Say, you have to multiply 94 and 98. Take their differences to 100: 100 - 94 = 6 and 100 - 98 = 2. Note that 94 - 2 = 98 - 6 so that for the next step it is not important which one you use, but you'll need the result: 92. These will be the first two digits of the product. The last two are just 2×6 = 12. Therefore, 94×98 = 9212

Example 2:

95 x 97 ?

100-95=5, 100-97=3

95-3=92, 97-5=92

5 x 3 =15

Ans

9215

quaring a number ending in 6

Ex [1]

66^2 =_________.

a) Write down 6.

b) 2 x (6 + 1) + 1 = 15. Write 5, carry 1.

c) 6 x (6 + 1) = 42 + 1 = 43. Write 43.

d) The answer is 4356.

Ex [2]

86^2 =_________.

a) Write down 6

b) 2 x (8 + 1) + 1 = 19. Write 9, carry 1.

c) 8 x (8 + 1) = 72 + 1 = 73. Write 73.

d) The answer is 7396.

If any number is multiplied by 99 for example 99*98=9702

Trick used is 98-1 & 100-98 is 9702

To find the square of a two-digit number ending with 5,

Take the first digit, multiply by itself plus one, and then put "25" after it.

Example1:To find 55², compute 5 × 6 = 30. The answer is 30 25==> 3025

Example 2: To find 25², compute 2 x 3 = 6. the answer is 6 25==> 625

If you have a large number to multiply and one of the numbers is even, you can easily subdivide to get to the answer:

32 x 125, is the same as:

16 x 250 is the same as:

8 x 500 is the same as:

4 x 1000 = 4,000

To check if addition is correct -

-add up the single digits of each individual number in the sum, until you are left with a single digit.

-add these single digits together until you are, once again, left with a single digit.

-do the same with the total

-these figures should be the same

To multiply a number by 5

Step 1: Divide by 2

Step 2: Move the decimal point to the right. (Multiply by 10)

For example: 1450x5

Step 1: 1450/2 ==> 725

Step 2: 725x10==> 7250 Ans.

Dividing by 5

Dividing a large number by five is actually very simple. All you do is multiply by 2 and move the decimal point:

195 / 5

Step1: 195 * 2 = 390

Step2: Move the decimal: 39.0 or just 39

2978 / 5

step 1: 2978 * 2 = 5956

Step2: 595.6

what is the square of 25? Solve it in 2 seconds!!

multiply 2 by the next preceding number (3 in this case)==>2x3=6

and square 5==>25

write both the results adjacent to each other==>625

Same goes for every other number that ends with a '5'

THE 11 TRICK!!

If you encounter a problem where you have to multiply any number with 11, for eg.

36 x 11

write 3 and 6 to both the extremes and write the sum of these two in the middle..

Result==>396

same goes for any two digit number

13 x 11

Result==> 143

squaring a two digit number that begins with a '5'

-square the first digit

-add this number to the second number to find the first part of the answer

-square the second digit: that is the last part of the answer.

Example:what is the square of 58==> 58^2?

5^2=25==>25+8=33 _ _

8^2=64==> 3364Ans.

To find the squares of numbers near numbers of which squares are known

To find 41^2, Add 40+41 to 1600 = 1681

To find 59^2, Subtract 60^2-(60+59) = 3481

1) If an equation contains all positive co-efficients of any powers of x, then it has no positive roots.

e.g. x^4+3x^2+2x+6=0 has no positive roots .

2) If all the even powers of x have same sign coefficients and all the odd powers of x have the opposite sign coefficients, then the equation has no negative roots.

e.g. x^2 - x +2 = 0

1 x 1 = 1

11 x 11 = 121

111 x 111 = 12321

1111 x 1111 = 1234321

11111 x 11111 = 123454321

111111 x 111111 = 12345654321

1111111 x 1111111 = 1234567654321

11111111 x 11111111 = 123456787654321

111111111 x 111111111 = 12345678987654321

Did you know..!? Largest calculation (9^9)^9 Ninth power of the ninth power of nine
is the largest in the world of number that can be expressed with just 3 digit. No
one has been able to compute this yet. The very task is staggering to the mind Example.
The answer to this number will contain 369 million digits. And to read it normally
it would take more than a year. To write down the answer, you would require 1164
miles of paper.

Multiplication of two numbers that differ by 6:

If the two numbers differ by 6 then their product is the square of their average minus 9.

Let me explain this rule by taking examples

10*16 = 13^2 - 9 = 160

22*28 = 25^2 - 9 = 616

Example. Understand the rule by 1 more example

997*1003 = 1000^2 - 9 = 999991

Square of any 2 digit number

Let me explain this trick by taking examples

67^2 = [6^2][7^2]+20*6*7 = 3649+840 =4489

similarly

25^2 = [2^2][5^2]+20*2*5 = 425+200 = 625

Take one more example

97^2 = [9^2][7^2]+20*9*7 = 8149+1260 =9409

Here [] is not an operation, it is only a separation between initial 2 and last 2 digits

Multiplication of 2 two-digit numbers where the first digit of both the numbers are same and the last digit of the two numbers sum to 10

Let me explain this rule by taking examples

To calculate 56×54:

Multiply 5 by 5+1. So, 5*6 = 30. Write down 30.

Multiply together the last digits: 6*4 = 24

Write down 24.

The product of 56 and 54 is thus 3024.

Example 2 : Understand the rule by 1 more example

78*72 = [7*(7+1)][8*2] = 5616

Magic squares Magic numbers was first recorded by Chinese in 2200BC and known to
Arab mathematicians, when they conquered India and learnt about Indian mathematics,
astronomy and other aspects of combinatorial mathematics. Magic squares is the arrangement
of the distinct numbers (each number used once) in a square array, in which the
sum of the Row, Column and all diagonals have the same number known as Magic constant.
Magic square that contains the number from 1 to n2 is called as normal magic numbers.
Number of rows and column in the magic squares is always equal and represented by
'n'. The constant that is the sum of every row, column and diagonal is called as
Magic constant. It can be determined with the formula M = n(n2 + 1) / 2 Consider
normal magic square of the order 3 x 3. For 3 x 3 grid, fill numbers 1, 2, 3...9
in the square array, such that the sum of the number in the row, column and diagonal
should be 15. For example, if n = 3, 4, 5.... then the magic consonants are 15,
34 , 65 respectively.

Vedic maths multiplication tips and tricks for two digit numbers multiplication.

Cross Multiplying Two Digit Numbers

Problem : 16 x 28

Step1:

First, write your problem down, sitting on top of each other, like you would do when multiplying normally.

1 6

x 2 8

-------

Step2:

Multiply the numbers in the ones place and put the product underneath the problem as shown. In this case, 8*6 is greater than 10 (48).

1 6

x 2 8

-------

48

Step3:

Cross-multiply the ones with the opposing tens and add them together. In this case, (2*6) + (1*8) = 20. Write 20 underneath 48 one space to the left (ending on the tens column)

1 6

x 2 8

-------

48

20

Step4:

Multiply the tens. 1*2 = 2. Place this product another space to the left, in the hundreds column as shown.

1 6

x 2 8

-------

48

20

2

Step5:

Now, add the products. Add the three rows as you do in normal multiplication method. The sum of the three rows you created equal 448, our answer.

1 6

x 2 8

-------

48

20

2

-------

448

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