Categories
Multiplication Multiplying Numbers with Common Last digits Speed Math

[Speed Math] MULTIPLYING NUMBERS WITH COMMON LAST DIGITS

Here’s an example of a SPEED MATH shortcut for MULTIPLYING NUMBERS WITH COMMON LAST DIGITS : (Mul) LDSdx from the MULTIPLICATION category.

Multiplying Numbers with Common Last digits

When can I use this method?

For multiplying any 2-digit number with another 2-digit number such that the last digit of the multiplier and multiplicand are same. The first digits can be different.

For multiplying any 3-digit number with another 3-digit number such that the last digit of the multiplier and multiplicand are same. The initial 2 digits can be different.

You can also use this method to multiply numbers with unequal number of digits, i.e. multiplying a 2-digit number with a 3-digit number such that the last digit of the multiplier and multiplicand are the same.

 

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Notes –

  1. Notice the way the products are added.

Related Shortcuts –

Multiplying Numbers with Common Initial digits: (Mul) FDSdx

 

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Categories
Multiplication Multiplying Numbers using Aliquot Method Speed Math

[Speed Math] MULTIPLYING NUMBERS USING ALIQUOT METHOD

Here’s an example of a SPEED MATH shortcut for MULTIPLYING NUMBERS USING ALIQUOT METHOD : (Mul) NxM(Aq)
from the MULTIPLICATION category.

Multiplying Numbers using Aliquot Method

When can I use this method?

For multiplying any two numbers provided at least one of them can be converted to an Aliquot format.

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Notes –

  1. An aliquot of an integer is any of its integer proper divisors.
  2. As you convert the numbers to its aliquot, make sure to take care of the zeros and the decimal points.

Related Shortcuts –

Multiplying a Number ending with 1: (Mul) NxM(LD1)
Multiplying a Number ending with 5: (Mul) NxM(LD5)
Multiplying a Number ending with 9: (Mul) NxM(LD9)

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Categories
Multiplication Multiplying a Number ending with 1 Speed Math

[Speed Math] MULTIPLYING A NUMBER ENDING WITH 1

Here’s an example of a SPEED MATH shortcut for MULTIPLYING A NUMBER ENDING WITH 1:(Mul) NxM(LD1) from the MULTIPLICATION category.

Multiplying a Number ending with 1

When can I use this method?

Although this can be used for multiplying any number with another number whose last digit is = 1, it is better suited for 2 or 3-digit numbers. Larger numbers could get increasingly difficult to multiply with this method.

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Notes –

  1. This method uses the concept a x (b+1) = ab + a

Related Shortcuts –

Multiplying a Number ending with 5: (Mul) NxM(LD5)
Multiplying a Number ending with 9: (Mul) NxM(LD9)
Multiplying Numbers using Aliquot Method: Mul) NxM(Aq)

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Categories
Multiplication Multiplying Numbers with last digit sum 10 Speed Math

[Speed Math] MULTIPLYING NUMBERS WITH LAST DIGIT SUM 10

Here’s an example of a SPEED MATH shortcut for MULTIPLYING NUMBERS WITH LAST DIGIT SUM 10: (Mul) S10dx from the MULTIPLICATION category.

Multiplying Numbers with last digit sum 10

When can I use this method?

For multiplying any 2-digit number with another 2-digit number such that the sum of the last digits of the multiplier and multiplicand = 10 and the remaining digits of multiplier are same as that of the multiplicand.

For multiplying any 3-digit number with another 3-digit number such that the sum of the last digits of the multiplier and multiplicand = 10 and the remaining digits of multiplier are same as that of the multiplicand.

You cannot use this method to multiply numbers with unequal number of digits, i.e. multiplying a 2-digit number with a 3-digit number.

 

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pdf Download Practice sheet for MULTIPLYING NUMBERS WITH LAST DIGIT SUM 10

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Notes –

  1. The RHS of the answer should always be written in 2-digit form by prefixing a zero, if the value is single digit, e.g. write ‘9’ as ‘09’.

Related Shortcuts –

Multiplying Numbers with last digit sum 100: (Mul) S100dx
Multiplying Numbers with last digit sum 1000: (Mul) S1000dx

 

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Categories
Multiplication Multiplying Numbers near 10 Speed Math

[Speed Math] MULTIPLYING NUMBERS NEAR 10

Here’s an example of a SPEED MATH shortcut for MULTIPLYING NUMBERS NEAR 10 : (Mul) Nr10 from the MULTIPLICATION category.

Multiplying Numbers near 10

When can I use this method?

For multiplying numbers near 10. The numbers can be either more than 10 or less than 10 or a combination of the two.

You may also use this method to multiply numbers a little farther away from 10 as long as their differences from 10 are easy to multiply.

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pdf Download Practice sheet for MULTIPLYING NUMBERS NEAR 10

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Notes –

  1. This method uses the concept (10 + a) (10 + b) = [(10 + a) + b] + ab or [(10 + b) + a] + ab, where ‘(10 + a)’ and ‘(10 + b)’ are numbers near 10 and ‘a’ and ‘b’ are the respective differences.
  2. Whenever the number is more than 10, the difference is written as positive (+ve).
  3. Whenever the number is less than 10, the difference is written as negative (-ve).
  4. When both numbers are either less or more than 10, you add the product of differences.
  5. When one number is more than 10 and another less than 10, you subtract the product of differences.

Related Shortcuts –

Multiplying Numbers near 100: (Mul) Nr100
Multiplying Numbers near 1000: (Mul) Nr1000

 

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Categories
Multiplication Multiplying Numbers with last digit sum 1000 Speed Math

[Speed Math] MULTIPLYING NUMBERS WITH LAST DIGIT SUM 1000

Here’s an example of a SPEED MATH shortcut for MULTIPLYING NUMBERS WITH LAST DIGIT SUM 1000: (Mul) S1000dx from the MULTIPLICATION category.

Multiplying Numbers with last digit sum 1000

When can I use this method?

For multiplying any 4-digit number with another 4-digit number such that the sum of the last 3 digits of the multiplier and multiplicand = 1000 and the remaining digits of multiplier are same as that of the multiplicand.

For multiplying any 5-digit number with another 5-digit number such that the sum of the last 3 digits of the multiplier and multiplicand = 1000 and the remaining digits of multiplier are same as that of the multiplicand.

You cannot use this method to multiply numbers with unequal number of digits, i.e. multiplying a 4-digit number with a 5-digit number.

 

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Notes –

  1. The RHS of the answer should always be written in 6-digit form by prefixing zero(s), if the value is less than 4-digit, e.g. write ‘9’ as ‘000009’ or ’21 as ‘000021’ or ‘121’ as ‘000121’ and so on…

Related Shortcuts –

Multiplying Numbers with last digit sum 10: (Mul) S10dx
Multiplying Numbers with last digit sum 100: (Mul) S100dx

 

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Categories
Multiplication Multiplying Numbers using Line Intersection Speed Math

[Speed Math] MULTIPLYING NUMBERS USING LINE INTERSECTION

Here’s an example of a SPEED MATH shortcut for MULTIPLYING NUMBERS USING LINE INTERSECTION: (Mul) NxMy(Li)
from the MULTIPLICATION category.

Multiplying Numbers using Line Intersection

When can I use this method?

For multiplying any number with any other number.

Ideally, the numbers should have digits of value less than 5. This, although not a restriction, but is helpful to draw out the lines clearly and count the intersection points properly.

 

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Notes –

  1. This is one of the most generic methods of multiplication.
  2. As you would notice that it is not really a shortcut method, but just an alternative method of multiplication.

Related Shortcuts –

Multiplying Numbers using Grid Method: (Mul) NxMy(Gd)

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Categories
Multiplication Multiplying Numbers ending in 5 Speed Math

[Speed Math] MULTIPLYING NUMBERS ENDING IN 5

Here’s an example of a SPEED MATH shortcut for MULTIPLYING NUMBERS ENDING IN 5 : (Mul) LD5 from the MULTIPLICATION category.

Multiplying Numbers ending in 5

When can I use this method?

For multiplying any 2-digit number with another 2-digit number such that the last digit of the multiplier and multiplicand is = 5. The first digits can be different.

For multiplying any 3-digit number with another 3-digit number such that the last digit of the multiplier and multiplicand is = 5. The initial 2 digits can be different.

You can also use this method to multiply numbers with unequal number of digits, i.e. multiplying a 2-digit number with a 3-digit number such that the last digit of the multiplier and multiplicand is = 5.

As long as finding the product of initial digits is easy enough, one can use this method to multiply numbers bigger than 2 or 3-digits.

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Notes –

  1. When the average of the initial digits is an integer, the last 2 digits of the answer is = 25.
  2. When the average of the initial digits is in decimal, the last 2 digits of the answer is = 75.
  3. If the average of the initial digits is an integer, simply appending 25 to the sum of product and average of the initial digits gives you the answer.

Related Shortcuts –

“None”

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Categories
Multiplication Multiplying Numbers with first digits sum 10 Speed Math

[Speed Math] MULTIPLYING NUMBERS WITH FIRST DIGITS SUM 10

Here’s an example of a SPEED MATH shortcut for MULTIPLYING NUMBERS WITH FIRST DIGITS SUM 10 : (Mul) F10dx from the MULTIPLICATION category.

Multiplying Numbers with first digits sum 10

When can I use this method?

For multiplying any 2-digit number with another 2-digit number such that the sum of the first digits of the multiplier and multiplicand = 10 and the remaining digits of multiplier are same as that of the multiplicand.

For multiplying any 3-digit number with another 3-digit number such that the sum of the first digits of the multiplier and multiplicand = 10 and the remaining digits of multiplier are same as that of the multiplicand.

You cannot use this method to multiply numbers with unequal number of digits, i.e. multiplying a 2-digit number with a 3-digit number.

 

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Notes –

  1. Notice the way the common digits are added.
  2. When multiplying 2-digit numbers with common last digit, remember to write the RHS of the answer in 2-digit form by prefixing a zero, if the value is single digit, e.g. write ‘9’ as ‘09’.
  3. When multiplying 3-digit numbers with last 2 digits common, remember to write the RHS of the answer in 3-digit form by prefixing zero(s), if the value is less than 3-digit, e.g. write ‘9’ as ‘009’ or ‘21’ as ‘021’. If the value is in 4-digit form, add the first digit of the RHS to the last digit of the LHS to have the RHS in 3-digit form.

Related Shortcuts –

Multiplying Numbers with first digits sum 100: (Mul) F100dx
Multiplying Numbers with first digits sum 1000: (Mul) F1000dx

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Categories
Multiplication Multiplying Numbers with first digits sum 100 Speed Math

[Speed Math] MULTIPLYING NUMBERS WITH FIRST DIGITS SUM 100

Here’s an example of a SPEED MATH shortcut for MULTIPLYING NUMBERS WITH FIRST DIGITS SUM 100 : (Mul) F100dx from the MULTIPLICATION category.

Multiplying Numbers with first digits sum 100

When can I use this method?

For multiplying any 3-digit number with another 3-digit number such that the sum of the initial digits of the multiplier and multiplicand = 100 and the remaining digits of multiplier are same as that of the multiplicand.

For multiplying any 4-digit number with another 4-digit number such that the sum of the initial digits of the multiplier and multiplicand = 100 and the remaining digits of multiplier are same as that of the multiplicand.

You cannot use this method to multiply numbers with unequal number of digits, i.e. multiplying a 3-digit number with a 4-digit number.

 

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Notes –

  1. Notice the way the common digits are added.
  2. When multiplying 3-digit numbers with common last digit, remember to write the RHS of the answer in 2-digit form by prefixing a zero, if the value is single digit, e.g. write ‘9’ as ‘09’.
  3. When multiplying 4-digit numbers with last 2 digits common, remember to write the RHS of the answer in 4-digit form by prefixing zero(s), if the value is less than 4-digit, e.g. write ‘9’ as ‘0009’ or ‘21’ as ‘0021’ or ‘121’ as ‘0121’.

Related Shortcuts –

Multiplying Numbers with first digits sum 10: (Mul) F10dx
Multiplying Numbers with first digits sum 1000: (Mul) F1000dx

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