What is Subtraction?
Subtraction means taking away or removing things from a group to find out how many are left. When we subtract, we make a group smaller.
Imagine you have 5 candies. You eat 2 candies. Now you want to know: How many candies are left? This is subtraction!
We use the minus sign (−) to show subtraction, and the equals sign (=) to show the answer.
5 − 2 = 3
We read this as: “Five minus two equals three.”
Why Do We Need Subtraction?
Subtraction helps us solve many problems in our everyday life! Here are some examples:
At Home: You have 8 chocolates. You give 3 chocolates to your friend. How many chocolates do you have left?
In Class: There are 10 pencils in a box. Your teacher takes out 4 pencils. How many pencils are still in the box?
At the Zoo: You see 7 monkeys playing. Then 2 monkeys go away to eat. How many monkeys are still playing?
Playing Games: You have 6 marbles. You lose 1 marble while playing. How many marbles do you have now?
Subtraction helps us find out what’s left after we take something away!
Part 1: Subtracting Single-Digit Numbers
Let’s start with subtracting small numbers first!
Method 1: Subtracting with Pictures (Counting Objects)
This is the easiest way to understand subtraction. Let’s use pictures!
Example 1: 5 − 2 = ?
Start with 5 apples: 🍎 🍎 🍎 🍎 🍎
Take away 2 apples: ~~🍎 🍎~~ (cross them out)
Count what’s left: 🍎 🍎 🍎
So, 5 − 2 = 3
Example 2: 7 − 3 = ?
Start with 7 stars: ⭐ ⭐ ⭐ ⭐ ⭐ ⭐ ⭐
Take away 3 stars: ~~⭐ ⭐ ⭐~~
Count what’s left: ⭐ ⭐ ⭐ ⭐
So, 7 − 3 = 4
Example 3: 9 − 4 = ?
Start with 9 flowers: 🌸 🌸 🌸 🌸 🌸 🌸 🌸 🌸 🌸
Take away 4 flowers: ~~🌸 🌸 🌸 🌸~~
Count what’s left: 🌸 🌸 🌸 🌸 🌸
So, 9 − 4 = 5
Method 2: Subtracting Horizontally (In a Line)
When we write subtraction problems in a line from left to right, we call it horizontal subtraction.
Example 1: 8 − 3 = ?
Step 1: Start with the first number: 8 Step 2: Count backward 3 times: “7, 6, 5” Step 3: The answer is 5!
So, 8 − 3 = 5
Example 2: 6 − 2 = ?
Start at 6, count backward 2 times: “5, 4”
So, 6 − 2 = 4
Example 3: 9 − 5 = ?
Start at 9, count backward 5 times: “8, 7, 6, 5, 4”
So, 9 − 5 = 4
Method 3: Subtracting on a Number Line
A number line helps us see subtraction by moving backward!
What is a Number Line?
0 — 1 — 2 — 3 — 4 — 5 — 6 — 7 — 8 — 9 — 10
Example 1: 7 − 3 = ?
Step 1: Start at 7 on the number line Step 2: Jump backward 3 spaces (one hop at a time) Step 3: First hop lands on 6, second hop lands on 5, third hop lands on 4 Step 4: You land on 4!
So, 7 − 3 = 4
0 — 1 — 2 — 3 — 4 ⬅ 5 ⬅ 6 ⬅ 7 — 8 — 9 — 10
Example 2: 9 − 4 = ?
Start at 9, jump backward 4 spaces: 8, 7, 6, 5
So, 9 − 4 = 5
0 — 1 — 2 — 3 — 4 — 5 ⬅ 6 ⬅ 7 ⬅ 8 ⬅ 9 — 10
Method 4: Subtracting Vertically (Top to Bottom)
Sometimes we write numbers one below the other. This is called vertical subtraction.
Example 1:
8
− 3
---
5
Step 1: Write the bigger number on top: 8 Step 2: Write the number to subtract below it: 3 Step 3: Subtract: 8 − 3 = 5 Step 4: Write the answer below the line: 5
Example 2:
9
− 4
---
5
9 − 4 = 5
Example 3:
7
− 2
---
5
7 − 2 = 5
Part 2: Subtracting Double-Digit Numbers (Without Borrowing)
Now let’s learn something more exciting – subtracting bigger numbers!
What Does “Without Borrowing” Mean?
Without borrowing means the top number in each place (ones and tens) is bigger than or equal to the bottom number. This makes subtraction easier!
Example of WITHOUT borrowing:
- In 58 − 23, we can subtract because 8 is bigger than 3, and 5 is bigger than 2.
Understanding Place Value
Before we subtract double-digit numbers, we need to understand place value.
Example: The number 47
Tens | Ones
4 | 7
- The digit 4 is in the tens place = 4 tens = 40
- The digit 7 is in the ones place = 7 ones = 7
- So, 47 = 40 + 7
Legend:
- 🟦 = 1 ten (10)
- 🟩 = 1 one (1)
Let’s visualize this:
47 = 🟦🟦🟦🟦 + 🟩🟩🟩🟩🟩🟩🟩
(4 groups of 10) + (7 single ones)
Method 1: Vertical Subtraction with Place Values
This is the most common and important method!
Example 1: 58 − 23 = ?
Step 1: Write the numbers vertically, lining up the place values
Tens | Ones
5 | 8
− 2 | 3
---------
Step 2: Start with the ONES place (right side)
Subtract: 8 − 3 = 5
Tens | Ones
5 | 8
− 2 | 3
---------
| 5
Step 3: Now subtract the TENS place (left side)
Subtract: 5 − 2 = 3
Tens | Ones
5 | 8
− 2 | 3
---------
3 | 5
Answer: 58 − 23 = 35
Let’s check with pictures:
58 = 🟦🟦🟦🟦🟦 🟩🟩🟩🟩🟩🟩🟩🟩 (5 tens + 8 ones)
Take away 23 = ~~🟦🟦~~ ~~🟩🟩🟩~~ (2 tens + 3 ones)
Left = 🟦🟦🟦 🟩🟩🟩🟩🟩 (3 tens + 5 ones) = 35 ✓
Example 2: 67 − 34 = ?
Step 1: Write vertically
Tens | Ones
6 | 7
− 3 | 4
---------
Step 2: Subtract ONES: 7 − 4 = 3
Tens | Ones
6 | 7
− 3 | 4
---------
| 3
Step 3: Subtract TENS: 6 − 3 = 3
Tens | Ones
6 | 7
− 3 | 4
---------
3 | 3
Answer: 67 − 34 = 33
Example 3: 89 − 45 = ?
Tens | Ones
8 | 9
− 4 | 5
---------
Step 1: Ones place: 9 − 5 = 4 Step 2: Tens place: 8 − 4 = 4
Tens | Ones
8 | 9
− 4 | 5
---------
4 | 4
Answer: 89 − 45 = 44
Example 4: 76 − 42 = ?
Tens | Ones
7 | 6
− 4 | 2
---------
3 | 4
Step 1: Ones: 6 − 2 = 4 Step 2: Tens: 7 − 4 = 3
Answer: 76 − 42 = 34
Method 2: Expanded Form Subtraction
This method helps you see what’s happening with tens and ones separately!
Example 1: 68 − 24 = ?
Step 1: Break both numbers into tens and ones
68 = 60 + 8
24 = 20 + 4
Step 2: Subtract tens and ones separately
Tens: 60 − 20 = 40
Ones: 8 − 4 = 4
Step 3: Add the results together
40 + 4 = 44
Answer: 68 − 24 = 44
Example 2: 79 − 35 = ?
Step 1: Break into parts
79 = 70 + 9
35 = 30 + 5
Step 2: Subtract separately
Tens: 70 − 30 = 40
Ones: 9 − 5 = 4
Step 3: Combine
40 + 4 = 44
Answer: 79 − 35 = 44
Method 3: Using Base-10 Blocks (Visual Method)
Base-10 blocks help us see subtraction visually!
Legend:
- 🟦 = 1 ten (10)
- 🟩 = 1 one (1)
Example: 56 − 32 = ?
Step 1: Show 56 with blocks
56 = 🟦🟦🟦🟦🟦 🟩🟩🟩🟩🟩🟩
(5 tens + 6 ones)
Step 2: Take away 32 (3 tens + 2 ones)
Remove: ~~🟦🟦🟦~~ ~~🟩🟩~~
Step 3: Count what's left
Left: 🟦🟦 🟩🟩🟩🟩
(2 tens + 4 ones = 24)
Answer: 56 − 32 = 24
Method 4: Number Line with Double Digits
You can use a number line for bigger numbers too!
Example: 48 − 23 = ?
Strategy: Jump backward by tens first, then by ones!
Step 1: Start at 48
Step 2: Jump back 2 tens (20): 48 → 38 → 28
Step 3: Jump back 3 ones: 28 → 27 → 26 → 25
20 — 25 ⬅⬅⬅ 28 ⬅⬅⬅⬅⬅⬅⬅⬅⬅⬅ 38 ⬅⬅⬅⬅⬅⬅⬅⬅⬅⬅ 48 — 50
Answer: 48 − 23 = 25
Tips and Tricks for Subtraction Success! 🌟
Tip 1: Always Start with the ONES Place
When subtracting vertically, always start from the right side (ones place) and move to the left (tens place).
Remember: Right to Left! ➡️ ⬅️
Tip 2: Check Your Answer with Addition
Subtraction and addition are opposites! You can check if your subtraction is correct by adding.
Example:
- If 9 − 5 = 4, then check: 4 + 5 = 9 ✓
For double digits:
- If 67 − 34 = 33, then check: 33 + 34 = 67 ✓
Tip 3: Subtracting Zero
When you subtract 0 from any number, the answer stays the same!
- 8 − 0 = 8
- 45 − 0 = 45
- 99 − 0 = 99
Tip 4: Same Numbers = Zero
When you subtract a number from itself, you always get zero!
- 5 − 5 = 0
- 7 − 7 = 0
- 38 − 38 = 0
- 56 − 56 = 0
Tip 5: Use Your Fingers
For small subtractions, you can use your fingers to count backward!
Example: 7 − 3 = ?
- Hold up 7 fingers
- Put down 3 fingers
- Count the fingers still up = 4
Tip 6: Line Up the Numbers Carefully
When writing vertical subtraction, make sure ones are under ones and tens are under tens!
Correct:
47
− 23
----
Wrong:
47
− 23 (Not lined up!)
----
Tip 7: The Bigger Number Goes on Top
In vertical subtraction, always write the bigger number on top!
Correct:
56
− 32
----
24
Wrong:
32
− 56 (Can't do this without negative numbers!)
----
Tip 8: Practice Subtraction Facts
Just like addition, memorizing basic subtraction facts makes you faster!
Subtraction facts from 10:
- 10 − 1 = 9
- 10 − 2 = 8
- 10 − 3 = 7
- 10 − 4 = 6
- 10 − 5 = 5
Doubles:
- 8 − 4 = 4
- 6 − 3 = 3
- 10 − 5 = 5
Tip 9: Count Back for Small Numbers
When subtracting small numbers (1, 2, or 3), it’s easy to just count backward!
- 9 − 2: Count “8, 7” = 7
- 8 − 3: Count “7, 6, 5” = 5
Tip 10: Use “Think Addition”
Sometimes thinking about addition helps with subtraction!
Example: 9 − 6 = ?
Think: “6 plus what equals 9?” 6 + 3 = 9
So, 9 − 6 = 3
Special Subtraction Patterns
Pattern 1: Subtracting from 10
10 − 1 = 9
10 − 2 = 8
10 − 3 = 7
10 − 4 = 6
10 − 5 = 5
10 − 6 = 4
10 − 7 = 3
10 − 8 = 2
10 − 9 = 1
Notice: The answers count down from 9 to 1!
Pattern 2: Subtracting Tens
When subtracting tens, only the tens place changes!
50 − 10 = 40
50 − 20 = 30
50 − 30 = 20
50 − 40 = 10
70 − 10 = 60
70 − 20 = 50
70 − 30 = 40
Pattern 3: Subtracting the Same Ones Digit
When both numbers have the same ones digit, the answer will have 0 in the ones place!
25 − 15 = 10
37 − 27 = 10
48 − 38 = 10
56 − 46 = 10
Common Mistakes to Avoid! ⚠️
Mistake 1: Subtracting the Wrong Way
Wrong: In 8 − 3, doing 3 − 8 instead Right: Always subtract the smaller number from the bigger number
Mistake 2: Not Lining Up Place Values
Wrong:
54
− 6
----
Right:
54
− 06 (Put 0 in tens place)
----
48
Mistake 3: Forgetting to Subtract Tens
Wrong:
68
− 24
----
64 (Forgot to subtract tens!)
Right:
68
− 24
----
44 (Subtract both ones and tens)
Fun Subtraction Story
The Cookie Jar Mystery! 🍪
Mom baked 48 cookies and put them in a jar. In the morning, there were 48 cookies. 🍪🍪🍪…
Little sister ate 12 cookies after lunch. 48 − 12 = 36 cookies left!
Big brother ate 14 cookies after dinner. 36 − 14 = 22 cookies left!
Dad ate 11 cookies while watching TV. 22 − 11 = 11 cookies left!
The next morning, only 11 cookies remained in the jar! Everyone had enjoyed Mom’s delicious cookies!
Remember! 🎯
- Subtraction means taking away
- The minus sign (−) shows subtraction
- Always start from the ones place when subtracting vertically
- Line up the place values carefully
- Check your work by adding back
- Practice makes you a subtraction superstar!
Keep practicing, and you’ll master subtraction in no time! 🌟
