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.
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​​
Ones:4 is less than 8. Regroup. Since the tens and hundreds digits are 0, take 1 thousand from the 2 thousands. The 2 becomes 1. Turn the 0 hundreds into (10) hundreds, then trade 1 hundred for (10) tens, and trade 1 ten for (10) ones. Now there are (14) ones and 9 tens.
14−8=6
Tens:
9−2=7
Hundreds: There are 9 hundreds left.
9−6=3
Thousands:1 is less than 7, so regroup 1 ten thousand. The 5 becomes 4, and the 1 thousand becomes (11) thousands.
11−7=4
Ten-thousands:
4−1=3
So,
52,004−17,62834,376​​
Check by addition:
17,628+34,376=52,004
Therefore, (52,004−17,628=34,376​).
Learn by doing: Subtract multi-digit whole numbers
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