You are going to learn a cool and easy way to multiply numbers together. Are you ready to try a couple of duplation problems of your own? Well, ready or not, here they come! Of course, because of the commutative property of multiplication, the answer is 525, no matter which way you do it. Here are two more examples for you to study. In the right hand column, start with 26 and double away. This time, in the left column, you check off numbers that add up to 17 it's coincidental that I had to double to 16 again and stop. In other words, use the duplation method to compute: \(17 \times 26\).
Let's do the same problem over again, but use the commutative property of multiplication. Watch how the rest of the problem is done: It's those numbers in the right column that you add together to get the answer. After you check off the numbers in the left column, circle or point to their corresponding numbers in the right column. Simply start at the bottom of the first column, and check off numbers that add up to 26 (this is like doing it in base two). Okay, now we only need to add 26 seventeens together. Isn't it neat how we know that \(16 \times 17 = 272\) and we just double a few numbers to get there?
Now if \(2 \times 17\) is 34, then \(4 \times 17\) is twice as many as \(2 \times 17\), so double 34 to get 68. So, \(2 \times 17\) is simply 17 doubled. The left side keeps track of how many of some number you are adding together. Now, you may need to think about this for a few minutes. \)ĭo you see the corresponding numbers? 1 corresponds with 17, because 17 is \(1 \times 17\), 2 corresponds with 34, because 34 is \(2 \times 17\), 4 corresponds with 68, because 68 is \(4 \times 17\), 8 corresponds with 136, because 136 is \(8 \times 17\), and 16 corresponds with 272, because 272 is \(8 \times 17\).
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