Questions: Multi-Digit Addition and Subtraction

Question 1

In the addition problem 27 + 15, you get 12 in the ones column. What do you do with this result?

• A. Write '12' in the ones place of the answer
• B. Ignore the extra digit and write '2' in the ones place
• C. Regroup: write '2' in the ones place and carry '1' to the tens column
• D. Start over — getting 12 in the ones column means you made an error

Answer: (C)

The ones place can only hold a single digit (0–9). When you get 12 ones, that means you have 1 group of ten and 2 leftover ones. You regroup by writing 2 in the ones place and 'carrying' (adding) 1 to the tens column. This regrouping is not a trick — it is the rule that 10 ones equals 1 ten, applied mechanically.

Question 2

A student sets up 35 + 214 vertically and aligns the leftmost digits: the 3 in 35 is placed under the 2 in 214. What is wrong?

• A. Nothing — you always align the leftmost digits when adding
• B. The numbers are misaligned; the 5 in 35 should be under the 4 in 214, aligning by the ones place
• C. 35 is too small to add to 214 — you need numbers of equal length
• D. The student should convert 35 to 035 before beginning

Answer: (B)

Numbers must be aligned by place value — ones under ones, tens under tens, hundreds under hundreds. The 5 in 35 is in the ones place; it belongs under the 4 in 214 (also ones). The 3 in 35 is in the tens place; it belongs under the 1 in 214 (also tens). If you align leftmost digits instead, you end up adding tens to hundreds, which produces a completely wrong answer.

Question 3

In subtraction with borrowing, you are trading 1 ten for 10 ones, which keeps the total value of the number the same.

• T. True
• F. False

Answer: True

Borrowing is a trade, not a loss. When you take 1 ten from the tens column and convert it to 10 ones in the ones column, the total value of the number is unchanged (1 ten = 10 ones). You are just repackaging the same quantity into smaller units so you can subtract. This is the reverse of what regrouping in addition does (trading 10 ones for 1 ten).

Question 4

When adding multi-digit numbers using the standard algorithm, you can start from either the left or the right and get the same result.

• T. True
• F. False

Answer: False

The standard addition algorithm requires working right to left (ones first, then tens, then hundreds) because regrouping goes from smaller to larger place values. If you start from the left, you cannot yet know whether a carry will come in from the right, so you cannot correctly fill in the tens or hundreds columns until you have processed the ones. Starting from the left only works if you come back and adjust, which defeats the purpose.

Question 5

Why must you align numbers by place value before adding or subtracting? What goes wrong if you don't?

Model answer: Place value alignment ensures that you are adding digits that represent the same-sized units together: ones with ones, tens with tens, hundreds with hundreds. If you misalign, you end up adding, say, tens to hundreds — combining units of different sizes — which produces a nonsense result. For example, adding 35 and 214 with leftmost alignment would put the 3 (30) under the 2 (200), yielding 230 + 14 + 5 = a completely wrong answer.

Alignment is the foundation of the algorithm, not a cosmetic convention. The entire logic of column-by-column arithmetic depends on each column holding digits with the same place value. This is why the vertical format matters — it is a visual tool for enforcing alignment.