Long multiplication
Multiply a whole number of up to four digits by a one-digit number, and multiply two two-digit numbers, using formal written methods including long multiplication; illustrate with area models
What a learner can do afterwards
- Calculate 2,347 × 6 using formal written layout
- Calculate 34 × 27 using long multiplication
- Draw an area model for 45 × 23 and connect to the written method
1 · Read
You already know how to multiply and how to split a rectangle into an area model. Now you'll use both ideas to multiply bigger numbers: a four-digit number by a one-digit number, and two two-digit numbers, all set out neatly in columns.
Line up 2,347 above 6, ones under ones. Multiply the ones: 6 x 7 = 42. Write 2, carry 4. Multiply the tens: 6 x 4 = 24, plus the carried 4 makes 28. Write 8, carry 2. Multiply the hundreds: 6 x 3 = 18, plus 2 makes 20. Write 0, carry 2. Multiply the thousands: 6 x 2 = 12, plus 2 makes 14. Write 14. Reading the digits together gives 14,082.
Now try two two-digit numbers: 34 x 27. First multiply 34 by the ones digit of 27, which is 7: 34 x 7 = 238. Write that row down. Next multiply 34 by the tens digit of 27, which is really 20. Write a placeholder 0, then work out 34 x 2 = 68, giving 680. Add the two rows: 238 + 680 = 918.
Keep your digits lined up in neat columns, ones under ones and tens under tens. That placeholder zero is easy to forget, so write it in before you multiply by the tens digit.
Long multiplication multiplies each part of the numbers in careful columns, using placeholder zeros and the same splitting idea as an area model, then adds the parts together.
More to read
1.4 Multiply Whole Numbers
Long multiplication stacks numbers so every digit is multiplied in turn. For 2,347 x 6, multiply each digit by 6 from right to left, carrying tens as you go. The ones give 7 x 6 = 42, so write 2 and carry 4. Keep going through the tens, hundreds and thousands. The final answer is 14,082.
Multiply with four partial products
Partial products split a multiplication into easy pieces. For 34 x 27, break both numbers by place value: 30 and 4, 20 and 7. Multiply each pair: 30 x 20 = 600, 30 x 7 = 210, 4 x 20 = 80, 4 x 7 = 28. Add them: 600 + 210 + 80 + 28 = 918. Long multiplication is the same work packed into columns.
Multiplication equations
An area model draws multiplication as a rectangle cut into smaller rectangles. For 45 x 23, split the sides into 40 + 5 and 20 + 3. The four small areas are 800, 120, 100 and 15. Adding them gives 1,035, which matches the written method. If the area total and the column total agree, the answer is almost certainly right.
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2 · Watch
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Where it sits
17 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.