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Special Multiplication - 1 (Speed Math)

This method can be used to multiply two numbers having equal number of digits under following conditions.

  • There is a common left part.
  • Sum of right parts is $10,100,1000,$ etc.

(Note: speed math calculator can be used to practise problems using this method.)

Example: Calculate 62 × 68

These numbers have equal number of digits, and common left part $6.$ Also, sum of right parts, $2$ and $8$ is $10.$ Therefore, we can use this special multiplication method.

Multiply common left part by its next number to obtain left side of answer.

$6 × 7 = 42$

Multiply right parts to obtain right side of answer.

$2 × 8 = 16$

Combine left and right sides, that is, $42$ and $16$

Answer is $4216$

Example: Calculate 32 × 38

These numbers have equal number of digits, and common left part $3.$ Also, sum of right parts, $2$ and $8$ is $10.$ Therefore, we can use this special multiplication method.

Multiply common left part by its next number to obtain left side of answer.

$3 × 4 = 12$

Multiply right parts to obtain right side of answer.

$2 × 8 = 16$

Combine left and right sides, that is, $12$ and $16$

Answer is $1216$

Example: Calculate 41 × 49

These numbers have equal number of digits, and common left part $4.$ Also, sum of right parts, $1$ and $9$ is $10.$ Therefore, we can use this special multiplication method.

Multiply common left part by its next number to obtain left side of answer.

$4 × 5 = 20$

Multiply right parts to obtain right side of answer.

$1 × 9 = 9$

Both $1$ and $9$ have one digit each. That is, total two digits. Therefore write $9$ with two digits, $09.$

Combine left and right sides, that is, $20$ and $09$

Answer is $2009$

Example: Calculate 143 × 147

These numbers have equal number of digits, and common left part $14.$ Also, sum of right parts, $3$ and $7$ is $10.$ Therefore, we can use this special multiplication method.

Multiply common left part by its next number to obtain left side of answer.

$14 × 15 = 210$

Multiply right parts to obtain right side of answer.

$3 × 7 = 21$

Combine left and right sides, that is, $210$ and $21$

Answer is $21021$

Example: Calculate 103 × 197

These numbers have equal number of digits, and common left part $1.$ Also, sum of right parts, $03$ and $97$ is $100.$ Therefore, we can use this special multiplication method.

Multiply common left part by its next number to obtain left side of answer.

$1 × 2 = 2$

Multiply right parts to obtain right side of answer.

$03 × 97 = 291$

Both $03$ and $97$ have two digits each. That is, total four digits. Therefore write $291$ with four digits, $0291.$

Combine left and right sides, that is, $2$ and $0291$

Answer is $20291$

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