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What is The Concept of Borrowing?
Grade Level:
Pre-School – Class 2
All domains without exception
Definition
What is it?
The concept of borrowing is used when you need a value from a higher place value column to complete a subtraction in a lower place value column. It's like taking a 'loan' from the next digit to help you subtract when the top digit is smaller than the bottom digit.
Simple Example
Quick Example
Imagine you have 3 laddoos but your friend wants 5. You don't have enough! You might 'borrow' from a bigger box of laddoos if you had one. In subtraction, if you need to subtract 7 from 3 in the ones place, you borrow from the tens place.
Worked Example
Step-by-Step
Let's subtract 45 from 72.
Step 1: Write the numbers one below the other, aligning the ones and tens places.
72
- 45
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Step 2: Start with the ones place. We need to subtract 5 from 2. Since 2 is smaller than 5, we cannot subtract directly.
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Step 3: 'Borrow' from the tens place. The 7 in the tens place becomes 6. The 1 'borrowed' is actually 1 ten, which is 10 ones. Add these 10 ones to the 2 in the ones place, making it 12.
6 12
7 2
- 4 5
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Step 4: Now, subtract in the ones place: 12 - 5 = 7.
6 12
7 2
- 4 5
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7
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Step 5: Move to the tens place. Subtract the numbers: 6 - 4 = 2.
6 12
7 2
- 4 5
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2 7
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Answer: So, 72 - 45 = 27.
Why It Matters
Borrowing is a fundamental skill for subtraction, which is used everywhere from managing your pocket money to calculating change at the local kirana store. Understanding borrowing helps you accurately solve problems in fields like accounting, engineering, and even while planning your travel budget.
Common Mistakes
MISTAKE: Forgetting to reduce the digit from which you borrowed. | CORRECTION: Always remember to subtract 1 from the digit in the higher place value after you borrow from it.
MISTAKE: Treating the borrowed '1' as just 1, instead of 10. | CORRECTION: When you borrow from the tens place, you are borrowing 1 ten (which is 10 ones). Add 10 to the digit in the ones place.
MISTAKE: Not borrowing when the top digit is smaller. | CORRECTION: If the top digit is smaller than the bottom digit in any column, you MUST borrow from the next higher place value.
Practice Questions
Try It Yourself
QUESTION: Subtract 38 from 63. | ANSWER: 25
QUESTION: A bus had 81 passengers. At a stop, 27 passengers got off. How many passengers are left? | ANSWER: 54 passengers
QUESTION: Subtract 149 from 305. (Hint: You might need to borrow multiple times!) | ANSWER: 156
MCQ
Quick Quiz
When subtracting 18 from 52, what happens to the '5' in 52 when you borrow?
It remains 5
It becomes 6
It becomes 4
It becomes 15
The Correct Answer Is:
C
When you borrow from the tens place (5), you take one 'ten' away, so the 5 becomes 4. This borrowed 'ten' is added to the ones place.
Real World Connection
In the Real World
When a shopkeeper gives you change after you buy something, they often use subtraction, and sometimes they need to 'borrow' mentally. For example, if your bill is ₹48 and you give ₹100, the shopkeeper mentally calculates ₹100 - ₹48 to give you ₹52 back. This involves borrowing if done digit by digit.
Key Vocabulary
Key Terms
BORROWING: Taking a value from a higher place value to complete a subtraction | PLACE VALUE: The value of each digit in a number based on its position | SUBTRACTION: The process of finding the difference between two numbers | DIGIT: A single symbol used to make numbers (0-9)
What's Next
What to Learn Next
Now that you understand borrowing, you can move on to 'Subtraction with Multiple Digits and Borrowing Across Zeros'. This will teach you how to handle more complex subtractions where you might need to borrow from a place value that has a zero.
