![]() To find the position of the decimal point in the final answer, one can draw a vertical line from the decimal point in 5.8, and a horizontal line from the decimal point in 2.13. For example, to multiply 5.8 by 2.13, the process is the same as to multiply 58 by 213 as described in the preceding section. The lattice technique can also be used to multiply decimal fractions. Step 3 Multiplication of decimal fractions In the example shown, the result of the multiplication of 58 with 213 is 12354. Numbers are filled to the left and to the bottom of the grid, and the answer is the numbers read off down (on the left) and across (on the bottom). If the sum contains more than one digit, the value of the tens place is carried into the next diagonal (see Step 2). Each diagonal sum is written where the diagonal ends. Step 1Īfter all the cells are filled in this manner, the digits in each diagonal are summed, working from the bottom right diagonal to the top left. If the simple product lacks a digit in the tens place, simply fill in the tens place with a 0. Write their product, 10, in the cell, with the digit 1 above the diagonal and the digit 0 below the diagonal (see picture for Step 1). In this case, the column digit is 5 and the row digit is 2. After writing the multiplicands on the sides, consider each cell, beginning with the top left cell. Then each cell of the lattice is filled in with product of its column and row digit.Īs an example, consider the multiplication of 58 with 213. The two multiplicands of the product to be calculated are written along the top and right side of the lattice, respectively, with one digit per column across the top for the first multiplicand (the number written left to right), and one digit per row down the right side for the second multiplicand (the number written top-down). Method Ī grid is drawn up, and each cell is split diagonally. It is still being taught in certain curricula today. ![]() The method had already arisen by medieval times, and has been used for centuries in many different cultures. It is mathematically identical to the more commonly used long multiplication algorithm, but it breaks the process into smaller steps, which some practitioners find easier to use. You're not just blindly doing some type of steps toįind the product of two numbers.Lattice multiplication, also known as the Italian method, Chinese method, Chinese lattice, gelosia multiplication, sieve multiplication, shabakh, diagonally or Venetian squares, is a method of multiplication that uses a lattice to multiply two multi-digit numbers. This whole exercise, this whole video, is so Of the day, you really are doing the same thing that And look at the different stepsĪnd why they are making sense and why, at the end And I encourage you to now justĭo this same multiplication problem, the same What is 3 times 80? We already calculated that. What is 60 times 7? Well, that's going to be 420. Well, what's 60 times 80? Well, we alreadyĬalculated that. This was a bit of a pain to have to do the distributive Going to be equal to? Well, we could add them all up. ![]() The distributive property and, hopefully, a little Way you knew how to do it, it's not some magical formula I'm doing this is to show you that that fast ![]() But it's going to be 10 timesĪs much, because this is a 60. Right over here, so 48 followed by the two 0's. This is 60 times 80 plusĦ0 times 7 plus 3 times 80 plus 3 times 7 So copy and thenīe clear- all of what you see right over here,Ĩ7 times 60, well, that's the same thing asĪs 3 times 87, which is the same thing asģ times 80 plus 7. 80 plus 7 plus 3 timesĨ0 plus 7, or 3 times 87. But I'll write thatĪs 60 times 80 plus 7. Same thing as 87 times 60 plus 87 times 3. Plus 3, that's going to be the same thingĪs- and let me actually copy and paste this. Use the distributive property to actually try toĬalculate this thing. Just by using some process, just showing you some steps. ![]()
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