ruututekijöiden

Ruututekijöiden is a Finnish term that translates to "square factors" or "lattice multipliers" in English. It refers to a method used in elementary arithmetic, particularly for multiplication, that visually breaks down a multiplication problem into smaller, more manageable parts. The method is often taught using a grid or a "square" where the digits of the numbers being multiplied are placed along the top and side.

The core idea behind ruututekijöiden is to represent the multiplication of multi-digit numbers by decomposing each digit into its place value (e.g., 23 becomes 20 + 3). Then, a grid is drawn, and each part of one number is multiplied by each part of the other number. For example, to multiply 23 by 45, you would multiply 20 by 40, 20 by 5, 3 by 40, and 3 by 5. Each of these products is written in a separate cell within the grid.

Once all the products are calculated and placed in their respective cells, the values within the cells are added together. This sum gives the final product of the original two numbers. The visual nature of the grid helps students understand the distributive property of multiplication and how it applies to larger numbers. It provides a structured way to ensure no parts of the multiplication are missed and can aid in developing a conceptual understanding of place value within multiplication. This method is typically introduced before more abstract algorithms like the standard long multiplication.