Product of numbers close to 100
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
Squaring a number ending in 6
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.
Multiply any number with 99
If any number is multiplied by 99 for example 99*98=9702
Trick used is 98-1 & 100-98 is 9702
Square of two digit number ending with 5
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
Subdivision Multiplication Trick
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
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
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.
To Divide a Number by 5
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
Square of a Number ending with 5
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
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'
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 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
Trick to find number of positive and negative roots
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
Multiply all ones by all ones i.e 11111 x 11111
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
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
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
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 digit numbers having tens digit same and unit digits sum to
10
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
Facts about Magic squares
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.
Multiplication Trick for any two digit numbers
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