To represent the product 7 × 6 using the lattice method, we would create a lattice grid with 7 rows and 6 columns.
Starting from the bottom right corner of the lattice, we would write the number 7 vertically in the first column, and the number 6 horizontally in the first row.
Next, we would multiply the digits at each intersection of rows and columns and write the partial products in the corresponding cells.
In this case, the partial products would be:
- In the cell where the 7th row and 6th column intersect: 6 × 7 = 42
- In the cell where the 7th row and 5th column intersect: 5 × 7 = 35
- In the cell where the 7th row and 4th column intersect: 4 × 7 = 28
- In the cell where the 7th row and 3rd column intersect: 3 × 7 = 21
- In the cell where the 7th row and 2nd column intersect: 2 × 7 = 14
- In the cell where the 7th row and 1st column intersect: 1 × 7 = 7
Finally, we would add up the numbers along the diagonal cells starting from the bottom right to obtain the product:
2 + 35 + 28 + 21 + 14 + 7 = 107
Therefore, the lattice method correctly calculates the product of 7 × 6 as 107.
Describe the positions of the fingers for 7 × 6. Does the method work for this product?
One of the popular schemes used for multiplying in the fifteenth century was called the lattice method. The two numbers to be multiplied, 4826 and 57 in the example shown here, are written above and to the right of the lattice. The partial products are written in the cells. The sums of numbers along the diagonal cells, beginning at the lower right with 2, 4 + 4 + 0, etc., form the product 275,082.
Show how the lattice method can be used to compute the products
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