4-digit × 2-digit

1Summary 重點摘要

1234 × 23 = 28382. Multiply in parts, then add.

2Vocabulary cards Vocabulary

3Step by step Steps

1. Step 1: Set out the vertical formWrite the multiplicand 1234 on top and the multiplier 23 below, with the ones digits aligned, then draw a line under the multiplier. Good alignment keeps every digit in its correct column for all the steps that follow.
2. Step 2: Multiply by the ones digitMultiply 1234 by the ones digit 3: 1234 × 3 = 3702. Work from the ones column, carrying whenever a product reaches ten. This line is the first partial product.
3. Step 3: Multiply by the tens digitMultiply 1234 by the tens digit 2, which really means 1234 × 20 = 24680. Start this row one place to the left, so its last digit lines up with the tens column.
4. Step 4: Add the partial productsAdd the two partial products: 3702 + 24680 = 28382. Keep the columns aligned and carry as usual while adding. The total is the answer to 1234 × 23.
5. Step 5: Handle the carriesWhen one column reaches ten or more, write the ones digit and carry: 4 × 3 = 12, so write 2 and carry 1 into the tens column. Every missed carry makes the answer wrong.
6. Step 6: Estimate to checkRound first: 1234 ≈ 1200 and 23 ≈ 20, so the answer should be near 1200 × 20 = 24000. The exact answer 28382 is close, so the calculation looks right.
7. Step 7: Avoid common errorsThe three usual mistakes are not shifting the tens row one place left, dropping a carry, and misaligning the columns when adding. Write carries small and keep the digits neat.

4Diagrams Diagrams

5Worked example Example

6Common mistakes Mistakes

7Quick check Quick check

8Recap Recap

• 4-digit × 2-digit: multiply in two parts (ones, tens), then add.
• Tens row shifts left (ones align to tens).
• Carry when sum ≥ 10.
• Estimate to check.
• Align digits carefully.