4-digit multiplication

1Summary 重點摘要

1234 × 3 = 3702. Multiply digit by digit, carry.

2Vocabulary cards Vocabulary

3Step by step Steps

1. Part 1: Set up the column formFor 1234 × 3, write 1234 on top and 3 below, with ones under ones. A tidy column form keeps the places straight, and this is the first step of multi-digit multiplication. Why line up? Each digit multiplies within its own place, and a slipped digit changes the product completely. Start multiplying from the ones digit and move up place by place. Take care that the one-digit multiplier sits directly under the ones with empty space before it, never drifting under the tens or the hundreds.
2. Part 2: Ones firstMultiply the ones: 4 × 3 = 12. Twelve fills one whole ten, so write 2 in the ones place and carry 1 to the tens. The carried 1 means one ten and must be added to the tens result. Handling the ones first gives the next places their start. Why start at the ones? Carries only travel upward, so working from the low places means nothing already written gets changed. Take care that the ones place holds the 2 from inside 12, not the 12; one place holds one digit, and the extra ten must move up.
3. Part 3: Each digit plus the carryTens: 3 × 3 = 9, plus the carried 1 makes 10, so write 0 and carry 1 to the hundreds. Hundreds: 2 × 3 = 6, plus the carried 1 makes 7. Thousands: 1 × 3 = 3. Reading the digits gives 3702. Never forget to add each carry, for this is where multi-digit multiplication slips most easily. Take care to note each carry in small writing beside the columns while working, so none is lost; after finishing, check every place once more for a carry left unadded, and the double check keeps everything safe.
4. Part 4: The full column formWrite the work as a column: 1234 on top, 3 below, then a line, and after working, 3702 under the line. The line is like a gate; below it lives the answer. Practise keeping the columns neat so that checking is easy. Take care to draw the line straight and to align the digits of both rows in their columns; in scrawled, slipped digits even you cannot find the error afterwards, while a tidy column is itself a checking tool, a habit well worth building.
5. Part 5: Multiplying by 10 and 100345 × 10 = 3450, one zero appended at the end; 345 × 100 = 34500, two zeros appended. Multiplying by 10 or 100 shifts every digit's value one or two places to the left, a rule of place value. With this rule, such products can be worked out mentally. Why do the digits shift? 10 is one ten, so multiplying by 10 promotes every digit one place. Take care that 345 × 100 is 34500 and the zeros must not be miscounted; as many zeros as the multiplier carries at its end are appended to the product, no more and no fewer.
6. Part 6: Word problemA school has 4 floors with 306 seats on each; how many seats in all? Compute 306 × 4: ones 6 × 4 = 24, write 4 and carry 2; tens 0 × 4 + 2 = 2; hundreds 3 × 4 = 12. The answer is 1224 seats. Even a 0 in the middle takes part in the work: 0 × 4 gives 0, yet the carried 2 must still be added. Take care not to jump from the ones straight to the hundreds and skip the tens, which would wrongly give 144; every place is multiplied in order, the 0 included, and not one place may be skipped.

4Diagrams Diagrams

5Worked example Example

6Common mistakes Mistakes

7Quick check Quick check

8Recap Recap

• Column multiplication starts at the ones digit
• At ten, write the ones and carry the tens left
• Each next digit adds the carry before multiplying
• ×10 appends one 0; ×100 appends two
• Check the size with an estimate afterwards