Common Mistakes
Learn
Understanding common mistakes helps you avoid them. In this lesson, we will look at the most frequent errors students make when multiplying multi-digit numbers and learn how to prevent them.
Mistake 1: Forgetting to Add Placeholder Zeros
When multiplying by the tens digit, you must add a zero in the ones place before writing your partial product.
Wrong: For 23 x 14, some students write:
23 x 4 = 92
23 x 1 = 23 (missing the zero!)
92 + 23 = 115 (incorrect)
Right:
23 x 4 = 92
23 x 10 = 230 (the 1 in 14 is in the tens place)
92 + 230 = 322 (correct)
Mistake 2: Carrying Errors
When carrying numbers, write them small above the correct column and remember to add them.
Example: 47 x 6
7 x 6 = 42 (write 2, carry 4)
4 x 6 = 24, plus the carried 4 = 28
Answer: 282
Mistake 3: Misaligning Columns
Keep your work neat! Digits must line up properly, or you will add incorrectly when combining partial products.
Mistake 4: Forgetting to Add All Partial Products
When multiplying by a 3-digit number, you have three partial products to add. Do not forget any of them!
Mistake 5: Basic Multiplication Fact Errors
Multi-digit multiplication depends on knowing your multiplication facts. Review any facts you are unsure about.
Examples
Spot the Error #1
Problem: A student calculated 56 x 23 = 1,108. Is this correct?
Check:
- 56 x 3 = 168
- 56 x 20 = 1,120
- 168 + 1,120 = 1,288
The correct answer is 1,288. The student likely made an error adding the partial products.
Spot the Error #2
Problem: A student calculated 145 x 12 = 1,450. Is this correct?
Check:
- 145 x 2 = 290
- 145 x 10 = 1,450
- 290 + 1,450 = 1,740
The correct answer is 1,740. The student forgot to add the first partial product (290).
Practice
Find the errors in these problems. Click to reveal the correct answer and explanation.
Question 1: A student says 34 x 21 = 614. What is the correct answer?
Correct Answer: 714
Solution: 34 x 1 = 34, and 34 x 20 = 680. Then 34 + 680 = 714. The student likely made a carrying error.
Question 2: A student says 52 x 13 = 572. Is this correct? If not, what is the right answer?
Incorrect. Correct Answer: 676
Solution: 52 x 3 = 156, and 52 x 10 = 520. Then 156 + 520 = 676.
Question 3: A student calculated 78 x 45 as follows: 78 x 5 = 390, 78 x 4 = 312. Then 390 + 312 = 702. What did they do wrong?
Correct Answer: 3,510
The student forgot the placeholder zero. It should be: 78 x 5 = 390, and 78 x 40 = 3,120. Then 390 + 3,120 = 3,510.
Question 4: What is 63 x 27? Show your work.
Answer: 1,701
Solution: 63 x 7 = 441, and 63 x 20 = 1,260. Then 441 + 1,260 = 1,701.
Question 5: A student says 125 x 16 = 1,500. Check their work.
Incorrect. Correct Answer: 2,000
Solution: 125 x 6 = 750, and 125 x 10 = 1,250. Then 750 + 1,250 = 2,000. The student may have calculated 125 x 12 instead.
Question 6: What common mistake might lead someone to get 84 x 32 = 2,288 instead of the correct answer?
Correct Answer: 2,688
Solution: 84 x 2 = 168, and 84 x 30 = 2,520. Then 168 + 2,520 = 2,688. The student may have made a carrying error in the second partial product (84 x 30).
Question 7: Calculate 256 x 14 carefully, showing your work.
Answer: 3,584
Solution: 256 x 4 = 1,024, and 256 x 10 = 2,560. Then 1,024 + 2,560 = 3,584.
Question 8: A student forgot a partial product and got 324 x 23 = 6,480 + 324 = 6,804. What is the correct answer?
Correct Answer: 7,452
Solution: 324 x 3 = 972, and 324 x 20 = 6,480. Then 972 + 6,480 = 7,452. The student used the wrong partial product (324 instead of 972).
Question 9: Estimate first, then calculate: 48 x 52. Is your answer reasonable?
Answer: 2,496
Estimate: 50 x 50 = 2,500. Actual: 48 x 2 = 96, and 48 x 50 = 2,400. Then 96 + 2,400 = 2,496. This is very close to our estimate, so it is reasonable.
Question 10: What is 375 x 24? Use estimation to check your answer.
Answer: 9,000
Estimate: 400 x 25 = 10,000. Actual: 375 x 4 = 1,500, and 375 x 20 = 7,500. Then 1,500 + 7,500 = 9,000. Our estimate was close, so 9,000 is reasonable.
Check Your Understanding
Before moving on, make sure you can:
- Identify the five common mistakes in multi-digit multiplication
- Use placeholder zeros correctly
- Keep columns aligned when working vertically
- Double-check carrying
- Use estimation to verify your answers
Next Steps
- Review any concepts that felt challenging
- Move on to the Unit Quiz when ready
- Return to practice problems periodically for review