Two-Digit by Two-Digit

If both numbers are split, the rectangle has four pieces instead of two.

An example

24 × 13 splits into 20 × 10, 20 × 3, 4 × 10, and 4 × 3.

Add all four

200 + 60 + 40 + 12 = 312.

One piece is much bigger

The tens-by-tens piece is by far the largest. That is worth noticing before you start.

Four pieces, not two

For 34 × 27, split both numbers: 34 into 30 and 4, and 27 into 20 and 7. The rectangle now has four pieces: 30×20 = 600, 30×7 = 210, 4×20 = 80, 4×7 = 28. Add them: 918. Every piece must be counted or the answer is short.

Keep the four pieces organised

Draw the rectangle with its four regions and write each product inside its own region. Missing a piece is the classic error here, and a diagram with four visible boxes makes an empty one obvious in a way a list of numbers does not.

How this becomes the short method

The compact algorithm computes the same four products but combines them in pairs as it goes, which is why it has two rows instead of four lines. If the short method ever confuses you, fall back to the four pieces — you will get the same answer and see where each digit came from.

The estimate is essential here

34 × 27 is roughly 30 × 30 = 900. The answer 918 sits close. If you had lost the 80 piece you would get 838, which still looks plausible — so estimate to the leading digits and be suspicious of anything more than about ten percent away.