How to Add Numbers by Breaking Them Down (Decomposition Steps & Examples)
The Addition Of Numbers Using The Decomposition Method is a foundational maths concept that helps students add numbers quickly and accurately by breaking them into simpler parts. This strategy is especially useful for school and competitive exams, and it strengthens students' mental maths skills for everyday life.
What is Addition Using the Decomposition Method?
The decomposition method in addition involves splitting numbers into their place value parts (like tens, ones, hundreds) before adding. This makes calculations easier and builds a solid understanding of place value and number sense. For example, instead of adding 48 + 36 directly, we split them into tens and ones: (40 + 8) + (30 + 6).
Understanding Place Value & Number Decomposition
Every number has a place value, which tells us how much each digit is worth. For example, in 57, the 5 is in the tens place (worth 50), and the 7 is in the ones place. Decomposition means writing numbers as the sum of their place values or as breaking them into addends that are easy to work with.
- Expanded form: 57 = 50 + 7
- Decomposition for addition: break both numbers into tens and ones.
| Number | Tens | Ones | Expanded Form |
|---|---|---|---|
| 24 | 20 | 4 | 20 + 4 |
| 37 | 30 | 7 | 30 + 7 |
How to Add Using Decomposition Method?
- Break each number into place value parts (tens, ones, hundreds).
- Add matching place value parts together (tens + tens, ones + ones, etc.).
- Combine all the results to find the total sum.
For example: Add 36 + 57 using decomposition.
- Break the numbers: 36 = 30 + 6, 57 = 50 + 7
- Add tens: 30 + 50 = 80
- Add ones: 6 + 7 = 13
- Combine: 80 + 13 = 93
This technique is also called addition using expanded form or the breaking numbers strategy.
Worked Examples of Decomposition Addition
Example 1: Two-digit numbers (No Regrouping)
Add 23 + 54
- 23 = 20 + 3
- 54 = 50 + 4
- Add tens: 20 + 50 = 70
- Add ones: 3 + 4 = 7
- Total: 70 + 7 = 77
Example 2: Two-digit numbers (With Regrouping)
Add 27 + 38
- 27 = 20 + 7
- 38 = 30 + 8
- Add tens: 20 + 30 = 50
- Add ones: 7 + 8 = 15
- Total: 50 + 15 = 65
Notice: 15 ones = 10 + 5, so you could further regroup if needed for larger additions.
Example 3: Three-digit numbers
Add 145 + 236
- 145 = 100 + 40 + 5
- 236 = 200 + 30 + 6
- Add hundreds: 100 + 200 = 300
- Add tens: 40 + 30 = 70
- Add ones: 5 + 6 = 11
- Total: 300 + 70 + 11 = 381
Practice Problems
- 1. Add 48 + 31 using decomposition.
- 2. Add 76 + 45 using the method above.
- 3. What is 239 + 157 using place value splitting?
- 4. Decompose and add 555 + 423.
- 5. Find the sum of 68 + 27 by breaking into tens and ones.
Try these questions for practice, then check your answers at the end of this page or use the Vedantu Addition Worksheets for more practice.
Common Mistakes to Avoid
- Mixing up tens and ones when breaking numbers.
- Forgetting to regroup when the sum of ones or tens exceeds 9 (e.g., getting 15 ones but not converting 10 ones to 1 ten + 5 ones).
- Not adding all the decomposed parts together for the final sum.
- Trying to add numbers without fully decomposing first, leading to confusion.
Real-World Applications
The decomposition method is practical for mental maths in daily activities: splitting prices when shopping (e.g., ₹37 + ₹28), totaling scores, telling time (45 mins + 35 mins), and quickly working out sums without paper. It's also foundational for mental maths strategies taught at Vedantu in live classes and study materials.
Page Summary
In this topic, we learned how to perform Addition Of Numbers Using The Decomposition Method by splitting numbers into place value parts. This strategy makes addition easier, supports error-free calculation, and strengthens number sense. Practicing this method equips students for both exams and real-life calculations. For more guided practice and stepwise learning, explore maths resources and live classes on Vedantu.
- Class 2 Maths
- Place Value
- Ones, Tens and Hundreds
- Addition Worksheets
- Addition Using Number Line
- Addition of Fractions
FAQs on Addition of Numbers Using the Decomposition Method
1. What is the decomposition method in addition as per the CBSE curriculum?
The decomposition method in addition is a strategy where numbers are broken down into their place value parts, such as hundreds, tens, and ones, before being added. For instance, to add 52 + 34, you would decompose them into (50 + 2) and (30 + 4). This approach helps students understand the value of each digit and simplifies the addition process.
2. What are the basic steps to add two numbers using the decomposition method?
To add numbers using decomposition, you can follow these simple steps:
- Step 1: Decompose (or break apart) each number into its place value components. For example, 47 becomes 40 + 7.
- Step 2: Add the corresponding place value parts together. Add all the tens, then add all the ones.
- Step 3: Combine the totals from each place value to get the final sum.
3. Can you show an example of adding 68 + 27 using decomposition?
Certainly. To add 68 + 27 using the decomposition method, follow these steps:
- First, break down the numbers: 68 = 60 + 8 and 27 = 20 + 7.
- Next, add the tens together: 60 + 20 = 80.
- Then, add the ones together: 8 + 7 = 15.
- Finally, combine the results: 80 + 15 = 95.
So, 68 + 27 = 95.
4. How does the decomposition method work for adding three-digit numbers?
The logic extends to larger numbers. To add three-digit numbers like 251 + 146, you decompose them into hundreds, tens, and ones:
- Decompose 251 into 200 + 50 + 1.
- Decompose 146 into 100 + 40 + 6.
- Add the hundreds: 200 + 100 = 300.
- Add the tens: 50 + 40 = 90.
- Add the ones: 1 + 6 = 7.
- Combine all parts: 300 + 90 + 7 = 397.
5. Why is learning to add by decomposition important for students?
Learning the decomposition method is crucial because it builds a strong foundation in number sense and place value. Instead of just memorising steps, students understand why addition works. This method improves mental maths skills, reduces calculation errors, and prepares students for more complex mathematical concepts like regrouping (carrying over).
6. How does the decomposition method help with regrouping in addition?
The decomposition method makes regrouping (or carrying over) very clear. For example, in 47 + 35, the ones add up to 7 + 5 = 12. Using decomposition, students can see that 12 is actually 1 ten and 2 ones. They then add this 'extra' ten to the other tens (40 + 30 + 10) and keep the 2 in the ones place, leading to a final answer of 82.
7. What is a common mistake students make when using this addition method?
A common mistake is incorrectly breaking down the numbers. For example, a student might decompose 54 as 5 + 4 instead of the correct 50 + 4. Another frequent error is forgetting to combine all the parts at the end, such as adding the tens and ones but forgetting to add their sums together for the final answer.
8. How is the decomposition method useful for mental maths in daily life?
This method is excellent for quick mental calculations in everyday situations. For instance, when calculating a total shopping bill of ₹48 and ₹36, you can mentally add the tens (40 + 30 = 70), add the ones (8 + 6 = 14), and then combine them (70 + 14 = 84) without needing a calculator or paper.
9. Is there a difference between decomposing a number and writing its expanded form?
Yes, there is a subtle difference. Expanded form is a specific type of decomposition based strictly on place value (e.g., 245 = 200 + 40 + 5). While we use this for the decomposition method of addition, the term 'decomposition' can also mean breaking a number into any parts that add up to it, like decomposing 245 into 200 + 45. However, for this addition strategy, we stick to the place value expanded form.
