Basic Subtraction
Subtraction Within 10 - Taking Away and Finding Difference
What is Subtraction?
Subtraction is taking away one number from another to find what is left. It answers "how many are left?" The symbol for subtraction is – (minus). The answer is called the difference.
Example: 5 cookies – 2 cookies = 3 cookies (5 – 2 = 3)
Parts of a Subtraction Sentence:
\[
5 - 2 = 3
\]
(minuend) – (subtrahend) = (difference)
Two Ways to Think About Subtraction:
| Way | Meaning | Example |
|---|---|---|
| **Taking Away** | Remove some objects from a group | 7 apples, eat 3 → 4 left |
| **Finding the Difference** | Compare two groups | How many more? 8 is how many more than 5? (3 more) |
Subtraction Within 10:
All the numbers we subtract and the answer are less than or equal to 10.
Using Pictures to Subtract:
Start with all objects, cross out the ones being taken away, count what's left.
Using a Number Line to Subtract:
Start at the first number. Jump backward the number of spaces for the second number. Where you land is the difference.
Number Line Example:
To subtract 7 – 3: Start at 7, jump back 3 steps → 6, 5, 4. So 7 – 3 = 4.
Subtraction Facts Within 10 (Practice These!):
- 1 – 1 = 0, 2 – 1 = 1, 3 – 1 = 2, 4 – 1 = 3, 5 – 1 = 4, 6 – 1 = 5, 7 – 1 = 6, 8 – 1 = 7, 9 – 1 = 8, 10 – 1 = 9
- 2 – 2 = 0, 3 – 2 = 1, 4 – 2 = 2, 5 – 2 = 3, 6 – 2 = 4, 7 – 2 = 5, 8 – 2 = 6, 9 – 2 = 7, 10 – 2 = 8
- 3 – 3 = 0, 4 – 3 = 1, 5 – 3 = 2, 6 – 3 = 3, 7 – 3 = 4, 8 – 3 = 5, 9 – 3 = 6, 10 – 3 = 7
- 4 – 4 = 0, 5 – 4 = 1, 6 – 4 = 2, 7 – 4 = 3, 8 – 4 = 4, 9 – 4 = 5, 10 – 4 = 6
- 5 – 5 = 0, 6 – 5 = 1, 7 – 5 = 2, 8 – 5 = 3, 9 – 5 = 4, 10 – 5 = 5
Use pictures to subtract: 7 – 4 = ?
- Draw 7 circles: ●●●●●●●
- Cross out 4 circles: ●●●●✗✗✗
- Count remaining circles: ●●● (3 circles)
-
Answer: 3 **Example 2:** Use the number line to subtract: 9 – 5 = ? *Solution:* - Start at 9 on the number line - Jump back 5 steps: 9 → 8 → 7 → 6 → 5 → 4 - Land on 4 - **Answer:** 4 **Example 3:** Lisa has 8 balloons. 3 balloons fly away. How many balloons are left? *Solution:* - Start with 8 balloons - Take away 3 (fly away) - 8 – 3 = 5 - **Answer:** 5 balloons
Key Points
- Subtraction means taking away (minus sign: –)
- The answer is called the difference
- Taking away = removing objects from a group
- Finding the difference = comparing two groups
- Number line helps subtract by jumping backward
Subtraction Within 20 and Two-Digit Numbers
Subtraction Within 20:
Subtracting numbers where the bigger number is up to 20 and the answer is also within 20.
Strategies for Subtracting Within 20:
| Strategy | How to Do It | Example |
|---|---|---|
| **Count Back** | Start with bigger number, count backward | 14 – 3 = 14,13,12,11 → 11 |
| **Think Addition** | What plus subtrahend equals minuend? | 15 – 7 = ? → 7 + 8 = 15 → answer 8 |
| **Use Doubles** | Use known double facts | 16 – 8 = 8 (double 8 is 16) |
| **Make Ten** | Subtract to make ten, then subtract rest | 13 – 5 = (13–3)–2 = 10–2 = 8 |
Subtraction Without Regrouping (Within 100):
When subtracting two-digit numbers, we subtract the ones column first, then the tens column. No regrouping is needed when the top digit is bigger than or equal to the bottom digit in each column.
Steps for Vertical Subtraction (Without Regrouping):
1. Write numbers in a column (align ones under ones, tens under tens)
2. Subtract the ones column (right side)
3. Subtract the tens column (left side)
4. Write the answer
Example: 47 – 23 = ?
| Tens | Ones |
|---|---|
| 4 | 7 |
| – 2 | 3 |
| ─── | ─── |
| 2 | 4 |
Answer: 24
Horizontal Subtraction:
Subtract tens first, then ones: 56 – 32 = (50–30) + (6–2) = 20 + 4 = 24
Subtract using count back: 16 – 4 = ?
- Start at 16
- Count back 4: 16,15,14,13,12
-
Answer: 12 **Example 2:** Subtract vertically: 56 – 23 = ? *Solution:* - Write in column: 5 6 – 2 3 ───── - Ones: 6 – 3 = 3 - Tens: 5 – 2 = 3 - Answer: 33 **Example 3:** Tom has 18 stickers. He gives 5 stickers to his friend. How many stickers does Tom have left? *Solution:* - Start with 18 stickers - Give away 5: 18 – 5 = 13 - **Answer:** 13 stickers
Key Points
- Count back on number line or in your head
- Think addition to check subtraction
- Vertical subtraction subtract ones first, then tens
- Without regrouping means each top digit is bigger than bottom digit
- Practice subtraction facts to 20 for speed
Subtraction Using Pictures, Number Lines, and Vertical Subtraction
Different Ways to Subtract:
| Method | Best For | How It Works |
|---|---|---|
| **Pictures** | Visual learners | Draw objects, cross out taken away |
| **Number Line** | Understanding jumps | Jump backward from starting number |
| **Vertical** | Two-digit numbers | Stack numbers, subtract column by column |
Using Pictures to Subtract (Up to 20):
Draw the bigger number of objects. Cross out the number you are subtracting. Count what is left.
Using Number Line to Subtract (Up to 20):
Start at the bigger number. Make jumps backward equal to the smaller number. The number you land on is the answer.
Vertical Subtraction Without Regrouping (Within 100):
| Step | Action | Example: 67 – 34 |
|---|---|---|
| 1 | Write numbers (align ones and tens) | 67 –34 |
| 2 | Subtract ones: 7 – 4 = 3 | Write 3 in ones place |
| 3 | Subtract tens: 6 – 3 = 3 | Write 3 in tens place |
| 4 | Read the answer | 33 |
Subtraction Vocabulary:
- Minuend = the number you start with (top number)
- Subtrahend = the number you subtract (bottom number)
- Difference = the answer
Use pictures to subtract: 14 – 6 = ?
- Draw 14 circles: ●●●●●●●●●●●●●●
- Cross out 6 circles: ●●●●●●●●✗✗✗✗✗✗
- Count remaining: 8 circles
-
Answer: 8 **Example 2:** Use a number line to subtract: 18 – 7 = ? *Solution:* - Start at 18 on the number line - Jump back 7 steps: 18→17→16→15→14→13→12→11 - Land on 11 - **Answer:** 11 **Example 3:** Subtract vertically: 76 – 42 = ? *Solution:* - Write in column: 7 6 – 4 2 ───── - Ones: 6 – 2 = 4 - Tens: 7 – 4 = 3 - Answer: 34
Key Points
- Pictures help you see subtraction as taking away
- Number line shows subtraction as jumping backward
- Vertical subtraction is best for two-digit numbers
- Always subtract ones column first, then tens column
- Without regrouping means top digit is ≥ bottom digit in each column