A student solves 432 - 175 and writes 343 as the answer. Which error explains this result?
AThey forgot to reduce the hundreds digit after borrowing
BThey subtracted the smaller digit from the larger in each column, reversing the direction when the bottom digit was bigger
CThey borrowed correctly but then added instead of subtracted
DThey regrouped in the wrong column
The student saw 2 < 5 in the ones column and did 5 - 2 = 3 instead of borrowing; in the tens column, 3 < 7, so they did 7 - 3 = 4; hundreds: 4 - 1 = 3 normally. Result: 343. The correct approach requires borrowing: ones column borrows (12 - 5 = 7, tens becomes 2); tens column borrows (12 - 7 = 5, hundreds becomes 3); hundreds: 3 - 1 = 2. Correct answer: 257.
Question 2 Multiple Choice
To solve 3,000 - 1,456, a student must borrow for the ones column. Which column can they actually borrow from?
AThe tens column — 3,000 has plenty of tens
BThey cannot solve this because there are no tens, hundreds, or ones to borrow from directly
CThe thousands column — borrow 1 thousand and convert it through hundreds and tens to get 10 ones
DSkip borrowing and round 3,000 to 2,999 first
In 3,000, the ones, tens, and hundreds are all zero — there is nothing to borrow from directly. The student must go to the thousands place (3) and borrow 1 thousand. That becomes 10 hundreds; then borrow 1 hundred, which becomes 10 tens; then borrow 1 ten, which becomes 10 ones. This chain converts value down three columns. The result: 3,000 - 1,456 = 1,544.
Question 3 True / False
When subtracting across zeros (like 4,000 - 1,234), you must borrow from the thousands place because the hundreds, tens, and ones places are all zero.
TTrue
FFalse
Answer: True
Correct. When the column you need to borrow from holds a 0, you must look further left until you find a nonzero digit. In 4,000, the hundreds (0), tens (0), and ones (0) have nothing to lend. You borrow 1 thousand and chain it down: 1,000 → 10 hundreds → 10 tens → 10 ones. Each step in the chain is just the standard regroup move repeated.
Question 4 True / False
The counting-up strategy for subtraction only works when the two numbers are close together.
TTrue
FFalse
Answer: False
Counting up — adding from the smaller number to the larger — works for any subtraction problem. For 4,003 - 1,257: count up from 1,257 by adding 3 (→1,260), then 40 (→1,300), then 700 (→2,000), then 2,000 (→4,000), then 3 (→4,003), totaling 2,746. The strategy avoids borrowing entirely and is especially useful for problems involving zeros.
Question 5 Short Answer
Explain what must happen when you try to subtract 4,001 - 2,345 and need to borrow for the ones column. Why can't you borrow from the tens place?
Think about your answer, then reveal below.
Model answer: You can't borrow from the tens place because it holds a 0 — there is nothing there. The hundreds place also holds 0. You must go to the thousands place (4), borrow 1 thousand (thousands becomes 3), convert it to 10 hundreds; then borrow 1 hundred (hundreds becomes 9), convert to 10 tens; then borrow 1 ten (tens becomes 9), convert to 10 ones. Now the ones column has 11 and the subtraction can proceed.
Regrouping across zeros requires a chain: you can only borrow from a column that has a nonzero digit. Each borrowed unit converts to 10 of the next smaller unit. This chain is the standard regroup move repeated until you find a nonzero digit — a key skill in multi-digit subtraction.