What is Decomposing Numbers? | Simple Explanation for Class 1-2

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What is Decomposing Numbers (Strategy)?

Grade Level:

Pre-School – Class 2

All domains without exception

Definition

What is it?

Decomposing numbers is a strategy where you break down a number into smaller, simpler parts to make calculations easier. It helps you understand the 'value' of each digit in a number, like how 25 is 2 tens and 5 ones. This method makes big math problems feel less scary and more manageable.

Simple Example

Quick Example

Imagine you need to buy two packets of biscuits, one costs ₹20 and the other ₹15. Instead of adding 20 + 15 directly, you can decompose 15 into 10 and 5. Then, you add 20 + 10 = 30, and then 30 + 5 = 35. So, the total cost is ₹35.

Worked Example

Step-by-Step

Let's add 34 + 23 using decomposition.

Step 1: Decompose the first number, 34. It breaks down into 30 (3 tens) and 4 (4 ones).
---Step 2: Decompose the second number, 23. It breaks down into 20 (2 tens) and 3 (3 ones).
---Step 3: Now, group the tens together and add them: 30 + 20 = 50.
---Step 4: Next, group the ones together and add them: 4 + 3 = 7.
---Step 5: Finally, add the results from Step 3 and Step 4: 50 + 7 = 57.

Answer: So, 34 + 23 = 57.

Why It Matters

Decomposing numbers is a fundamental skill that builds your number sense and mental math abilities. It's crucial for understanding larger numbers in subjects like Algebra and Geometry. Engineers use this concept to break down complex problems, and financial analysts use it to understand large financial data, making big calculations simpler.

Common Mistakes

MISTAKE: Mixing up place values, like decomposing 45 as 4 and 50 instead of 40 and 5. | CORRECTION: Always remember the place value of each digit. The digit in the tens place represents tens, and the digit in the ones place represents ones.

MISTAKE: Only decomposing one number when both can be broken down for easier addition. | CORRECTION: For addition or subtraction, try decomposing both numbers involved to simplify the process as much as possible.

MISTAKE: Forgetting to add all the decomposed parts back together at the end. | CORRECTION: After breaking down and adding/subtracting the parts (tens with tens, ones with ones), always combine all the partial sums to get the final answer.

Practice Questions

Try It Yourself

QUESTION: Decompose the number 67 into its tens and ones. | ANSWER: 60 and 7

QUESTION: Use decomposition to add 42 + 16. | ANSWER: 42 (40 + 2) + 16 (10 + 6) = (40 + 10) + (2 + 6) = 50 + 8 = 58

QUESTION: A shopkeeper sold 35 samosas in the morning and 24 samosas in the evening. How many samosas did he sell in total using the decomposition method? | ANSWER: 35 (30 + 5) + 24 (20 + 4) = (30 + 20) + (5 + 4) = 50 + 9 = 59 samosas

MCQ

Quick Quiz

Which of the following shows the correct decomposition of the number 58?

5 and 8

50 and 8

500 and 8

5 and 80

The Correct Answer Is:

Option B is correct because 58 is made up of 5 tens (which is 50) and 8 ones (which is 8). The other options incorrectly represent the place values of the digits.

Real World Connection

In the Real World

When you pay for groceries at a kirana store using UPI, the bill might be ₹145. If you want to give exact change, you might think of ₹100, ₹40, and ₹5. This is decomposing the total amount into simpler currency notes/coins, making it easier to manage money. Similarly, budgeting for a trip involves breaking down total expenses into smaller categories like travel, food, and stay.

Key Vocabulary

Key Terms

DECOMPOSING: Breaking a number into smaller parts | PLACE VALUE: The value of each digit in a number based on its position | TENS: Groups of ten | ONES: Single units

What's Next

What to Learn Next

Once you've mastered decomposing numbers, you can move on to 'Regrouping Numbers' and 'Mental Math Strategies'. Regrouping builds directly on decomposition, showing you how to carry over or borrow tens and hundreds, which is super useful for more complex addition and subtraction problems.