You don't need a "model" for that; you just need to know the multiplication method taught in elementary school.
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Presumably, the theory is that it's easier to multiply by small numbers than larger ones. If there's a number that you need multiplied by 18, multiply it by 3, then multiply that total by 3, then multiply that total by 2.
Adding doubles can help you multiply by 2 through the property of commutativity in multiplication. By adding two equal numbers together (doubles), you are essentially multiplying one of the numbers by 2. For example, 5 + 5 = 10, which is the same as 5 x 2 = 10. This strategy can simplify multiplication problems and help build a deeper understanding of the relationship between addition and multiplication.
Fractions help with numbers that are not whole numbers.
You should memorize the times tables and then practice multiplying larger numbers with someone to help correct you work until you get more comfortable with it. In the mean time, use a calculator.
Its related to each other because in both you multiply. Whole numbers are positive integers, expect zero which is neutral (no sign). If you know the time table, this will help you to multiply fractions written as integer/integer (rational number). So you will find the right value of the product. Positive or negative value, it depends on the sign of the numbers involved in the multiplication.