There are four sets of intersection points. To compute 22 × 13, for example, draw two sets of vertical lines, the left set containing two lines and the right set two lines (for the digits in 22) and two sets of horizontal lines, the upper set containing one line and the lower set three (for the digits in 13). Here’s an unusual way to perform multiplication. Other Algorithms: Lines and Intersections That is, the area of the 4 x 3 rectangle is 12 square units. Since each unit was actually a square, we refer to the area using "square units". The product, 12, is the total number of squares in that rectangle. So we can think about 4 × 3 as a rectangle that has length 3 and width 4. Using the repeated addition perspective of multiplication, we can picture 4 × 3 as 4 groups of 3 squares each, as shown below.īut if we stack up the groups, we would have 4 rows, with 3 squares in each row. So, you could describe 3 units using three squares. Suppose our basic unit is one square, as shown below. It is also important that we understand why the area perspective of multiplication makes sense. But it is important to explicitly note what area actually is: a measurement describing two-dimensional space. We know that multiplication and area are related. In mathematics, we see this in the fact that often the first way we model relationships between numbers abstractly is with the number line. That is because one of the first forms of measurement we learn are based on a linear measurement model. When people refer to "measurement", often they think of using a ruler, yardstick, or tape measure.
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