Multiplication is a rectangle

Draw 23 × 14 as a rectangle 23 wide and 14 tall. Cut the width into 20 and 3 and the height into 10 and 4. You now have four smaller rectangles.

Their areas are 20 × 10 = 200, 3 × 10 = 30, 20 × 4 = 80 and 3 × 4 = 12. Added up they make 322, the whole rectangle.

The long multiplication you learned at school does exactly these four multiplications; the columns just hide the rectangle.

One question

Cut 23 × 14 into tens and ones. Which four areas make up the rectangle?

Say it backIn your own words: where is the rectangle hiding in long multiplication?

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