Common Mistakes
Learn
Everyone makes mistakes when learning math - that is how we learn! In this lesson, you will see the most common errors students make when adding and subtracting large numbers. Learning to spot these mistakes will help you avoid them.
Why Study Mistakes?
- Understanding errors helps you catch them in your own work
- You can check your answers more carefully
- You become a stronger math student by learning what NOT to do
Examples of Common Mistakes
Mistake #1: Forgetting to Carry
WRONG
347 + 285 ----- 522
The student forgot to carry when 7 + 5 = 12
CORRECT
347 + 285 ----- 632
Remember: 7 + 5 = 12. Write 2, carry 1!
Mistake #2: Forgetting to Borrow
WRONG
524 - 168 ----- 444
The student subtracted 4 from 8 instead of borrowing
CORRECT
524 - 168 ----- 356
You cannot take 8 from 4. Borrow first!
Mistake #3: Not Lining Up Place Values
WRONG
425 + 36 ----- 785
The 36 is not lined up correctly
CORRECT
425 + 36 ----- 461
Always line up ones under ones, tens under tens!
Mistake #4: Borrowing Errors with Zeros
WRONG
500 - 234 ----- 334
The student did not borrow correctly from 500
CORRECT
500 - 234 ----- 266
When borrowing from 0, borrow across to the next digit
Mistake #5: Forgetting the Carried Number
WRONG
456 + 378 ----- 724
The student carried but forgot to add the carried 1
CORRECT
456 + 378 ----- 834
5 + 7 = 12. Write 2, carry 1. Then 4 + 3 + 1 = 8
Practice
Find the mistake in each problem below. Then solve it correctly.
1. A student wrote: 256 + 187 = 333. What mistake did they make? What is the correct answer?
2. A student wrote: 603 - 245 = 442. What mistake did they make? What is the correct answer?
3. A student wrote: 489 + 234 = 613. What mistake did they make? What is the correct answer?
4. A student wrote: 700 - 358 = 458. What mistake did they make? What is the correct answer?
5. A student wrote: 367 + 85 = 1217. What mistake did they make? What is the correct answer?
6. A student wrote: 541 - 276 = 335. What mistake did they make? What is the correct answer?
7. A student wrote: 199 + 205 = 394. What mistake did they make? What is the correct answer?
8. A student wrote: 800 - 467 = 447. What mistake did they make? What is the correct answer?
9. Now solve these correctly: 475 + 368 = ___
10. Solve correctly: 902 - 547 = ___
11. Solve correctly: 284 + 559 = ___
12. Solve correctly: 650 - 283 = ___
Check Your Understanding
Question 1: What is the most common mistake when adding numbers with sums greater than 9 in a column?
Answer: Forgetting to carry to the next column
Question 2: When subtracting, what should you do if the top digit is smaller than the bottom digit?
Answer: Borrow 1 from the next column to the left
Question 3: Why is it important to line up numbers by place value?
Answer: So you add or subtract the correct digits (ones with ones, tens with tens, hundreds with hundreds)
Question 4: How can you check if your subtraction answer is correct?
Answer: Add your answer to the number you subtracted. You should get the original number.
Next Steps
- Always double-check your work, especially regrouping steps
- Use the opposite operation to verify your answers
- Take the Unit Quiz to test everything you have learned!