Using the calculator
Type a multiplication with × or x between the numbers, like 47 × 36 or 3.2 x 1.5. The answer appears straight away, with the working drawn underneath and every step written out. Whole numbers and decimals both work, with up to four decimal places, and negative numbers too.
The Method menu switches between the column method shown here, the area model (also called the box or grid method) and the lattice. All three give the same answer, so a child taught one way can check it against another.
How long multiplication works
Write the number with more digits on top and the other underneath, lined up on the right. Multiply the whole top number by the ones digit of the bottom number, working from right to left and carrying as you go. For 47 × 36, that's 6 × 7 = 42 (write 2, carry 4), then 6 × 4 = 24, plus the 4 carried makes 28. The first row is 282.
Next, multiply by the tens digit. Because it's 3 tens, not 3, write a 0 in the ones place first, then multiply as before. 3 × 7 = 21 (write 1, carry 2), 3 × 4 = 12, plus 2 makes 14. The second row is 1,410. Add the rows, 282 + 1,410, to get 1,692.
With a three-digit bottom number there's a third row with two zeros on the end, and so on. Each row is called a partial product. The placeholder zeros are drawn faintly in the working above, since they are the part most often forgotten.
Multiplying decimals
Ignore the decimal points, multiply as if they were whole numbers, then put the point back. Count the decimal places in both numbers together, and count that many places in from the right of the answer. 3.2 × 1.5 has two decimal places in all, and 32 × 15 = 480, so the answer is 4.80, which is 4.8.
A quick estimate catches a misplaced point. 3.2 × 1.5 is about 3 × 1.5, which is 4.5, so 4.8 is sensible and 48 or 0.48 are not.
Questions
Why do you add a zero in long multiplication?
Because the second digit of the bottom number is tens. Multiplying by 3 tens is the same as multiplying by 3 and then by 10, and the 0 does the times 10. The third row gets two zeros, for hundreds.
Does it matter which number goes on top?
Not for the answer. Putting the longer number on top makes fewer rows to add, so the calculator does that.
Is long multiplication the same as the standard algorithm?
Yes. US schools call it the standard algorithm, and UK schools call it long multiplication or the column method. The calculator's working follows the same layout.
How do I check a long multiplication?
Round both numbers and multiply in your head. 47 × 36 is about 50 × 40 = 2,000, so 1,692 is about the right size. Or swap to the area model and see if the boxes add up to the same thing.
Sources
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