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In this section, we review the process of multiplication with whole numbers. We previously stated that the multiplication of whole numbers is a shortcut for repeated addition. When we think of multiplication with single-digit numbers, the process is learned by memorizing the multiplication table or times table. What can we do when we want to multiply larger numbers: 2 digit numbers, 3 digit numbers, etc…? We multiply multi-digit whole numbers using a process known as vertical multiplication (also known as multiplication with regrouping). The process of vertical multiplication allows us to multiply really large whole numbers by breaking the multiplication down into a series of smaller and more manageable steps. We will explain how this process is a condensed form of the distributive property. Essentially, this process will take each digit of the bottom number and multiply it by each digit of the top number. It will take into consideration the various place values of each digit as the multiplication occurs. In the end, we will sum the individual results to obtain our product.
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