The learner understands subtraction of multi-digit whole numbers, typically through 1,000,000, as a place-value operation in which one unit of a place may be decomposed into ten units of the next lower place when a digit is insufficient. The standard algorithm records this regrouping across aligned places, including across zeros, and its results can be interpreted and checked using the inverse relationship between addition and subtraction; decimal subtraction, negative numbers, and more generalized algorithms are outside this scope.
Detailed Explanation: Subtract using the standard algorithm
Line up the numbers by place value, with ones under ones, tens under tens, and so on. Start subtracting at the ones place and move left.
Example:
−​52​07​08​04​06​​
The ones column has 0−6, so regroup. There are zeros in the tens, hundreds, and thousands places, so regroup across them:
Take 1 ten-thousand from the 5 ten-thousands. This leaves 4 ten-thousands.
The 1 ten-thousand becomes 10 thousands. Give 1 thousand to the hundreds, leaving 9 thousands.
The 1 thousand becomes 10 hundreds. Give 1 hundred to the tens, leaving 9 hundreds.
The 1 hundred becomes 10 tens. Give 1 ten to the ones, leaving 9 tens.
The ones become 10 ones.
Now subtract each place from right to left:
−​422​972​981​945​1064​​
So,
50,000−27,846=22,154.
Check by adding the difference to the number subtracted:
22,154+27,846=50,000.
Learn by doing: Subtract using the standard algorithm
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