L2 · Subtracting with the standard algorithm (including decimals to hundredths)

Learning goal

“I can subtract whole numbers and decimals within 10 000 using the standard algorithm - regrouping from the place to the left when a column does not have enough - and check my answer 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.

Check by adding — adding the difference to the number you subtracted; if you get the starting number back, the subtraction is right.

Worked example

5,032 - 1,847. Step 1 (estimate): 5,000 - 1,800 is about 3,200. Step 2 (align and subtract right to left): ones 2 - 7 will not go - the ones need a trade. But the tens place is 0 and the hundreds place is 0 too, so the trade has to travel all the way from the thousands. Full chain: regroup 1 thousand into 10 hundreds (thousands 5 -> 4, hundreds 0 -> 10); regroup 1 of those hundreds into 10 tens (hundreds 10 -> 9, tens 0 -> 10); regroup 1 of those tens into 10 ones (tens 10 -> 9, ones 2 -> 12). Now every column can subtract. Step 3 (subtract): ones 12 - 7 = 5; tens 9 - 4 = 5; hundreds 9 - 8 = 1; thousands 4 - 1 = 3. Step 4: Difference = 3,185. Check by adding: 3,185 + 1,847 = 5,032. Estimate about 3,200 - reasonable.

Check yourself — explain it

Before subtracting, the ones column of 5,032 - 1,847 needed a chain of trades because...

Paired problem — example still visible

6,403 - 2,568 -> 3,835 (regroup chain through the 0 tens: ones 13 - 8 = 5; tens 9 - 6 = 3; hundreds needs a regroup from the thousands: 13 - 5 = 8; thousands 5 - 2 = 3)

Faded completion — last step is yours

"8,120 - 3,475: after regrouping, ones 10 - 5 = 5; tens 11 - 7 = 4; hundreds 0 - 4 needs a trade from thousands: 10 - 4 = 6; thousands 7 - 3 = ___" -> 4 (difference 4,645)

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