Skill: Subtract multi-digit whole numbers

Explanation and Free Practice Resources

Subtraction of multi-digit whole numbers means finding how much one quantity differs from another, using place value to decompose a unit of one place into ten units of the next lower place when necessary, including across zeros. For typically up to six-digit numbers, the standard algorithm represents this regrouping accurately and can be checked through estimation or the inverse relationship with addition; decimals, negative numbers, and more generalized forms are outside this scope.

Detailed Explanation: Subtract multi-digit whole numbers

Line up the numbers by place value: ones under ones, tens under tens, and so on. Subtract from right to left. When a top digit is too small, regroup by trading 1 unit from the place to its left for 10 units in the current place.

Example:

52,004−17,628\begin{array}{r} 52{,}004\\ - 17{,}628\\ \hline \end{array}
  1. Ones: 44 is less than 88. Regroup. Since the tens and hundreds digits are 00, take 1 thousand from the 22 thousands. The 22 becomes 11. Turn the 00 hundreds into (10)(10) hundreds, then trade 1 hundred for (10)(10) tens, and trade 1 ten for (10)(10) ones. Now there are (14)(14) ones and 99 tens.
14−8=6 14-8=6
  1. Tens:
9−2=7 9-2=7
  1. Hundreds: There are 99 hundreds left.
9−6=3 9-6=3
  1. Thousands: 11 is less than 77, so regroup 1 ten thousand. The 55 becomes 44, and the 11 thousand becomes (11)(11) thousands.
11−7=4 11-7=4
  1. Ten-thousands:
4−1=3 4-1=3

So,

52,004−17,62834,376\begin{array}{r} 52{,}004\\ - 17{,}628\\ \hline 34{,}376 \end{array}

Check by addition:

17,628+34,376=52,00417{,}628+34{,}376=52{,}004

Therefore, (52,004−17,628=34,376)(52{,}004-17{,}628=\boxed{34{,}376}).

Learn by doing: Subtract multi-digit whole numbers

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Subtraction - Whole Number 4 x 3, With Borrow


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