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Subtract multi-digit whole numbers

Subtracting multi-digit whole numbers involves interpreting each digit by place value and decomposing one unit of a place into ten units of the next lower place when necessary, including regrouping across zeros. Accurate computation is connected to estimation, number-line or place-value representations, and checking with addition, helping distinguish subtraction from digit-by-digit procedures that ignore place value. The scope is whole-number subtraction only; negative numbers, decimals, and algebraic generalizations are not included.

Detailed Explanation: Subtract multi-digit whole numbers

Line up the numbers by place value, with ones under ones, tens under tens, and so on. Subtract from right to left. When the top digit is too small, regroup by decomposing 1 unit of the next place into 10 units of the current place.

Example:

50,302−17,846\begin{array}{r} 50{,}302\\ -17{,}846\\ \hline \end{array}

  1. Ones: 22 is too small to subtract 66. Regroup across the zeros:

    • Take 11 hundred from 33 hundreds, leaving 22 hundreds.
    • This gives (10)(10) tens. Take 11 ten and give it to the ones, making (12)(12) ones.
    • The tens place now has 99 tens.

    Subtract: (12−6=6)(12-6=6).

  2. Tens: (9−4=5)(9-4=5).

  3. Hundreds: 22 is too small to subtract 88. Regroup across the zero thousands:

    • Take 11 ten-thousand from 55 ten-thousands, leaving 44.
    • This makes (10)(10) thousands. Give 11 thousand to the hundreds, leaving 99 thousands.
    • The hundreds become (12)(12).

    Subtract: (12−8=4)(12-8=4).

  4. Thousands: (9−7=2)(9-7=2).

  5. Ten-thousands: (4−1=3)(4-1=3).

Therefore,

50,302−17,84632,456\begin{array}{r} 50{,}302\\ -17{,}846\\ \hline 32{,}456 \end{array}

You can estimate to check: (50,000−18,000≈32,000)(50{,}000-18{,}000\approx32{,}000), so (32,456)(32{,}456) is reasonable. Check exactly by adding:

32,456+17,846=50,302.32{,}456+17{,}846=50{,}302.

Learn by doing: Subtract multi-digit whole numbers

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    Subtraction - Whole Number - Across Zeros

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