Decimal Practice Worksheet for Grade 4

Comprehensive decimal practice worksheet with detailed explanations and step-by-step solutions.

Worksheet Problems and Solutions
1 Adding Decimals
Problem 1
Calculate: \(7.24 + 1.58\)
Definition:

Decimal Addition: Combining two or more decimal numbers by adding their corresponding place values

Addition Method:
  1. Align decimal points vertically
  2. Add digits column by column from right to left
  3. Carry over when sum is 10 or more
  4. Place decimal point in the answer aligned with others
Expression
\(7.24 + 1.58\)
Setup
7.24
+1.58
----
8.82
Step 1: Align decimal points

Line up the decimal points in each number

Step 2: Add hundredths column

\(4 + 8 = 12\), write 2, carry 1

Step 3: Add tenths column

\(2 + 5 + 1 = 8\)

Step 4: Add units column

\(7 + 1 = 8\)

\(7.24 + 1.58 = 8.82\)
Final Answer:

\(7.24 + 1.58 = 8.82\)

2 Subtracting Decimals
Problem 2
Calculate: \(9.53 - 4.27\)
Definition:

Decimal Subtraction: Finding the difference between two decimal numbers

Expression
\({9.53 - 4.27}\)
Setup
9.53
-4.27
----
5.26
Step 1: Align decimal points

Line up the decimal points in each number

Step 2: Subtract hundredths column

\(3 - 7\) requires borrowing: \(13 - 7 = 6\)

Step 3: Subtract tenths column

\(4 - 2 = 2\) (after borrowing)

Step 4: Subtract units column

\(9 - 4 = 5\)

\(9.53 - 4.27 = 5.26\)
Final Answer:

\(9.53 - 4.27 = 5.26\)

3 Mixed Operations
Problem 3
Calculate: \(13.75 - 6.50 + 2.25\)
Definition:

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

Expression
\({13.75 - 6.50 + 2.25}\)
First Operation
\(7.25 + 2.25\)
Final Result
\(9.50\)
Step 1: Perform first operation (left to right)

\(13.75 - 6.50 = 7.25\)

Step 2: Perform second operation

\(7.25 + 2.25 = 9.50\)

\(13.75 - 6.50 + 2.25 = 9.50\)
Final Answer:

\(13.75 - 6.50 + 2.25 = 9.50\)

Worksheet Summary
Complete Guide to Decimal Operations
Key Definitions

Decimal: A number with one or more digits to the right of the decimal point

Decimal Point: Separates the whole number part from the fractional part

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

Core Rules

• Alignment Rule: Always line up decimal points vertically

• Place Value Rule: Add or subtract digits in the same place value positions

• Carry/Borrow Rule: Use carrying for addition and borrowing for subtraction when needed

Step-by-Step Methods

1. Align decimal points vertically

2. Add zeros if needed to make decimal places equal

3. Perform operation column by column from right to left

4. Place decimal point in the answer aligned with inputs

Tips & Tricks

• Think of money to understand decimals (cents are hundredths)

• Estimate first to check if your answer is reasonable

• Add zeros to make decimal places equal (e.g., 3.5 = 3.50)

Common Pitfalls

• Misaligning decimal points leading to incorrect place values

• Forgetting to carry or borrow when needed

• Placing the decimal point in the wrong position

Memory Aids

"Line up the dots!" - Remember to align decimal points

"Right to left" - Always work from the rightmost column

"Same place value" - Only add/subtract digits in the same position

\(a.bc + d.ef = g.hi\)
Decimal Addition Pattern
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
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.
Additional Practice Problems
Practice Worksheet

Instructions: Solve each problem and write your answer in the space provided. Show your work by aligning decimal points and carrying/borrowing as needed.

Problem 4:
\(5.67 + 2.48 =\)
Answer: 8.15
Problem 5:
\(8.34 - 3.29 =\)
Answer: 5.05
Problem 6:
\(10.50 - 4.75 + 1.25 =\)
Answer: 7.00
Problem 7:
\(6.28 + 3.72 =\)
Answer: 10.00
Problem 8:
\(12.45 - 7.38 =\)
Answer: 5.07
Problem 9:
\(9.75 + 2.25 - 4.50 =\)
Answer: 7.50
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
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.