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Multiplying numbers using a Known Product as a reference
Sometimes, the product of two numbers may already be known, and one may wish

to find the product when one of the numbers is slightly greater or smaller.
For example: a. If 17 × 23 = 391, then we can find the value of 18 × 23.

We can write 18 × 23 as (17 + 1) × 23 = 17 × 23 + 23.
Substitute the value of 17 × 23 = 391.

So, 18 × 23 = 391 + 23 = 414.
b. If 26 × 19 = 494, then we can find the value of 25 × 19.

Here, we can write 25 × 19 as (26 - 1) × 19 = 26 × 19 - 19.

Substitute the value of 26 × 19 = 494.
So, 25 × 19 = 494 - 19 = 475.

In both examples, we observe that:
• When one number increases by 1, the product increases by the value of the
other number.

• When one number decreases by 1, the product decreases by the value of the
other number.

Multiplication using the Lattice Method

In the lattice multiplication method, the multiplicand and multiplier are placed
separately along the top and side of the grid. We multiply each digit of one number

by each digit of the other number and write the product in the corresponding boxes.
Split each box diagonally. The units digit must be placed below and the tens digit
above of the diagonal. In case the product is a single-digit number, then place 0

above the diagonal.
3 × 4 = ? 3 2 × 3 = ? 2
1 0 3
2 4 6
Once all the boxes are filled, add the numbers along the diagonals, moving from right
to left.
example 11. Multiply 86 by 67.

Solution. Make a 2 × 2 grid and write the numbers as shown below. Multiply the
corresponding digits and write the products in the split boxes.

6 × 6 = 36
8 × 6 = 48

7 × 6 = 42
7
7 × 8 = 56

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Mathematical Operations