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Subtract 3-digit numbers with regrouping

Whole-number subtraction within 1,000 is understood as comparing quantities and decomposing one hundred or one ten into ten units of the next place when a digit in the minuend is too small; this preserves value while making the difference computable. The standard vertical method connects to base-ten representations, expanded notation, and equations, including cases requiring regrouping across a zero; decimals, negative numbers, and larger or more general numbers are outside this scope.

Detailed Explanation: Subtract 3-digit numbers with regrouping

To subtract 3-digit numbers, line up the hundreds, tens, and ones. Start subtracting in the ones place.

Example:

503− 278\begin{array}{r} 503\\ -\ 278\\ \hline \end{array}

  1. Ones: We need to subtract 88 ones from 33 ones. Since 33 is too small, regroup.

    • There are no tens to trade, so trade 11 hundred for 1010 tens.
    • Now 55 hundreds becomes 44 hundreds, and there are 1010 tens.
    • Trade 11 of those tens for 1010 ones. Now there are 99 tens and 1313 ones.

    Subtract the ones:

13−8=513-8=5

  1. Tens: Subtract the tens:

9−7=29-7=2

  1. Hundreds: Subtract the hundreds:

4−2=24-2=2

So,

4 9 135 0 3− 2 7 82 2 5\begin{array}{r} 4\ 9\ 13\\ 5\ 0\ 3\\ -\ 2\ 7\ 8\\ \hline 2\ 2\ 5 \end{array}

Therefore,

503−278=225503-278=\boxed{225}

Regrouping does not change the number’s value: 503503 is still 44 hundreds, 99 tens, and 1313 ones.

Learn by doing: Subtract 3-digit numbers with regrouping

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    Subtraction - Whole Number 3 x 3, With Borrow

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