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Subtraction – with and without borrowing

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Introduction to Subtraction

Subtraction is one of the four basic operations in mathematics. It means taking away some quantity from another or finding the difference between two numbers. Understanding subtraction helps us solve everyday problems, like calculating how much money is left after spending, or how much distance remains to travel.

For example, if you have Rs.50 and you buy a book costing Rs.20, subtraction helps you find out how much money you have left:

Rs.50 - Rs.20 = Rs.30

Similarly, if you walked 8 kilometers yesterday and 5 kilometers today, subtraction helps find the difference in distance:

8 km - 5 km = 3 km

In this chapter, we will learn how to subtract numbers both without borrowing and with borrowing, using clear examples and helpful diagrams.

Subtraction without Borrowing

Subtraction without borrowing happens when the digit in the top number (called the minuend) is greater than or equal to the digit in the bottom number (called the subtrahend) in each place value.

This means you can subtract each digit directly without needing to "borrow" from the next higher place value.

Let's look at how subtraction works on a number line. Suppose we want to subtract 21 from 43 (43 - 21):

20 30 40 50 43 21 Subtract 21

On the number line, starting at 43, we move 21 steps backward to reach 22. So, 43 - 21 = 22.

Let's try a simple subtraction without borrowing:

Example 1: Subtracting 56 - 23 without borrowing Easy
Subtract 23 from 56.

Step 1: Write the numbers vertically, aligning the digits by place value:

  5  6
- 2  3
_______

Step 2: Subtract the ones place: 6 - 3 = 3

Step 3: Subtract the tens place: 5 - 2 = 3

Answer: 56 - 23 = 33

Subtraction with Borrowing

Sometimes, the digit in the minuend is smaller than the digit in the subtrahend in a particular place value. In such cases, we cannot subtract directly. We need to borrow from the next higher place value to make the subtraction possible.

Before learning borrowing, let's quickly review place value. Each digit in a number has a place value depending on its position:

  • Ones place: The rightmost digit (units)
  • Tens place: The second digit from right (groups of ten)
  • Hundreds place: The third digit from right (groups of hundred)

For example, in the number 52, 5 is in the tens place (meaning 50) and 2 is in the ones place.

Let's see how borrowing works with an example: 52 - 29.

Tens Ones 5 2 2 9 - Borrow 1 ten 4 12

Here's what happens step-by-step:

  1. Look at the ones place: 2 (minuend) is less than 9 (subtrahend). We cannot subtract 9 from 2 directly.
  2. Borrow 1 ten (which equals 10 ones) from the tens place. The 5 tens become 4 tens.
  3. Add the borrowed 10 ones to the 2 ones, making it 12 ones.
  4. Now subtract the ones: 12 - 9 = 3.
  5. Subtract the tens: 4 - 2 = 2.
  6. The answer is 23.
Example 2: Subtracting 72 - 48 with borrowing Medium
Subtract 48 from 72.

Step 1: Write the numbers vertically:

  7  2
- 4  8
_______

Step 2: Ones place: 2 is less than 8, so borrow 1 ten from the tens place.

Step 3: Tens place: 7 becomes 6 (after borrowing).

Step 4: Ones place: 2 + 10 = 12.

Step 5: Subtract ones: 12 - 8 = 4.

Step 6: Subtract tens: 6 - 4 = 2.

Answer: 72 - 48 = 24

Example 3: Subtracting 305 - 178 with borrowing Hard
Subtract 178 from 305.

Step 1: Write vertically:

 3  0  5
- 1  7  8
_______

Step 2: Ones place: 5 - 8 is not possible. Borrow 1 ten from tens place (0 tens).

Step 3: Tens place is 0, so borrow 1 hundred from hundreds place (3 hundreds), making it 2 hundreds.

Step 4: The borrowed hundred converts to 10 tens. Now tens place has 10 tens.

Step 5: Borrow 1 ten from tens place (10 tens become 9 tens), add 10 ones to ones place: 5 + 10 = 15.

Step 6: Ones: 15 - 8 = 7.

Step 7: Tens: 9 - 7 = 2.

Step 8: Hundreds: 2 - 1 = 1.

Answer: 305 - 178 = 127

Pro Tips for Borrowing

  • Always start subtracting from the ones place and move leftwards.
  • When borrowing, reduce the digit you borrow from by 1.
  • If the next higher place value digit is zero, borrow from the next higher place value further left.
  • Write down the steps clearly to avoid confusion.
  • Check your answer by adding the difference and subtrahend to see if it equals the minuend.

Formula Bank

Formula Bank

Basic Subtraction
\[ A - B = C \]
where: A = Minuend, B = Subtrahend, C = Difference

Worked Examples

Example 1: Subtracting 45 - 22 without borrowing Easy
Subtract 22 from 45.

Step 1: Write the numbers vertically:

  4  5
- 2  2
_______

Step 2: Ones place: 5 - 2 = 3

Step 3: Tens place: 4 - 2 = 2

Answer: 45 - 22 = 23

Example 2: Subtracting 63 - 29 with borrowing Medium
Subtract 29 from 63.

Step 1: Write vertically:

  6  3
- 2  9
_______

Step 2: Ones place: 3 < 9, so borrow 1 ten from tens place.

Step 3: Tens place: 6 becomes 5.

Step 4: Ones place: 3 + 10 = 13.

Step 5: Subtract ones: 13 - 9 = 4.

Step 6: Subtract tens: 5 - 2 = 3.

Answer: 63 - 29 = 34

Example 3: Subtracting 204 - 89 with borrowing Medium
Subtract 89 from 204.

Step 1: Write vertically:

 2  0  4
-   8  9
_______

Step 2: Ones place: 4 - 9 not possible, borrow 1 ten from tens place (0 tens).

Step 3: Tens place is 0, so borrow 1 hundred from hundreds place (2 hundreds become 1 hundred).

Step 4: Tens place becomes 10 tens.

Step 5: Borrow 1 ten from tens place (10 tens become 9 tens), add 10 ones to ones place: 4 + 10 = 14.

Step 6: Ones: 14 - 9 = 5.

Step 7: Tens: 9 - 8 = 1.

Step 8: Hundreds: 1 - 0 = 1.

Answer: 204 - 89 = 115

Example 4: Subtracting 1000 - 567 with multiple borrowing Hard
Subtract 567 from 1000.

Step 1: Write vertically:

1  0  0  0
-  5  6  7
_______

Step 2: Ones place: 0 - 7 not possible, borrow 1 ten from tens place (0 tens).

Step 3: Tens place is 0, borrow 1 hundred from hundreds place (0 hundreds).

Step 4: Hundreds place is 0, borrow 1 thousand from thousands place (1 thousand becomes 0).

Step 5: Hundreds place becomes 10 hundreds, tens place becomes 10 tens, ones place becomes 10 ones.

Step 6: Borrow 1 ten from tens place (10 tens become 9 tens), add 10 ones to ones place: 0 + 10 = 10.

Step 7: Ones: 10 - 7 = 3.

Step 8: Borrow 1 hundred from hundreds place (10 hundreds become 9 hundreds), add 10 tens to tens place: 9 + 10 = 19 tens.

Step 9: Tens: 19 - 6 = 13 (write 3, carry 1 hundred).

Step 10: Hundreds: 9 - 5 = 4 (after adjusting for carry).

Answer: 1000 - 567 = 433

Example 5: Word problem involving subtraction with borrowing Medium
Riya had Rs.850. She bought a bag for Rs.475. How much money does she have left?

Step 1: Write the subtraction: 850 - 475.

Step 2: Ones place: 0 - 5 not possible, borrow 1 ten from tens place (5 tens become 4 tens).

Step 3: Ones place: 0 + 10 = 10, 10 - 5 = 5.

Step 4: Tens place: 4 - 7 not possible, borrow 1 hundred from hundreds place (8 hundreds become 7 hundreds).

Step 5: Tens place: 4 + 10 = 14, 14 - 7 = 7.

Step 6: Hundreds place: 7 - 4 = 3.

Answer: Riya has Rs.375 left after buying the bag.

Tips & Tricks

Tip: Always start subtracting from the ones place and move leftwards.

When to use: When performing vertical subtraction to maintain place value accuracy.

Tip: Use estimation to check if the answer is reasonable before finalizing.

When to use: After solving subtraction problems to quickly verify correctness.

Tip: Remember that borrowing reduces the next higher place value digit by 1.

When to use: When performing subtraction with borrowing to avoid common errors.

Tip: Practice subtraction facts regularly to improve speed and confidence.

When to use: Daily practice sessions to build fluency.

Tip: Use number lines or draw place value charts if stuck.

When to use: When students find subtraction with borrowing confusing.

Common Mistakes to Avoid

❌ Subtracting a larger digit from a smaller digit without borrowing.
✓ Borrow from the next higher place value before subtracting.
Why: Students often forget borrowing rules or rush through steps, leading to wrong answers.
❌ Forgetting to reduce the digit from which borrowing is done by 1.
✓ Always decrease the digit you borrow from by one.
Why: Overlooking this step causes incorrect subtraction results.
❌ Mixing place values during subtraction.
✓ Align digits properly according to ones, tens, hundreds columns.
Why: Misalignment causes subtraction of wrong digits, leading to errors.
❌ Not checking answers by addition.
✓ Add the difference and subtrahend to verify the minuend.
Why: Skipping verification leads to unnoticed mistakes.
❌ Confusing subtraction with addition operations.
✓ Focus on the operation sign and the meaning of subtraction as taking away.
Why: Young learners sometimes confuse operations due to similar number arrangements.
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