Decomposing Addition Worksheets in Grade 4

Master decomposing addition: breaking down numbers into parts, calculating sums, and understanding addition relationships through these 3 detailed exercises.

Worksheet Solutions: Exercises 1 to 3
1 Decomposing tens and ones
Exercise 1
Add 47 + 25 by decomposing each number into tens and ones.
Definition:

Decomposing numbers: Breaking numbers into their place value parts (tens, ones, etc.)

Solution method:
  1. Break each number into tens and ones
  2. Add the tens together
  3. Add the ones together
  4. Combine the sums
47 =
40 + 7
25 =
20 + 5
Sum =
(40 + 20) + (7 + 5) = 72
Step 1: Decompose each number

47 = 40 + 7 (4 tens and 7 ones)

25 = 20 + 5 (2 tens and 5 ones)

Step 2: Add the tens

40 + 20 = 60

Step 3: Add the ones

7 + 5 = 12

Step 4: Combine the sums

60 + 12 = 72

47 + 25 = 72
Final answer:

47 + 25 = 72

Applied rules:

• Place value decomposition: Break numbers into tens and ones

• Add like values: Add tens with tens, ones with ones

• Regrouping: When ones sum to 10 or more, carry to tens

2 Making tens strategy
Exercise 2
Add 38 + 15 by making a ten. Decompose the second number to create a round number.
Definition:

Making tens strategy: Adjusting numbers to create round numbers (multiples of 10) for easier addition

38 + 15 =
38 + (2 + 13) = 40 + 13
Final sum =
53
Step 1: Identify how much is needed to make a ten

38 needs 2 more to make 40

Step 2: Decompose the second number

15 = 2 + 13 (take 2 to make 40)

Step 3: Add the round number

38 + 2 = 40

Step 4: Add the remaining part

40 + 13 = 53

38 + 15 = 53
Final answer:

38 + 15 = 53

Applied rules:

• Making tens: Adjust one number to create a round number

• Compensation: Add what you took away to maintain balance

• Flexible addition: Rearrange numbers for easier computation

3 Decomposing three-digit numbers
Exercise 3
Add 146 + 237 by decomposing each number into hundreds, tens, and ones.
Definition:

Three-digit decomposition: Breaking numbers into hundreds, tens, and ones places

146 =
100 + 40 + 6
237 =
200 + 30 + 7
Sum =
300 + 70 + 13 = 383
Step 1: Decompose each number

146 = 100 + 40 + 6

237 = 200 + 30 + 7

Step 2: Add hundreds

100 + 200 = 300

Step 3: Add tens

40 + 30 = 70

Step 4: Add ones

6 + 7 = 13

Step 5: Combine all parts

300 + 70 + 13 = 383

146 + 237 = 383
Final answer:

146 + 237 = 383

Applied rules:

• Place value decomposition: Break numbers into hundreds, tens, and ones

• Add like values: Add hundreds with hundreds, tens with tens, ones with ones

• Regrouping: When any place value sums to 10 or more, carry to next higher place

Rules and methods, laws,...
A + B = (A_tens + B_tens) + (A_ones + B_ones)
Decomposition Addition
Two-Digit Addition
47 + 25 = (40 + 20) + (7 + 5)
Add tens and ones separately
Making Tens
38 + 15 = 38 + (2 + 13) = 40 + 13
Create round numbers
Three-Digit Addition
146 + 237 = (100 + 200) + (40 + 30) + (6 + 7)
Hundreds, tens, ones

Decomposition Strategies

🧮
Place Value Decomposition
Break numbers into their place values (tens, ones, hundreds, etc.) to make addition easier.
Example: 47 = 40 + 7
Making Tens Strategy
Adjust one number to make a round number (multiple of 10) and compensate accordingly.
Example: 38 + 15 = 40 + 13
Regrouping
When adding like values results in 10 or more, carry to the next higher place value.
Example: 7 + 5 = 12 → 1 ten and 2 ones
Decomposition Process
1
Decompose
2
Group Like Values
3
Add Each Group
4
Combine Results
Worksheets & Study Tips
47 + 25 = (40 + 7) + (20 + 5)
Decomposition Method

Practice Problems

Additional Problems:

1. Add 56 + 28 using decomposition

2. Add 74 + 19 using the making tens strategy

3. Add 243 + 156 using three-digit decomposition

Key definitions:

Decomposition: Breaking numbers into smaller, more manageable parts

Place value: The value of a digit based on its position (ones, tens, hundreds)

Regrouping: Carrying over when a place value sum reaches 10 or more

Like values: Numbers in the same place value position

Round numbers: Numbers that end in zero (multiples of 10, 100, etc.)

Complete methodology:
  1. Identify the strategy: Choose decomposition, making tens, or place value
  2. Break down numbers: Separate into appropriate place values
  3. Add like values: Combine numbers in the same place value
  4. Regroup if necessary: Carry over when sum reaches 10 or more
  5. Combine results: Add all partial sums together
Tip 1: Start with smaller numbers and work your way up to larger ones.
Tip 2: Always check your answer by adding the original numbers directly.
Tip 3: Use base-ten blocks or drawings to visualize the decomposition.
Tip 4: Practice making tens with different combinations (7+3, 6+4, 8+2).
Common errors: Forgetting to regroup, mixing place values, calculation mistakes.
Exam preparation: Practice all strategies, memorize basic facts, work on verification skills.
Facts to remember:

• Decompose by place value: hundreds, tens, ones

• Add like values together (tens with tens, ones with ones)

• Regroup when a sum reaches 10 or more

• Making tens simplifies addition

• Always verify your answer

Comprehensive Summary: Decomposing Addition

This summary covers all essential concepts, rules, and methods for understanding decomposing addition.

Definitions

Decomposition: Breaking numbers into smaller, more manageable parts.

Place value: The value of a digit based on its position (ones, tens, hundreds).

Regrouping: Carrying over when a place value sum reaches 10 or more.

Like values: Numbers in the same place value position.

Round numbers: Numbers that end in zero (multiples of 10, 100, etc.).

Core Rules

Place value decomposition: Break numbers into hundreds, tens, and ones.

Add like values: Add tens with tens, ones with ones.

Regrouping: When sum ≥ 10, carry to next place value.

Making tens: Adjust numbers to create round numbers for easier addition.

Methods & Procedures

Two-digit decomposition: Break into tens and ones, add each group.

Making tens: Adjust one number to create a round number.

Three-digit decomposition: Break into hundreds, tens, ones.

Verification: Always check your answer using another method.

Examples

Simple: 23 + 15 = (20 + 10) + (3 + 5) = 30 + 8 = 38.

Intermediate: 38 + 17 = 40 + 15 = 55 (making tens).

Advanced: 146 + 237 = (100 + 200) + (40 + 30) + (6 + 7) = 383.

Tips & Tricks

Memory aid: "Add tens with tens, ones with ones."

Visualization: Use base-ten blocks to see the decomposition.

Check work: Add the original numbers directly to verify.

Common Mistakes

Mixing place values: Adding tens with ones instead of like values.

Forgetting to regroup: Not carrying over when sum ≥ 10.

Calculation errors: Making arithmetic mistakes during addition.

Questions & Answers

Question: Why do we need to decompose numbers when adding? Isn't it easier to just add them directly?

Answer: Decomposing numbers actually makes addition easier for many problems! Here's why:

  • It breaks complex problems into simpler, more manageable parts
  • You can add round numbers (like 40 + 20) which are easier to compute mentally
  • It helps you understand the place value system better
  • It's especially helpful when regrouping is needed

For example, 47 + 25 might seem harder than (40 + 20) + (7 + 5) = 60 + 12 = 72. The decomposition strategy helps you work with friendlier numbers!

Question: How do I know when to use the "making tens" strategy versus regular decomposition?

Answer: The "making tens" strategy is particularly helpful when one number is close to a round number:

  • Use making tens when one number is 1, 2, or 3 away from a round number (like 29, 38, 57)
  • Use regular decomposition for most other cases
  • Both strategies can lead to the same answer, so choose what feels easier to you

For example, in 38 + 15, it's easier to think "38 + 2 = 40, and 40 + 13 = 53" than to add 38 + 15 directly. But for 24 + 35, regular decomposition (20 + 30 = 50, 4 + 5 = 9, 50 + 9 = 59) works well.

Question: How can I check if my answer is correct when using decomposition?

Answer: Here are several verification methods:

  • Direct addition: Add the original numbers directly to see if you get the same result
  • Reverse operation: Subtract one of the original numbers from your answer to see if you get the other number
  • Estimation: Round the numbers and see if your answer is close to the estimate
  • Alternative strategy: Try a different decomposition method

For example, if you calculated 47 + 25 = 72, you could verify by: 72 - 25 = 47 or 72 - 47 = 25.

Developing this verification habit will help you catch errors and build confidence in your solutions!