The lattice multiplication method is sometimes known as the Chinese method or Gelosia multiplication. In the lattice multiplication method, we read the totals from left to right and the digits that we have are 5, 7, 6 and 2. So, we write ‘7’ in this diagonal and carry the 1 over to the next diagonal.Ĥ) In the final diagonal, we have four and the one that we carried. So, we write ‘2’ below.Ģ) In the next diagonal, we have six, four and six.ģ) In the next diagonal, we have five, eight, three and the one that we carried. Now that we have multiplied all numbers in the lattice, we will add the numbers in the diagonals starting from the bottom right diagonal.ġ) In the first diagonal, we have two. We write the answer to each multiplication in the corresponding square. Next, we multiply each of the digits of 86 by each of the digits of 67. We begin by arranging the digits of 86 and 67 as shown in the image below, with 86 written above the lattice and 67 written to the right of the lattice. Lattice Multiplication Example 3: 86 x 67 We read the totals from left to right and the digits that we have are 1, 9, 6 and 0. So, we write ‘6’ in this diagonal and carry the 1 over to the next diagonal.ģ) In the next diagonal, we have two, five, one and the one that we carried. Now that all of the lattice squares have been completed, we add the diagonals, working from right to left.Ģ) In the next diagonal, we have five, three and eight. Remember that we write the tens of each answer on the left of the diagonal in each box and the units of each answer on the right of the diagonal. Next, we multiply each of the digits of 56 by each of the digits of 35. We write each digit in line with the boxes. We begin by arranging the digits of 56 and 35 as shown in the image below with one number written on the top of the lattice and the other number written on the right of the lattice. Lattice Multiplication Example 2: 56 x 35 The digits that we have are: 1, 4, 7 and 0. Once we have found the total of each diagonal, we now read the digits from left to right. So, we write ‘0’ below.Ģ) In the next diagonal, we have zero, one and six.ģ) In the next diagonal, we have two, two and zero.Ĥ) In the final diagonal, we have one. We add the numbers in each diagonal starting with the bottom right diagonal and moving left.ġ) In the first diagonal, we have just zero. Once we have multiplied all of the digits and filled every box in the grid, we add the digits that are in each diagonal. This is so that we know that we have worked out this multiplication already, whereas if we left a blank space, we might think that we have made a mistake or missed it out by mistake. Notice that when we multiplied 2 x 3 to make 6, we still wrote a ‘0’ to the left of the diagonal line. Next, we multiply each of the digits of 42 by each of the digits of 35. We begin by arranging the digits of 42 and 35 as shown in the image below, one number written on the top of the grid and the other number written on the right of the grid. Lattice Multiplication Example 1: 42 x 35 We can use this lattice structure to help us to multiply two 2-digit numbers. This is how we represent the number 12 in a lattice. If there are no tens in the answer, we write a zero to the left of the diagonal. So in this example, we write ‘1’ in the green shaded triangle shown. We always write any tens of the answer in to the top left of the diagonal. So, we write ‘2’ in the orange shaded triangle. We always write the units (or ones) of the answer to the bottom right of the diagonal line. We then draw a diagonal line from the top right corner to the opposite corner in the bottom left. We will consider the example of ‘3 x 4’ using lattice multiplication and we begin by drawing a square. We will introduce lattice multiplication by looking at a simple example to understand how to lay out the working out. Lattice multiplication is used to work out the multiplication of larger numbers. Lattice multiplication is an alternative multiplication method to long multiplication or the grid method.
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