Arrays, or sequences of dots in math, can be used as a visual representation of large numbers for multiplication and division. The groups of dots illustrate basic concepts that can be later applied to larger multiplication problems. One of the best methods is to separate larger arrays into several smaller ones and adding the results together.
Each row in an array must have the same number of units as the row before it, as well as the same number of columns. This makes it easier to remove and add parts of the total array when determining larger products. For example, a basic array to find the factors of 20 could feature four groups of five or two groups of 10.
A larger array could be used to find the product of 12 and 17. Rather than count each dot, the array could be subdivided into a 10x10, 10x7, 2x10 and 2x7 set. Finding the products of each of these yields 100, 70, 20, and 14. Adding the results yields 204.
Another example involves finding the product of 15 and 8. First, calculate the product of 15 and 10 (150), then subtract the product of 15 and 2 (30). The result is 120.