Why can you solve 34 + 52 by adding the ones digits and the tens digits separately?
ABecause the tens digits are always larger, so you save them for last
BBecause place value keeps tens and ones in separate groups that don't affect each other
CBecause that is just the rule for addition — always start with the ones
DBecause the ones column must finish before the tens column can have a value
Place value is the reason column-by-column addition works. A two-digit number is structured as tens plus ones — 34 is 30 + 4, and 52 is 50 + 2. Because tens and ones are separate place-value groups, you can add each group independently: 30 + 50 = 80, 4 + 2 = 6, giving 86. The columns are independent because they represent different-sized units. Starting with the ones is a helpful convention, but it isn't the fundamental reason the method works.
Question 2 Multiple Choice
A student writes 23 + 45 vertically. She adds the ones (3 + 5 = 8) and then the tens (2 + 4 = 6) and writes 68. Is she correct, and why?
ANo — she forgot to add the tens together before writing the answer
BYes — she correctly used place value to add each column independently
CNo — she should have added the tens column before the ones column
DYes — but only because the ones digits happen to be small numbers
Her method is exactly correct. 23 + 45 = (20 + 40) + (3 + 5) = 60 + 8 = 68. Because neither column sums to 10 or more, the result in each column is a single digit that fits directly in its place. What matters is that each column is treated independently, which is what place value makes possible. The order — ones first or tens first — doesn't affect the answer when there is no regrouping.
Question 3 True / False
In two-digit addition without regrouping, the ones digits must sum to 9 or less for the column method to work cleanly.
TTrue
FFalse
Answer: True
This is the defining condition of 'no regrouping.' When ones digits sum to 9 or less, the result is a single digit that fits in the ones place with nothing left over. If the sum were 10 or more, you'd need to trade 10 ones for 1 ten (regrouping), which would affect the tens column. As long as ones digits sum to 9 or less, the two columns stay independent and the method works without carrying.
Question 4 True / False
To add 47 + 31, you can add 4 + 3 = 7 (tens) and 7 + 1 = 8 (ones) to get 78, with no regrouping needed.
TTrue
FFalse
Answer: True
Yes — 47 + 31 requires no regrouping because the ones digits 7 + 1 = 8, which is less than 10. So the tens column gives 4 + 3 = 7 tens, and the ones column gives 7 + 1 = 8 ones, for an answer of 78. Each column adds independently and neither overflows. This is the key feature of no-regrouping problems: complete column independence.
Question 5 Short Answer
Why does place value make it possible to add two-digit numbers column by column?
Think about your answer, then reveal below.
Model answer: Place value separates a number into tens and ones — two independent groups with different-sized units. Because tens only affect tens and ones only affect ones, you can add each group separately and combine the results. 23 + 15 = (20 + 10) + (3 + 5) = 30 + 8 = 38. The columns don't interfere with each other as long as no column overflows past 9.
The entire logic of column addition rests on place value. A two-digit number isn't just a pair of digits — it's a structured quantity where the left digit counts tens and the right digit counts ones. Since tens and ones are separate units, adding them in groups is valid and exact. This is why aligning numbers vertically by place value is so important: it makes the column structure visible so you can add corresponding groups together correctly.