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Subtract multi-digit whole numbers

Subtraction of multi-digit whole numbers involves finding the difference between quantities by coordinating corresponding place-value units, decomposing one unit of a higher place when the minuend’s digit is insufficient, including regrouping across one or more zeros. Place-value notation and estimation clarify why the standard algorithm preserves value and help detect errors, supporting later work with decimal computation; the scope is whole numbers, not negative numbers, decimals, or algebraic subtraction.

Detailed Explanation: Subtract multi-digit whole numbers

To subtract multi-digit whole numbers, line up digits by place value: ones under ones, tens under tens, hundreds under hundreds, and so on. Start at the ones place and move left. If the top digit is too small, regroup one unit from the place to its left.

Example:

50,302−17,845\begin{array}{r} 50{,}302\\ - 17{,}845\\ \hline \end{array}
  1. Ones: We cannot subtract 55 from 22. Regroup one ten. Since the tens digit is 00, regroup from the hundreds:

    • The 33 hundreds becomes 22 hundreds.

    • The 00 tens becomes 1010 tens.

    • Regroup one of those tens as 1010 ones. Now there are 1212 ones and 99 tens.

12−5=712-5=7

  1. Tens:

9−4=59-4=5
  1. Hundreds: We cannot subtract 88 from 22. Regroup one thousand. Since the thousands digit is 00, regroup from the ten-thousands:

    • The 55 ten-thousands becomes 44 ten-thousands.

    • The 00 thousands becomes 1010 thousands.

    • Regroup one thousand as 1010 hundreds. Now there are 1212 hundreds and 99 thousands.

12−8=412-8=4

  1. Thousands:

9−7=29-7=2

  1. Ten-thousands:

4−1=34-1=3

Therefore,

50,302−17,84532,457\begin{array}{r} 50{,}302\\ - 17{,}845\\ \hline 32{,}457 \end{array}

The difference is 32,457\boxed{32{,}457}. An estimate confirms the answer:

50,000−18,000=32,00050{,}000-18{,}000=32{,}000

Since 32,45732{,}457 is close to 32,00032{,}000, the answer is reasonable.

Learn by doing: Subtract multi-digit whole numbers

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    Subtraction - Whole Number - Across Zeros

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