STEP 1: To begin, put one of the numbers at the top (47) of a rectangle (that has a space for each digit in the number) and the other number along the side (32) of the same rectangle (that has a space for each digit). It is a way to multiply numbers larger than 10 that only needs. The method you are now going to learn is called the LATTICE METHOD and it could be used for multiplying 2 digit or 3 digit or even bigger numbers together. Long Multiplication is a special method for multiplying larger numbers. Multiply the two digits together and put the answer in the box with the diagonal. Put one number on top and the other on the right of the square. But first, I’ll show you how to multiply 2 single digits together. 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). This video shows you how to use the lattice method of multiplication to multiply 3-digit numbers. 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. Going to try to understand why this worked.\)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 \(8 \times 17\). 44 discussed below is commonly known as the Russian Peasant Multiplication.It is even said that the algorithm 'is still used by peasants in some areas, such as Russia.' However, the source of the Russian Peasant designation is unexpectedly murky. Problem in a nice, neat and clean area like thatĪnd we got our answer. Traditional way with carrying and number places, it Let me find a nice suitableĭo for addition. We're done all ofīrains into addition mode. I think you get the ideaĪnd than we have just one, two more diagonals. Row for the 8, and one row for this other 7. And then each one of theseĬharacters got their own row. Just to show that this'll work for any problem. Have a 1 in your 1,000's place just like that. Place and you carry the 1 into your 1,000's place. The 100's place because this isn't just 19, it'sĪctually 190. In the 10's place and now you carry the 1 in 19 up there into Is really the 1's diagonal, you just have a 6 sitting here. So what you do is you goĭown these diagonals that I drew here. So you write down a 2 andĪn 8 just like that. Next video why these diagonals even work. Although there is carrying,īut it's all while you're doing the addition step. Switching gears by carrying and all of that. One time and then you can finish up the problem Multiplication is you get to do all of your multiplication at Own row and the 8 is going to get its own row. Right-hand side, and then you draw a lattice. Get separate columns and you write your 48 down the You write the digits of one number as different columns and the digit. Of lattice multiplication examples in this video. Lattice multiplication is a fast and easy way to multiply numbers and even polynomials. STEP 2: Multiply each of the digits on the top by each of the digits along the side, and put the answer where they would meet.
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