Three-Digit Subtraction Examples

Mental Math · Axiom Academy

EXAMPLE Subtracting 534 - 278 Left to Right Take the biggest place first, hold one running total, and let a place go negative — no borrowing anywhere. Work out 534 - 278 mentally using left-to-right subtraction — start at the hundreds, keep one running total, and let a place come out negative instead of borrowing. Nicely done — you subtracted two three-digit numbers from the left, and never borrowed once. Worth holding on to: Biggest place first: the hundreds settle the size of the answer before you look at a single small digit — everything after that moves the total by less than 100 . A place may come out negative: 30 - 70 = -40 is a deficit, not an error. Fold it into the running total instead of rewriting the number above it. Deficits stack, each one smaller: 534 - 278 runs 300 , then down 40 , then down 4 — the tens deficit moves the total ten times further than the ones deficit. Nothing gets rewritten: on paper both of these need two borrows before any subtracting starts. Here 534 and 812 are never touched — there is one moving part, the running total. The answers: 534 - 278 = 256 and 812 - 467 = 345 , and counting up confirms the second: 3 + 30 + 300 + 12 = 345 . Counting up, compensation and left-to-right subtraction all land on the same number. Left to right is the one that keeps working however many places you add — one running total, top to bottom.

This is the written version of the interactive lesson above. See the full Mental Math course.