A student solves 456 + 278 step by step. They correctly carry a 1 from the tens column but forget to add it when computing the hundreds column. What is wrong with their final answer?
AThe ones digit is wrong.
BThe tens digit is wrong.
CThe hundreds digit is 1 too small — one carried hundred was never added in.
DNothing — the carried digit from the tens column has no effect on the hundreds column.
When the tens-column sum (including any carry from the ones) reaches 10 or more, you carry a 1 to the hundreds column. If you forget to add that carry in the hundreds column, your hundreds digit is 1 less than it should be, making the entire answer 100 short. This is the most common error in three-digit addition: the carry is generated but then dropped.
Question 2 Multiple Choice
In the problem 364 + 278, after adding the ones column (4 + 8 = 12), what does the carried '1' above the tens column actually represent?
AA reminder note with no specific value.
BOne extra ten — because 12 ones equals 1 ten and 2 ones, and that ten must move to the tens column.
COne extra hundred that needs to be added at the end.
DAn instruction to add 1 to every remaining column.
When you add 4 + 8 = 12, you have 12 ones. That equals 1 ten and 2 ones. You record the 2 ones in the ones column and send the 1 ten to the tens column, where it belongs. The carried digit is a real place-value object — not an abstract bookkeeping mark. Understanding this is what lets you extend the algorithm to any number of columns.
Question 3 True / False
A three-digit addition problem can require regrouping in both the ones column and the tens column.
TTrue
FFalse
Answer: True
When the ones-column sum is 10 or more, you carry a ten. When the tens-column sum (including any carry from ones) is also 10 or more, you carry a hundred into the hundreds column. Problems like 364 + 278 require two regroupings. Each column is evaluated independently — one carry does not prevent another.
Question 4 True / False
If the ones column in a three-digit addition problem does not require regrouping, then the tens column will not require regrouping either.
TTrue
FFalse
Answer: False
The columns are independent. Whether the tens column requires regrouping depends on its own digit sums plus any carry from ones — not on what happened in the ones column. Even if the ones column sums cleanly (e.g., 2 + 3 = 5), the tens column could still sum to 10 or more (e.g., 7 + 8 = 15). You must evaluate each column on its own.
Question 5 Short Answer
What does the carried digit actually represent in three-digit addition, and why must it be included in the next column?
Think about your answer, then reveal below.
Model answer: The carried digit represents a real place-value group — a ten (or a hundred) — that was too large to stay in the current column. For example, if the ones column gives 14, that is 1 ten and 4 ones. The 4 stays in the ones place and the 1 ten must move left to the tens column because that is where tens belong. If you skip the carry, your answer is missing an entire group of ten (or hundred), making it 10 or 100 less than it should be.
Students who treat the carry as a memorized rule often forget it or misplace it. Students who understand it as a real place-value group naturally carry it to the correct column and notice when they've forgotten — because the answer feels too small.