A student solves 38 + 47. In the ones column, they get 8 + 7 = 15 and write '15' in the ones place. What should they do instead?
AWriting 15 is correct — the ones column can hold any sum
BWrite 5 in the ones place and carry 1 to the tens column, because 15 ones = 1 ten and 5 ones
CAdd only 5 and drop the 1 entirely
DStart over using a different method
The ones place can only hold a single digit (0–9). When the ones sum is 15, that's really 1 ten + 5 ones. You write the 5 in the ones place and carry the 1 ten over to the tens column, where it will be added with the other tens. Writing '15' in the ones column is a place-value error — it misrepresents the number.
Question 2 Multiple Choice
When you 'carry' a 1 to the tens column during addition, what does that 1 actually represent?
AOne leftover one that wasn't needed
BOne ten — because 10 ones were traded for 1 ten
CA correction for an addition mistake
DOne hundred, because you're moving to the next column
The carried digit is always 1 ten, not 1 one. When the ones sum reaches 10 or more, you've accumulated enough ones to form a complete ten. Trading 10 ones for 1 ten is an equal exchange — nothing is added or removed — and that 1 ten gets placed in the tens column. Understanding what the carried digit represents is what makes regrouping make sense rather than just being a mysterious rule.
Question 3 True / False
Regrouping in addition does not change the total — it just reorganizes the same amount in a different way.
TTrue
FFalse
Answer: True
Regrouping is an equal trade: 10 ones and 1 ten are exactly the same value. When you carry, you're converting between equivalent forms of the same number, not adding anything extra. The total remains the same — only the representation changes.
Question 4 True / False
When you carry a digit to the tens column, the total you are calculating gets larger because you are adding an extra number.
TTrue
FFalse
Answer: False
Carrying does not increase the total. The carried 1 represents a ten that was already part of the ones sum — it is being moved to the correct column, not added from outside the problem. Regrouping is a reorganization, not an addition.
Question 5 Short Answer
Explain in your own words why you 'carry' when adding two-digit numbers. What does the carried number actually represent?
Think about your answer, then reveal below.
Model answer: You carry because the ones column can only hold a single digit. When the ones sum reaches 10 or more, you have made a full ten. The carried '1' represents that one ten, which gets moved to the tens column to be counted with the other tens. It's like trading 10 pennies for 1 dime — the value is the same.
The key is understanding that the carried digit is not a bonus — it is part of the ones sum, just reorganized into its correct place-value column. This same logic extends to every column in addition: whenever a column's sum reaches 10, you trade 10 of that unit for 1 of the next larger unit and carry it left.