Explanation:
Vedic mathematics is a system of mathematics that originated in ancient India. It is a unique and powerful method of calculation based on simple rules and principles. Here are three rules of Vedic math along with five examples for each:
Nikhilam Multiplication (Subtraction and Proportion):
This method involves subtracting numbers from a base and taking proportional adjustments to get the final answer. The base is usually a power of 10.
Example 1: Multiply 58 by 52
Step 1: Choose the base. In this case, the base is 50.
Step 2: Subtract both numbers from the base. 58 - 50 = 8 and 52 - 50 = 2.
Step 3: Multiply the differences (8 × 2) = 16.
Step 4: Add the proportional adjustments (8 + 2 = 10) to the result (16 + 10 = 26). The answer is 26 × 50 = 1300.
Example 2: Multiply 98 by 96
Step 1: Choose the base. In this case, the base is 100.
Step 2: Subtract both numbers from the base. 98 - 100 = -2 and 96 - 100 = -4.
Step 3: Multiply the differences (-2 × -4) = 8.
Step 4: Add the proportional adjustments (-2 + -4 = -6) to the result (8 - 6 = 2). The answer is 2 × 100 = 200.
Example 3: Multiply 46 by 54
Step 1: Choose the base. In this case, the base is 50.
Step 2: Subtract both numbers from the base. 46 - 50 = -4 and 54 - 50 = 4.
Step 3: Multiply the differences (-4 × 4) = -16.
Step 4: Add the proportional adjustments (-4 + 4 = 0) to the result (-16 + 0 = -16). The answer is -16 × 50 = -800.
Example 4: Multiply 24 by 26
Step 1: Choose the base. In this case, the base is 25.
Step 2: Subtract both numbers from the base. 24 - 25 = -1 and 26 - 25 = 1.
Step 3: Multiply the differences (-1 × 1) = -1.
Step 4: Add the proportional adjustments (-1 + 1 = 0) to the result (-1 + 0 = -1). The answer is -1 × 25 = -25.
Example 5: Multiply 64 by 68
Step 1: Choose the base. In this case, the base is 70.
Step 2: Subtract both numbers from the base. 64 - 70 = -6 and 68 - 70 = -2.
Step 3: Multiply the differences (-6 × -2) = 12.
Step 4: Add the proportional adjustments (-6 + -2 = -8) to the result (12 - 8 = 4). The answer is 4 × 70 = 280.
Ekadhikena Purvena (One More than the Previous):
This method involves adding one more to the previous number to get the next number in a series.
Example 1: Find the next number in the series 1, 2, 4, 8, 16, ...
Step 1: The first number is 1.
Step 2: Add 1 to get the second number (1 + 1 = 2).
Step 3: