Mental Multiplication Strategies

• Mental maths is defined as the ability to solve the arithmetic calculation mentally using the tricks.
  
• It takes less time to solve the problem.
• It increases the problem-solving ability in children.
• Regular practice of mental sums improves the child sense in numbers.

Multiplication Tricks

Multiplication of a whole number with the multiples of 10:

• Multiply the non-zero part of both the factors.
• Count the number of zeros in each of the factor.
• Add the same number of zeros in the product.

Example 1:

Multiply 2100 by 400.

Solution:

Step 1: Multiply 21 by 4
    21 × 4 = 84
Step 2: Total number of zeros in each of the factor = 4.
Step 3: Add 4 zeros in the product 84.
    840000
Therefore, 21 × 4 = 8,40,000.

Example 2:

Multiply 100 by 1000.

Solution:

Step 1: Multiply 1 by 1
    1 × 1 = 1
Step 2: Total number of zeros in each of the factor = 5.
Step 3: Add 5 zeros in the product 1.
    100000
Therefore, 100 × 1000 = 1,00,000.

Multiplication of two digits number by a two digits number:

Step 1: Multiply the unit digit of both the numbers.
Step 2: Multiply the unit digit of multiplier by the ten digit of multiplicand and the ten digits of multiplier by the unit digit of multiplicand. Add them together.
Step 3: Multiply the ten digits of both the number.

Example:

Multiply 57 by 62.

Solution:

Multiplication of two digits number by a two digits number when the ten digits are same and the sum of unit digit is 10:

Step 1: Multiply both the unit digits.
Step 2: Multiply the ten digits by the succeeding digit.
Step 3: Combine both the results.

Example:

Multiply 27 by 23.

Solution:

The sum of unit digit is 10 = (7 + 3).
Multiply 3 by 7 = 3 × 7 = 21
The digit in tens place is 2. The successor of 2 is 3.
Multiply 2 by 3 = 2 × 3 = 6.
The solution is 621.

Multiplication of three digits number by a two digits number:

Example:

Multiply 157 by 23.

Solution:

Multiplication of three digits number by a three digits number:

Example:

Multiply 517 by 216.

Solution:

Therefore, 517 × 216 = 1,11,672.

Multiplication of three digits number by a three digits number when the ten digits and hundred digits are same and the sum of unit digit is 10:

Step 1: Multiply both the unit digits.
Step 2: Multiply the ten and the hundred digits by the succeeding digit.
Step 3: Combine both the results.

Example:

Multiply 277 by 273.

Solution:

The sum of unit digit is 10 = (7 + 3).
Multiply 3 by 7 = 3 × 7 = 21
The digit in tenths and the hundreds place is 27. The successor of 27 is 28.
Multiply 27 by 28 = 27 × 28 = 756.
The solution is 75,621.

Multiplication Tricks by Numbers

Rule for Multiplying by 9:

• Multiply the number by 10.
• Subtract the number from product.

Example 1:

Multiply 45 by 9

Solution:

Step 1: Multiply 45 by 10.

    45 × 10 = 450

Step 2: Subtract 45 from 450.

    450 – 9 = 405

Rule for Multiplying two digits number by 11:

Write the sum of the digits of the number in between the digits.

Example 1:

Multiply 27 by 11

Solution:

Rule for Multiplying three digits number by 11:

Example 2:

Multiply 157 by 11.

Solution: