Welcome to the World of Subtraction! π―
Today we’ll learn how to subtract bigger numbers, even when the top digit is smaller than the bottom digit. This is called borrowing or regrouping!
What is Borrowing?
Sometimes when we subtract, the digit on top is smaller than the digit on the bottom. When this happens, we need to borrow from the tens place!
Think of it like this: If you have 3 bags with 10 candies each and 2 loose candies (that’s 32 candies), and you need to give away 5 candies, you’ll need to open one bag to get enough loose candies!
Understanding Place Value First
Before we subtract, let’s remember:
T O
3 5
T = Tens place (3 tens = 30)
O = Ones place (5 ones = 5)
So 35 = 30 + 5
Method 1: The Traditional Borrowing Method π
Example 1: 42 – 18 = ?
Step-by-Step Solution:
Step 1: Write the numbers vertically
T O
4 2
- 1 8
------
Step 2: Look at the ONES place
Can we subtract 8 from 2? NO! (2 is smaller than 8)
So we need to BORROW from the tens place!
T O
4 2
- 1 8
------
Step 3: BORROW 1 ten from the tens place
- Cross out 4, make it 3
- The borrowed 1 ten = 10 ones
- Add 10 ones to the 2 ones: 10 + 2 = 12
3
4 12
- 1 8
------
Step 4: Now subtract the ONES place
12 - 8 = 4
3
4 12
- 1 8
------
4
Step 5: Subtract the TENS place
3 - 1 = 2
3
4 12
- 1 8
------
2 4
Answer: 42 – 18 = 24 β
Visual Representation with Blocks:
ββββ represent tens
β represent ones
42 = ββββ ββββ ββββ ββββ | β β
(4 tens) (2 ones)
We need to take away 18
Break one ten into 10 ones:
ββββ ββββ ββββ | β β β β β β β β β β β β
(3 tens) (12 ones)
Take away 8 ones:
ββββ ββββ ββββ | β β β β
(3 tens) (4 ones)
Take away 1 ten:
ββββ ββββ | β β β β
(2 tens) (4 ones)
Answer: 24
Example 2: 53 – 27 = ?
Step 1: Write vertically
T O
5 3
- 2 7
------
Step 2: Can we subtract 7 from 3? NO!
Step 3: BORROW from tens place
4
5 13 (borrowed 1 ten = 10, so 10 + 3 = 13)
- 2 7
------
Step 4: Subtract ONES: 13 - 7 = 6
Step 5: Subtract TENS: 4 - 2 = 2
4
5 13
- 2 7
------
2 6
Answer: 53 – 27 = 26 β
Method 2: The Number Line Method π―
This method uses a number line to “jump back” and subtract!
Example: 52 – 28 = ?
Start at 52, we need to go back 28
Strategy: Break 28 into easier jumps!
28 = 20 + 8
Step 1: Jump back 20
52 β 42 β 32
-10 -10
Step 2: Jump back 8
32 β 30 β 22
-2 -6
Answer: 24
Number Line Visualization:
|----|----|----|----|----|----|----|----|----|----|
20 24 28 32 36 40 44 48 52 56
β β
ANSWER START
(24) β------ 28 ------β (52)
Example: 61 – 35 = ?
Break 35 into 30 + 5
Step 1: Jump back 30
61 β 51 β 41 β 31
-10 -10 -10
Step 2: Jump back 5
31 β 26
-5
Answer: 26
Method 3: The Expanded Form Method π
This method breaks numbers into tens and ones!
Example: 74 – 38 = ?
Step 1: Break both numbers into tens and ones
74 = 70 + 4
38 = 30 + 8
Step 2: Try to subtract
70 + 4
- (30 + 8)
Step 3: Oh no! We can't subtract 8 from 4!
So we borrow 1 ten from 70
70 = 60 + 10
Now we have: 60 + 10 + 4 = 60 + 14
Step 4: Now subtract!
60 + 14
- (30 + 8)
----------
30 + 6 = 36
Answer: 74 – 38 = 36 β
Example: 85 – 49 = ?
Step 1: Break into tens and ones
85 = 80 + 5
49 = 40 + 9
Step 2: We can't subtract 9 from 5, so borrow!
80 = 70 + 10
Now: 70 + 15
Step 3: Subtract
(70 + 15) - (40 + 9)
= (70 - 40) + (15 - 9)
= 30 + 6
= 36
Answer: 85 – 49 = 36 β
Method 4: The “Add Up” Method (Counting Up) π
Instead of taking away, we COUNT UP from the smaller number to the bigger number!
Example: 63 – 37 = ?
Question: How much do we add to 37 to get 63?
Step 1: Start at 37, count up to the nearest ten (40)
37 + 3 = 40 β (We added 3)
Step 2: From 40, count up to 60
40 + 20 = 60 β (We added 20)
Step 3: From 60, count up to 63
60 + 3 = 63 β (We added 3)
Step 4: Add all the jumps
3 + 20 + 3 = 26
Answer: 63 – 37 = 26 β
Example: 82 – 56 = ?
Start at 56, count up to 82
56 β 60 β 80 β 82
+4 +20 +2
Total: 4 + 20 + 2 = 26
Answer: 82 – 56 = 26 β
Fun Real-Life Examples! π
Example 1: The Sticker Problem
Sarah had 45 stickers. She gave 17 stickers to her friend.
How many stickers does Sarah have left?
45
- 17
----
Borrow: 4 tens β 3 tens and 10 ones
3
45 15
- 17
----
28
Answer: Sarah has 28 stickers left! π
Example 2: The Marble Game
Tom collected 72 marbles. He lost 36 marbles.
How many marbles does Tom have now?
72
- 36
----
Can we subtract 6 from 2? No! Borrow!
6
72 12
- 36
----
36
Answer: Tom has 36 marbles! π΅
Example 3: The Cookie Jar
Mom baked 91 cookies. The children ate 48 cookies.
How many cookies are left?
91
- 48
----
Borrow from tens!
8
91 11
- 48
----
43
Answer: 43 cookies are left! πͺ
Example 4: The Birthday Party
There were 65 balloons at the party. 29 balloons popped.
How many balloons are still inflated?
65
- 29
----
Borrow!
5
65 15
- 29
----
36
Answer: 36 balloons are still good! π
Tips and Tricks for Success! π‘
Tip #1: The “Can I Subtract?” Check
Always ask: Is the top digit bigger than or equal to the bottom digit?
- If YES β Just subtract!
- If NO β BORROW first!
23 42
- 14 - 18
---- ----
3 > 4? 2 > 8?
YES! NO! Need to borrow!
Tip #2: The Borrowing Rhyme
π΅ "When the bottom's more, here's what to do,
Borrow from the neighbor, make it ten plus two!" π΅
Tip #3: Remember “10 and Plus”
When you borrow 1 ten, you get 10 ones to add to what you already have!
If you have 3 ones and borrow 1 ten:
10 + 3 = 13 ones
Tip #4: Cross Out Clearly
When borrowing, always cross out the old number and write the new one clearly:
4ΜΆ 3ΜΆ NOT 4ΜΆ3ΜΆ
52ΜΆ 12ΜΆ 5ΜΆ2ΜΆ12ΜΆ
- 28 - 28
---- ----
Tip #5: Check Your Work!
Use addition to check subtraction!
If 52 - 28 = 24
Check: 24 + 28 = 52 β Correct!
Tip #6: Start with the Ones Place
ALWAYS start subtracting from the ONES place (right side) first!
CORRECT Order:
42
- 18
----
1. Ones first (2 - 8, need to borrow!)
2. Then tens
Tip #7: Practice with Easy Numbers First
Start with problems where you need to borrow just once:
Easy Practice:
32 - 15
41 - 16
53 - 27
Then move to harder ones:
82 - 56
91 - 48
Tip #8: The “Friendly Numbers” Trick
Round to the nearest ten, then adjust!
63 - 38 = ?
Think: 63 - 40 = 23
But we subtracted 2 too many
So: 23 + 2 = 25 β
Tip #9: Use Your Fingers for Small Borrowing
When borrowing creates numbers like 11, 12, 13, use your fingers to count back!
41ΜΆ 11ΜΆ
5ΜΆ1ΜΆ
- 17
----
11 - 7 = ? Count back on fingers from 11
Tip #10: Make It Visual
Draw dots or sticks to represent the numbers if you’re stuck!
42 = |||| |||| |||| |||| β’ β’
(tens) (ones)
Common Mistakes to Avoid! β οΈ
Mistake #1: Forgetting to Cross Out
WRONG: RIGHT:
42 4ΜΆ 3ΜΆ
- 18 42ΜΆ 12ΜΆ
---- - 18
26 ----
24
Mistake #2: Subtracting Top from Bottom
WRONG: RIGHT:
42 4ΜΆ 3ΜΆ
- 18 42ΜΆ 12ΜΆ
---- - 18
26 ----
(8-2=6) 24
(12-8=4)
Mistake #3: Not Reducing the Tens After Borrowing
WRONG: RIGHT:
42 3ΜΆ
- 18 42ΜΆ 12ΜΆ
---- - 18
34 ----
(4-1=3) 24
(3-1=2)
Quick Reference Guide π
When Do I Borrow?
β When the ones digit on top is smaller than the ones digit on bottom
How Do I Borrow?
- Take 1 ten from the tens place (cross it out, reduce by 1)
- Add 10 to the ones place
- Now subtract!
The Borrowing Formula
If you can't subtract ones:
1 TEN = 10 ONES
Example: 3 tens 2 ones β 2 tens 12 ones
Summary Chart π
| Method | Best For | Difficulty |
|---|---|---|
| Traditional Borrowing | Paper and pencil work | ββ |
| Number Line | Visual learners | βββ |
| Expanded Form | Understanding place value | ββββ |
| Counting Up | Mental math | ββ |
Remember These Key Points! π―
- Always start with the ONES place
- Check if you need to borrow before subtracting
- 1 ten = 10 ones when you borrow
- Cross out the old number and write the new one
- Check your answer by adding back
- Practice every day to get faster and better!
Fun Challenge Problems! π
Try solving these using ANY method you like!
- A farmer had 84 apples. He sold 56 apples. How many apples are left?
- There are 92 pages in a book. Maya read 47 pages. How many pages are left to read?
- A toy store had 75 teddy bears. They sold 38 teddy bears. How many teddy bears remain?
Remember: There’s no one “right” method – use the method that makes the most sense to you! The important thing is understanding WHY we borrow and getting the correct answer!
Keep practicing, and you’ll become a subtraction superstar! β
Image Courtesy
