Multiply 2 numbers, sum of whose unit places is 10

Vedic Multiplication: This method of multiplication which is from Vedic Maths will make it very easy to multiply two numbers when sum of the last digits is 10 and previous parts are the same

You will get the answer in two parts.

First part, to get left hand side of the answer: multiply the left most digit(s) by its successor

Second part, to get right hand side of the answer: multiply the right most digits of both the numbers.

Example

First part: 4 x (4+1)

Second part: (4 x 6)

Combined effect:  (4 x 5)  | (4 x 6) = 2024

*| is just a separator. Left hand side denotes tens place, right hand side denotes units place

More Examples

37 x 33 = (3 x (3+1)) |  (7 x 3) = (3 x 4) | (7 x 3) = 1221

11 x 19 = (1 x (1+1)) |  (1 x 9) = (1 x 2)  | (1 x 9) = 209

As you can see this method is corollary of  “Squaring number ending in 5”

It can also be extended to three digit numbers like :

E.g. 1: 292 x 208.

Here 92 + 08 = 100, L.H.S portion is same i.e. 2

292 x 208 = (2 x 3) x 10 | 92 x 8  (Note: if 3 digit numbers are multiplied, L.H.S has to be multiplied by 10)

60 | 736 (for 100 raise the L.H.S. product by 0) = 60736.

E.g. 2: 848 X 852

Here 48 + 52 = 100,

L.H.S portion is 8 and its next number is 9.

848 x 852 = 8 x 9 x 10 | 48 x 52 (Note: For 48 x 52, use methods shown above)

720 | 2496

= 722496.

[L.H.S product is to be multiplied by 10 and 2 to be carried over because the base is 100].

Eg. 3: 693 x 607

693 x 607 = 6 x 7 x 10 | 93 x 7 = 420 / 651 = 420651.

Note: This Vedic Maths method can also be used to multiply any two different numbers, but it requires several more steps and is sometimes no faster than any other method. Thus try to use it where it is most effective

How do you like this Vedic Maths technique, please let us know. You can also share this with your friends.

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How to Quickly Find Square of Any Number Ending in 5

Finding square of any number with unit’s digit being 5 is the most common, yet very interesting trick of Vedic Maths.  Using this technique you can find the square of any number ending in 5 very easily.  Also explore a quick method of squaring numbers ending in 9. Given below is the step by step explanation of this Vedic Maths Method.

Let us take a 2 digit number in generic form, say the number is a5 (=10a+5), where a is the digit in ten’s place

Square of a5= a x (a+1) | 25

That means a is multiplied by the next higher number, i.e. (a+1). Now let’s take example of a real number ending in 5, say 45.

452 = Left hand side of the answer will be 4 multiplied by its successor i.e. 5 and the right hand side part will always be 25 for squares of numbers of which the unit’s digit is 5.

Giving the answer a x (a+1) | 25 ( |     stands for concatenation}

i.e. 4  x  (4+1) | 25 = 4 x 5 | 25 = 2025

Similarly we can proceed for 3 digit numbers ending in 5

Few more examples:

952=9 x 10 | 25 =9025

1252 = 12 x 13 | 25 = 15625

5052 = 50 x 51 | 25 = 255025

Test yourself

Find out the square of 85, 245, 145, 35, 15, and 95?

Answer: 7225, 60025, 21025, 1225, 225, 9025

Please let us know if you like this Vedic Maths trick

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Vedic Mathematics Course

Vedic Mathematics is the name given to the ancient system of Mathematics which was rediscovered from the Vedas between 1911 and 1918 by Sri Bharati Krsna Tirthaji (1884-1960). The aim of such sutra is to simplify the entire calculations and arithmetical operations.

Vedic Maths Course

There are 16 sutras in vedic mathematics as per Sri Bharati Krsna Tirthaji Maharaj.  The below mentioned list of topics (course content) is how I look at it.

 

  1. Vedic Addition
  2. Vedic Subtraction
    1. All from 9 and the last from 10
    2. Various other methods
  3. Multiplication (inclusive of mental multiplication)
    1. “By one more than the previous one”
    2. Multiplication by 9, 99,  ( and so on), 11, 111, (and son on..)
    3. Base method of multiplication and many more
    4. Vertically and crosswise multiplications – criss-cross method
  4. Part of Division (you will be amazed)
    1. “Transpose and apply”
    2. Special division cases
  5. Squaring (it’s so simple) : More than 10 different methods will be discussed for different cases
    1. Squaring numbers ending in 5
    2. Squaring any 2 digit number
  6. Square root of perfect squares and imperfect squares.
  7. Cubing(using things differently)
  8. Cube Roots (by seeing only & not by working on it). Different methods for perfect cube and non-perfect cube
  9. Dates and calendar
  10. Magic Square
  11. Special mathematical tricks and techniques
  12. Application of vedic mathematics in trigonometry, geometry, algebra and calculus
  13. Value (finding and remembering) of fractions
  14. Checking the accuracy of different mathematical operations
  15. Differential calculus
  16. Solving an algebraic equation of one variable
    1. “Transpose and adjust (the coefficient)”
  17. Solving simultaneous equation and quadratic equation
    1. “If the Samuccaya is the same (on both sides of the equation, then) that Samuccaya is (equal to) zero”
    2. By the Paravartya rule
    3. “If one is in ratio, the other one is zero.”
  18. Solving cubic equation
  19. Solving fractional equation
    1. “The ultimate (binomial) and twice the penultimate (binomial) (equals zero),”

Through www.QuickerMaths.com (QM) I’ll try to cover all the above vedic maths related topics. Lot of other topics, techniques, shortcuts will be part of QM. Mathematical games, puzzles, riddles, etc. are also included to make every kid sharp.

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Benefits of Vedic Mathematics

Advantages and Benefits of Vedic Mathematics

Helps students to get rid of math phobia and improve grades
Helps students solve mathematical problems about 15 times faster. See how fast multiplication can be using the shortcut for multiplication
Helps in intelligent interpolation.
Reduces burden on the student as he/she has to know tables up to nine only.
Improves mental calculation.
Improves concentration as well as confidence.

Very simple, direct, totally unconventional, original and consummate

Once you are aware of the basics of Vedic Maths you can practice and make yourself a human calculator. Vedic Mathematics is magical.

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