Area model multiplication

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 to the column method or the lattice for the same sum. The area model is drawn for numbers with up to six non-zero digits each; past that, the boxes get too many to be useful.

Split each number into its place values. 47 is 40 + 7, and 36 is 30 + 6. Draw a rectangle with a column for each part of the first number and a row for each part of the second, and write the parts along the top and down the side.

Each box is one part times another. 40 × 30 = 1,200, 7 × 30 = 210, 40 × 6 = 240 and 7 × 6 = 42. Add all the boxes and you have the answer, 1,200 + 210 + 240 + 42 = 1,692.

It's called the area model because a rectangle 47 wide and 36 tall really does have an area of 1,692, and the lines just cut it into pieces that are easy to work out. The boxes are drawn the same size here, so the picture is a guide to the working and not to scale.

The area model makes place value visible. A child who writes 4 × 3 = 12 in the column method can lose track of the fact that it's really 40 × 30 = 1,200; in a box labelled 40 and 30, that's hard to miss. It's also the same picture used later for multiplying out brackets in algebra, where (x + 7)(x + 6) splits into four boxes in exactly the same way.

The box method and grid method are other names for the same thing. Some classes add each row first, which gives the same partial products as the column method.