Long multiplication (age 10+)
Fluently multiply multi-digit whole numbers (up to 4 digits by 2 digits) using the formal written method of long multiplication
What a learner can do afterwards
- Correctly compute 2,463 × 37 using long multiplication
- Explain each partial product in a long multiplication and why they are added
- Multiply a four-digit number by a two-digit number without procedural errors
1 · Read
You already know how long multiplication works: multiply by the units digit, multiply by the tens digit, then add the two rows. Now you'll use those same steps on bigger numbers, including four digits multiplied by two digits.
A printer fills 37 boxes with 2,463 leaflets in each box: 2,463 x 37. First, multiply 2,463 x 7 to get 17,241. Next, multiply 2,463 x 30 to get 73,890, shifting this row one place left because it stands for tens, not units. Add 17,241 and 73,890 to get 91,131.
The reason you add the two rows is that 37 is really 30 plus 7. So 2,463 x 37 is the same as 2,463 x 30 plus 2,463 x 7. Each partial product is one piece of the full answer. A tens row without its placeholder zero is ten times too small.
With four-digit numbers it's easy to misalign a column or forget the placeholder zero on the tens row. Line up each column carefully and check that your tens row ends in a zero before you add.
Like 34 x 27, split the second number into tens and units, multiply each part, shift the tens row left, then add both rows for your final answer.
The rewritten readings were written for this dataset.
2 · Watch
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Where it sits
18 questions wait behind this lesson, each with its answer explained. Every answer feeds the sky: stars light as they are learned, and dim when it is time to come back.