In solving 300 − 154, after borrowing from the hundreds because the tens digit is 0, what value should appear in the tens column before performing the tens subtraction?
A10 — borrowing one hundred gives ten tens, and the tens column now holds 10
B9 — after giving one of those tens to the ones column, the tens column holds 9
C0 — the tens column started at 0 and nothing changed
D1 — because exactly one ten was borrowed from the hundreds
Borrowing across a zero requires two steps. First, borrow from the hundreds: the hundreds drop by 1 and the tens gain 10. Second, borrow one of those tens for the ones column: the tens drop from 10 to 9, and the ones gain 10. The tens column ends up with 9, not 10. Students who skip the second step and leave 10 in the tens column get the wrong answer in the tens subtraction.
Question 2 Multiple Choice
How can you verify that 783 − 248 = 535 is correct without redoing the subtraction?
ACheck that each digit in 535 is smaller than the corresponding digit in 783
BAdd 535 + 248 and confirm the result equals 783
CSubtract 535 − 248 and check that the result is 0
DRound both numbers to the nearest hundred and compare
Subtraction and addition are inverse operations — subtracting a number and then adding it back should return you to the original. So result + subtrahend = minuend is always true for a correct subtraction. Adding 535 + 248 = 783 confirms the answer. This strategy works for numbers of any size and reinforces the relationship between the two operations.
Question 3 True / False
When solving a problem like 400 − 163, you can borrow directly from the tens column to handle the ones column because borrowing is typically done from the column immediately to the left.
TTrue
FFalse
Answer: False
When the tens digit is 0, there is nothing to borrow from the tens column. You must first borrow from the hundreds: hundreds decrease by 1 and tens gain 10. Then borrow one of those tens for the ones column, leaving the tens with 9. Blindly going to the adjacent column without checking whether it has anything to lend is the most common source of error in three-digit subtraction.
Question 4 True / False
Adding your subtraction answer back to the number you subtracted should always equal the original starting number — this is a reliable check for any subtraction.
TTrue
FFalse
Answer: True
Correct. If you computed A − B = C, then C + B must equal A. This is the inverse relationship between subtraction and addition. It works for any numbers regardless of size, and it catches almost all arithmetic errors including regrouping mistakes and column mix-ups. The check is most valuable precisely for the problems where errors are most likely — those involving borrowing.
Question 5 Short Answer
Why does the tens digit become 9 (not 10) after borrowing across a zero in a problem like 500 − 247?
Think about your answer, then reveal below.
Model answer: When you borrow from the hundreds, the tens column temporarily receives 10. But then you must immediately borrow one of those tens for the ones column. That removes one ten from the tens, leaving 10 − 1 = 9. Students who forget this second step write 10 in the tens column and then subtract incorrectly.
The two-step nature of borrowing across a zero is what makes it the trickiest case in three-digit subtraction. Step 1: borrow from hundreds (tens gets 10). Step 2: borrow from tens for ones (tens goes from 10 to 9, ones get 10). Writing it out explicitly — showing the tens as 9 after both steps — prevents the most common error.