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
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.
To use the lattice method to compute the product of 7 × 6, follow these steps:
Step 1: Draw a lattice grid with 2 rows and 2 columns.
| 7 | 0 |
| 0 | 6 |
Step 2: Write the numbers 7 and 6 above and to the right of the lattice.
Step 3: Multiply the digits in each cell of the lattice.
| 7 | 0 |
| 0 | 6 |
| | |
| 42 | |
| | 0 |
| | 36 |
Step 4: Add the numbers along the diagonal cells starting from the lower right and moving upwards.
| 7 | 0 |
| 0 | 6 |
| | |
| 42 | |
| | 0 |
| | 36 |
| | |
| 2 | 8 |
| | 4 |
| | |
| | 2 |
Step 5: Read the final number from the top right cell of the lattice - in this case, 2.
Therefore, the product of 7 × 6 using the lattice method is 42.
This method works for any multiplication problem, including 7 × 6.
To use the lattice method for multiplying, follow these steps:
Step 1: Write the two numbers to be multiplied above and to the right of a lattice. In this case, the numbers are 7 and 6.
7
× 6
Step 2: Draw lines to create a lattice with cells. In this case, draw two vertical lines and two horizontal lines, creating a 3x3 grid.
7
× 6
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| |
-----
| |
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Step 3: Multiply the digits of the two numbers and write the partial products in the corresponding cells of the lattice.
7
× 6
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|42|
-----
| |
-----
| |
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Step 4: Starting from the bottom-right corner of the lattice, add the numbers diagonally up. Write the sum in the next cell above. Continue this process until you reach the top-left corner.
7
× 6
-----
|42|
-----
|12|
-----
|2|
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Step 5: The final product is the sum of the numbers along the diagonal cells, read from top-left to bottom-right. In this example, the product is 42 + 12 + 2 = 56.
Therefore, the positions of the fingers for 7 × 6 in the lattice method are as follows:
- Index finger: Placed on the digit 7 in the top row.
- Middle finger: Placed on the digit 6 in the rightmost column.
- Ring finger: Placed on the digit 2 in the bottom-left cell.
- Pinky finger: Placed on the digit 5 in the top-left cell.
As for whether the method works for this product, yes, it does. The lattice method correctly computes the product of 7 and 6 as 56.