Lesson 1: Working with Whole Numbers - Addition and Subtraction
Master the fundamentals of adding and subtracting whole numbers, essential skills for the GED Math test
🧮 Working with Whole Numbers: Addition and Subtraction
Introduction
Welcome to your first lesson in GED Math preparation! If you're feeling nervous about math, take a deep breath—you're in the right place. This lesson focuses on whole numbers, which are the counting numbers we use every day: 0, 1, 2, 3, 4, and so on. No fractions, no decimals, just the basics.
Why start here? Because whole number operations are the foundation of everything else in math. Whether you're calculating how much change you should receive at a store, figuring out how many hours you worked this week, or solving more complex GED problems, you'll use addition and subtraction constantly.
💡 Remember: Math is like building a house. You need a solid foundation before you can add the walls and roof. That's what we're building today!
🔢 What Are Whole Numbers?
Whole numbers are numbers without fractions or decimals. They include:
- Zero: 0
- Positive counting numbers: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12...
Whole numbers continue forever—there's no "largest" whole number!
🤔 Did you know? The concept of zero as a number was invented around 500 CE in India. Before that, many ancient civilizations didn't have a symbol for "nothing"!
➕ Addition: Putting Numbers Together
Addition means combining two or more numbers to find their total or sum. The numbers you add are called addends.
Basic Addition Terminology
25 ← addend
+ 13 ← addend
----
38 ← sum (the answer)
The Addition Process: Place Value Matters!
When adding larger numbers, we need to understand place value—the position of each digit in a number:
- Ones place: The rightmost digit (e.g., in 347, the 7 is in the ones place)
- Tens place: The second digit from the right (e.g., in 347, the 4 is in the tens place)
- Hundreds place: The third digit from the right (e.g., in 347, the 3 is in the hundreds place)
💡 Pro Tip: Always line up numbers by their place values when adding vertically. Ones under ones, tens under tens, hundreds under hundreds!
Adding Without Regrouping (No Carrying)
Let's start simple. When the digits in each place value add up to 9 or less, you don't need to "carry" anything:
243
+ 125
-----
368
Step-by-step:
- Add the ones: 3 + 5 = 8 (write 8 in the ones place)
- Add the tens: 4 + 2 = 6 (write 6 in the tens place)
- Add the hundreds: 2 + 1 = 3 (write 3 in the hundreds place)
Adding With Regrouping (Carrying)
When digits add up to 10 or more, we need to regroup (also called "carrying"):
¹
47
+ 28
----
75
Step-by-step:
- Add the ones: 7 + 8 = 15 (write 5 in the ones place, carry the 1 to the tens place)
- Add the tens: 4 + 2 = 6, plus the carried 1 = 7 (write 7 in the tens place)
🌍 Real-world example: You have $47 in your wallet and earn $28 from a side job. How much money do you have now? $75!
➖ Subtraction: Taking Numbers Away
Subtraction means taking one number away from another. The answer is called the difference.
Basic Subtraction Terminology
58 ← minuend (the number you start with)
- 23 ← subtrahend (the number you subtract)
----
35 ← difference (the answer)
Subtracting Without Regrouping (No Borrowing)
When each digit in the top number is larger than the digit below it, subtraction is straightforward:
89
- 34
----
55
Step-by-step:
- Subtract the ones: 9 - 4 = 5
- Subtract the tens: 8 - 3 = 5
Subtracting With Regrouping (Borrowing)
When a digit in the bottom number is larger than the digit above it, we need to borrow from the next place value:
⁴ ¹⁵
5̶ 5
- 27
----
28
Step-by-step:
- Look at the ones: We can't subtract 7 from 5
- Borrow 1 ten from the tens place: 5 tens becomes 4 tens
- Add 10 to the ones place: 5 ones becomes 15 ones
- Subtract the ones: 15 - 7 = 8
- Subtract the tens: 4 - 2 = 2
🌍 Real-world example: You have 55 minutes to complete a task, and you've already used 27 minutes. How much time do you have left? 28 minutes!
💡 Memory trick: Think of borrowing as "breaking a $10 bill into ten $1 bills" when you don't have enough ones.
📝 Example Problems
Let's work through some complete examples together.
Example 1: Addition with Multiple Regroupings
Problem: Add 487 + 365
¹ ¹
487
+ 365
-----
852
Solution Process:
- Ones place: 7 + 5 = 12. Write 2, carry 1
- Tens place: 8 + 6 = 14, plus carried 1 = 15. Write 5, carry 1
- Hundreds place: 4 + 3 = 7, plus carried 1 = 8. Write 8
- Answer: 852
🔧 Try this: Pause and add 596 + 278 on your own. You should get 874!
Example 2: Subtraction with Borrowing Across Zeros
Problem: Subtract 503 - 247
⁴ ⁹ ¹³
5̶ 0̶ 3̶
- 247
-----
256
Solution Process:
- Ones place: We can't subtract 7 from 3, so we need to borrow
- Problem: The tens place is 0! We need to borrow from the hundreds first
- Borrow from hundreds: 5 hundreds becomes 4 hundreds; the 0 tens becomes 10 tens
- Now borrow from tens: 10 tens becomes 9 tens; the 3 ones becomes 13 ones
- Subtract ones: 13 - 7 = 6
- Subtract tens: 9 - 4 = 5
- Subtract hundreds: 4 - 2 = 2
- Answer: 256
⚠️ Common mistake alert: When you have zeros in the middle, don't panic! Just keep borrowing from the next non-zero digit to the left.
Example 3: Adding Three Numbers
Problem: Add 156 + 89 + 247
Strategy: Add two numbers at a time, then add the third.
Step 1: Add 156 + 89
¹ ¹
156
+ 89
-----
245
Step 2: Add 245 + 247
¹
245
+ 247
-----
492
Answer: 492
💡 Alternative strategy: You can also add all the ones together, then all the tens, then all the hundreds. Use whichever method feels more comfortable!
Example 4: Real-World Word Problem
Problem: Maria works at a bookstore. On Monday, the store had 324 books. They sold 158 books on Tuesday and received a shipment of 275 new books on Wednesday. How many books does the store have now?
Solution:
This problem requires both subtraction AND addition!
Step 1: Subtract the books sold
² ¹⁴
3̶ 2̶ 4
- 158
-----
166
After selling books: 166 books
Step 2: Add the new shipment
¹ ¹
166
+ 275
-----
441
Answer: The store now has 441 books.
🧠 Word problem strategy:
- Read carefully and identify what you're looking for
- Determine which operation(s) to use
- Set up the problem step-by-step
- Check if your answer makes sense
⚠️ Common Mistakes to Avoid
Mistake 1: Not Lining Up Place Values
❌ Wrong:
456
+ 23
----
✅ Correct:
456
+ 23 (23 is lined up with ones and tens places)
-----
Always align the rightmost digits (ones place) first!
Mistake 2: Forgetting to Carry or Borrow
❌ Wrong: 48 + 37 = 75 (forgot to carry the 1 from 8 + 7 = 15)
✅ Correct: 48 + 37 = 85
💡 Tip: Write the carried or borrowed numbers small and above/below the problem to keep track.
Mistake 3: Borrowing Incorrectly
❌ Wrong: When borrowing, forgetting to reduce the digit you borrowed from
✅ Correct: If you borrow 1 from the tens place, remember to cross out the original digit and write the reduced number.
Mistake 4: Subtracting Smaller from Larger Automatically
❌ Wrong: In 52 - 38, calculating 8 - 2 = 6 in the ones place (you switched them!)
✅ Correct: Always subtract the bottom number from the top number. If you can't, borrow first.
Mistake 5: Not Checking Your Work
💡 Best practice: After subtraction, add your answer to the number you subtracted. You should get the original number!
Example: If 85 - 37 = 48, check by calculating 48 + 37 = 85 ✓
🎯 Key Takeaways
Let's review the most important concepts from this lesson:
+---------------------------------------+
| 📋 QUICK REFERENCE CARD |
+---------------------------------------+
| ADDITION TERMS |
| • Addends: numbers being added |
| • Sum: the answer |
| • Regrouping: carrying to next place |
| |
| SUBTRACTION TERMS |
| • Minuend: top number |
| • Subtrahend: bottom number |
| • Difference: the answer |
| • Borrowing: taking from next place |
| |
| KEY STRATEGIES |
| • Line up place values vertically |
| • Start from the ones place |
| • Write carried/borrowed numbers |
| • Check your work |
+---------------------------------------+
Essential Skills You've Learned:
- Place value understanding: Recognizing ones, tens, hundreds places
- Adding whole numbers: With and without regrouping
- Subtracting whole numbers: With and without borrowing
- Problem-solving: Breaking down word problems into steps
- Self-checking: Using inverse operations to verify answers
🧠 Memory Device: The "LACES" Method
Line up the numbers by place value Add or subtract from right to left (ones first) Carry or borrow when needed Examine each step carefully Self-check your answer
📚 Further Study
Ready to practice more and expand your skills?
Khan Academy - Arithmetic Operations: https://www.khanacademy.org/math/arithmetic/arith-review-add-subtract - Free video lessons and practice problems on addition and subtraction
GED Academy - Math Fundamentals: https://www.gedacademy.com/ged-math/basic-math - GED-specific practice with whole numbers and test-taking strategies
Math is Fun - Addition and Subtraction: https://www.mathsisfun.com/numbers/addition.html - Interactive examples and games to reinforce these concepts
🔧 Before You Go: Quick Self-Test
Try these three problems to check your understanding:
- Add: 647 + 285
- Subtract: 500 - 237
- Word problem: You have $425 in your bank account. You deposit $150 and then pay a bill for $298. How much is left?
Answers:
- 932
- 263
- $277 (425 + 150 = 575, then 575 - 298 = 277)
How did you do? If you got all three correct, fantastic! You're ready to move forward. If you missed any, review that section and try similar problems until you feel confident.
💪 Remember: Math is a skill that improves with practice. The more you work with whole numbers, the faster and more accurate you'll become. You've got this!
Next lesson preview: In Lesson 2, we'll explore multiplication and division of whole numbers, building on the foundation you've established here. See you there! 🚀