in measurements, money, and scientific calculations.
Decimal comparison rules:

• Start left: Compare digits from left to right

• Same whole part: Compare tenths, then hundredths if needed

• Adding zeros: You can add zeros to compare decimals more easily

• Number line: Larger decimals are further to the right on a number line

Questions & Answers

Question: I don't understand why I need to line up the decimal points when adding decimals. Why can't I just add them like regular numbers?

Answer: Great question! Lining up decimal points ensures that you're adding digits with the same place value together. Think of it this way:

  • When you add 2.45 + 1.37, you want to add the hundredths to hundredths (5 + 7), tenths to tenths (4 + 3), and ones to ones (2 + 1)
  • If you didn't line up the decimals, you might accidentally add hundredths to tenths, which would give you the wrong answer
  • It's like organizing your numbers in neat columns so each place value stays together

Example without lining up:
2.45
+1.37
---
3.82 (correct when lined up)
versus
2.45
+ 1.37 (not lined up properly)
This could lead to adding 5 hundredths to 3 tenths incorrectly.

Question: When I subtract decimals and need to borrow, I get confused. Can you explain how borrowing works with decimals?

Answer: Borrowing with decimals works exactly the same as with whole numbers! Let me show you with an example:

For 5.23 - 1.47:

  • In the hundredths place: 3 - 7, since 3 is less than 7, you need to borrow
  • Borrow 1 from the tenths place (2 becomes 1), and add 10 to the hundredths place (3 becomes 13)
  • Now calculate: 13 - 7 = 6 in the hundredths place
  • Continue with the tenths place: 1 - 4, again you need to borrow
  • Borrow 1 from the ones place (5 becomes 4), and add 10 to the tenths place (1 becomes 11)
  • Calculate: 11 - 4 = 7 in the tenths place
  • Finally: 4 - 1 = 3 in the ones place

So 5.23 - 1.47 = 3.76

The key is to remember that borrowing is taking 1 from a higher place value and converting it to 10 of the next lower place value.

Question: I sometimes forget where to put the decimal point in my answer. Any tips?

Answer: This is a very common question! Here are some helpful tips for placing the decimal point:

  • Line up your work: Keep your decimal points lined up in a straight vertical line throughout the problem
  • Copy the decimal point: Once you've lined up the decimal points in your numbers, draw the answer line with the decimal point directly below them
  • Count decimal places: For addition/subtraction, the answer has the decimal point in the same position as the numbers you're operating on
  • Estimate first: Before calculating, estimate your answer to see if your final answer makes sense

Example: 3.45 + 2.1
Line up: 3.45
+2.10 (added zero to match decimal places)
Answer line: .__

Since both original numbers had their decimal points in the same position, your answer should too: 5.55