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Subtract using regrouping

Subtraction with regrouping involves interpreting place value so that a unit in one place can be decomposed into 10 units in the next smaller place, including when one or more intervening places contain zero. The learner understands that this preserves the minuend’s value and supports finding differences between multi-digit whole numbers, while avoiding the misconception that regrouping changes the number rather than its representation; operations with fractions, algebraic symbols, or unrestricted number systems are outside this scope.

Detailed Explanation: Subtract using regrouping

Regrouping means rewriting a place-value unit as 10 units in the next smaller place. The number’s value does not change; only its representation changes.

Example:

5002− 2786\begin{array}{r} 5002\\ -\ 2786\\ \hline \end{array}

Start in the ones place. Since 22 is less than 66, regroup.

  1. There are no tens or hundreds to borrow, so borrow 11 thousand from the 55 thousands.
    This leaves 44 thousands and creates 1010 hundreds.

  2. Borrow 11 hundred from those 1010 hundreds.
    This leaves 99 hundreds and creates 1010 tens.

  3. Borrow 11 ten from those 1010 tens.
    This leaves 99 tens and creates 1010 ones.

Now 50025002 is represented as 44 thousands, 99 hundreds, 99 tens, and 1212 ones. Its value is still 50025002.

Subtract each place:

4 9 9 12− 2 7 8 62 2 1 6\begin{array}{r} 4\ 9\ 9\ 12\\ -\ 2\ 7\ 8\ 6\\ \hline 2\ 2\ 1\ 6 \end{array}
  • Ones: 12−6=612-6=6
  • Tens: 9−8=19-8=1
  • Hundreds: 9−7=29-7=2
  • Thousands: 4−2=24-2=2

Therefore,

5002−2786=2216.5002-2786=\boxed{2216}.

Learn by doing: Subtract using regrouping

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    Subtraction - Whole Number 4 x 4, With Borrow

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