The "multiplication by cross method" in Vedic mathematics refers to a technique often called "Vertically and Crosswise." It is an efficient method of multiplying numbers, especially useful for two-digit or larger numbers. Here's how it works:
Steps for Multiplication by Cross Method (Vertically and Crosswise):
Let's multiply two numbers using this method. For example, multiply 23 and 45.
- Write the numbers in vertical alignment:
23
× 45
- Multiply the units digits (last digits) of both numbers:
Multiply 3 (from 23) by 5 (from 45):
3 × 5 = 15
Write down 5 (units digit) and carry over the 1 (tens digit) to the next step.
- Crosswise multiplication (middle step):
Multiply 2 (from 23) by 5 (from 45), and 3 (from 23) by 4 (from 45). Add the results:
2 × 5 = 10
3 × 4 = 12
Now, add these results:
10 + 12 = 22
Write down 2 (tens digit) and carry over 2 to the next step.
- Multiply the tens digits (first digits) of both numbers:
Multiply 2 (from 23) by 4 (from 45):
2 × 4 = 8
Now, add the carry-over 2:
8 + 2 = 10
Write down 10.
- Combine all the results:
Now, place all the results together:
- The final units digit is 5.
- The tens digit is 2.
- The hundreds digit is 0.
- The thousands digit is 1.
So, the final product is 1035.
Summary:
- Step 1: Multiply the units digits (3 × 5 = 15) → 5 (carry 1).
- Step 2: Crosswise multiplication (2 × 5 + 3 × 4 = 10 + 12 = 22) → 2 (carry 2).
- Step 3: Multiply the tens digits (2 × 4 = 8) → 8 + 2 (carry) = 10.
- Final result: 1035
This method is incredibly fast once you get the hang of it, especially for multiplying large numbers or numbers with more digits!