L3 · Multiplying 3-Digit by 1-Digit: Standard Algorithm

Learning goal

“I can multiply a 3-digit number by a 1-digit number with the standard algorithm - multiplying ones, tens, then hundreds, carrying (regrouping) whenever a column product is 10 or more - and I can check my answer with a quick estimate.”

Standard algorithm — the conventional step-by-step written method: same moves every time, ones column first, working right to left.

Carry (regroup) — when a column product is 10 or more, write the ones digit and carry the tens digit to the next column. In 7 x 3 = 21: write 1, carry 2.

Digit — a single symbol 0-9. The number 247 has three digits: 2, 4 and 7.

Worked example

247 x 3. First, estimate: 247 is about 250, and 250 x 3 = 750. The answer should land near 750. Step 1 (ones): 7 x 3 = 21. Write 1 in the ones place; carry the 2 (it is 2 TENS) above the tens column. Step 2 (tens): 4 x 3 = 12, then ADD the carried 2: 12 + 2 = 14. Write 4; carry 1. Step 3 (hundreds): 2 x 3 = 6, then add the carried 1: 6 + 1 = 7. Write 7. Answer: 741. Estimate said about 750 - reasonable. Say it plainly: the algorithm is L2's partial products in a tighter coat. The "carry" is just a partial product's tens digit moving to its proper column - nothing is magic, and the carried digit must be ADDED after multiplying the next column, never before.

Check yourself — explain it

After multiplying the tens column, we add the carried digit because...

Paired problem — example still visible

165 x 4 -> ones: 5 x 4 = 20, write 0 carry 2; tens: 6 x 4 = 24 + 2 = 26, write 6 carry 2; hundreds: 1 x 4 = 4 + 2 = 6 -> 660.

Faded completion — last step is yours

"384 x 2: ones 4 x 2 = 8; tens 8 x 2 = 16, write 6 carry 1; hundreds 3 x 2 = 6, plus the carried 1 = ___." -> 7 - the product is 768

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

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