Use partial differences

For subtraction of whole numbers within 1,000, the learner decomposes the numbers into hundreds, tens, and ones, finds the corresponding place-value differences, and combines those partial results to determine the total difference. The reasoning includes regrouping when a place-value part of the minuend is too small, while maintaining equivalence between the decomposed and original quantities; more advanced algorithms, larger numbers, and generalized negative-number methods are not included.

Detailed Explanation: Use partial differences

To use partial differences, break each number into hundreds, tens, and ones. Then subtract each place-value part and combine the answers.

Example:

463-278

First decompose the numbers:

463=400+60+3

278=200+70+8

The ones part, $3$ , is too small to subtract $8$ . Regroup one ten as $10$ ones:

400+60+3=400+50+13

Now the tens part, $50$ , is too small to subtract $70$ . Regroup one hundred as $100$ tens:

400+50+13=300+150+13

The amount is still $463$ ; it is just written in a different way.

Now find the partial differences:

Hundreds: $300-200=100$
Tens: $150-70=80$
Ones: $13-8=5$

Combine the partial differences:

100+80+5=185

Therefore,

463-278=\boxed{185}

Learn by doing: Use partial differences

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Subtraction - Whole Number 3 x 2, With Borrow

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Use partial differences

Detailed Explanation: Use partial differences

Learn by doing: Use partial differences

Practice with unlimited practice problems

Practice:

Subtraction - Whole Number 3 x 2, With Borrow