L2 · Subtracting with standard algorithms (including decimals)

Learning goal

“I can subtract whole numbers and decimals within 1,000,000 with the standard algorithm - regrouping across zeros when I must - and check every difference by adding it back.”

Difference — the result of a subtraction.

Regroup (borrowing) — in subtraction, trading 1 of a place for 10 of the place to its right so a column has enough to subtract.

Align — to line up digits of the same place value; with decimals, the decimal points line up first.

Inverse check — using the opposite operation to test an answer: difference + subtracted number must rebuild the starting number.

Worked example

600,000 - 274,836. Step 1 (estimate): 600,000 - 275,000 is about 325,000. Step 2 (start at the ones): ones 0 - 6 won't go. The tens, hundreds, thousands and ten-thousands are all 0 - nobody can lend until the chain reaches the 6. Step 3 (run the chain): 6 hundred-thousands -> 5, lending 10 ten-thousands; one of those becomes 9 after lending 10 thousands onward; the chain continues until the number reads 5 | 9 | 9 | 9 | 9 | 10. Now subtract: ones 10 - 6 = 4; tens 9 - 3 = 6; hundreds 9 - 8 = 1; thousands 9 - 4 = 5; ten-thousands 9 - 7 = 2; hundred-thousands 5 - 2 = 3. Step 4: difference = 325,164. Inverse check: 325,164 + 274,836 = 600,000, and the estimate agrees.

Check yourself — explain it

Zeros in the middle become 9s during regrouping because...

Paired problem — example still visible

500,000 - 186,742 = ___ -> 313,258

Faded completion — last step is yours

"400,000 - 123,579: after the chain, the columns read 3 | 9 | 9 | 9 | 9 | 10; subtracting gives 2 | 7 | 6 | 4 | 2 | ___" -> 1 (difference 276,421)

Ready to practise?

10 scored questions with a 3-rung hint ladder. Mastery needs 8/10 plus both gate questions.

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