Multiplication made easy!

Multiplication is become easy! Most of my students are not agreeing. I like to give you some wonderful tips and you see it will give an amazing result. Try for it….
Suppose I ask you to multiply 99992 with 99923. I know you hesitate and if some try then show me their ugly face that it is very time consuming. I say no. Let us discuss the trick behind it.
1, 00,000 is greater than both 99992 and 99923.
Subtract 99992 and 99923 from 1, 00,000. What you get? It is 8 and 77 respectively.
Now 8 is the smallest one between 8 and 77. Right.
Multiply 8 and 77. You will get 616 is a three digit number. Convert it into five digit number 00696 (as the multiplicand and multiplier are of equivalent digits – this is important REMEMBER).
Subtract 8 from 99923 (BOTH ARE SMALL IN THEIR RESPECTIVE NUMBERS). You get 99915.
Hey…here is my result 99915 00616.
Hello students are you now using calculator. Ok I think you will get the same result.
The above principle is applicable to any number of digits.

Limitations:
1.The number should be very close to its higher 10’s digits. For example 99992 and 99923 are close to 1, 00,000.
2.The multiplication of differences should be converted to equal number of digits as the multiplicand and multiplier.
3.The multiplication results of differences should not more than the multiplicand and multiplier.

Now students use this small trick in your calculations in mathematics.

And cheers.

Square of a Four Digit Number

Square of four digit numbers:

By using the duplex method, now let us find out the square of a four digit number. Use the similar method as you using in squaring four digit numbers in previous discussion.

Square of 1435:-

Let N = square of 1435

Step – 1 – Taking Thousands place digit first,

<<1>> = 12 = 1

Step – 2 – Taking Hundreds and Thousands place digits,

<<14>> = 2 × (1× 4) = 8

Step – 3 – Taking Thousands, Hundreds and Tens place digits,

<<143>> = 42 + 2 × (1 × 3) = 22,

Step – 4 – Taking Thousands, Hundreds, Tens and Unit place digits,

<<1435>> = 2 × ( 1 × 5 ) + 2×(4×3) = 34

Step – 5 – Taking Hundreds, Tens and Unit place digit,

<<435>> = 32 + 2(4×5) = 49
Step- 6- Taking Tens and Unit place digit,

<<35>> = 2×(3×5) = 30

Step – 7 – Taking Units place digit,

<<5>> = 52 = 25

Then,

N = 25 + (30 × 10) + (49 × 102) + (34×103) + (22×104) + (8×105) + (1×106) = 2059225.


Student practice the squaring process and you may save your time on solving the numerical.

Square of a Three Digit Number

By using the duplex method, now let us find out the square of a three digit number. Use the similar method as you using in squaring two digit numbers in “SQUARE OF A – THREE DIGIT NUMBER”.

1. Square of 452 :-

Let N = square of 452
Step – 1 –: Taking Hundreds place digit first,
<< 4 >> = square of 4 = 16
Step – 2 –: Taking Hundreds and Tens place digits,
<< 45 >> = 2 × (4 × 5) = 40
Step – 3 –: Taking Unit, Tens and Hundreds place digits,
<< 452 >> = 52 + 2 × (4 × 2) = 41,
Step – 4 –: Taking Tens and unit place digits,
<<52>> = 2 × ( 5 × 2 ) = 20
Step – 5 –: Taking Unit place digit,
<<2>> = square of 2 = 4
Then,
N = 4 + (20 × 10) + (41 × 100) + (40×1000) + (16×10000) = 204304.

2. Square of 879 :-

Let N = Square of 879
Step – 1 –: Taking Hundreds place digit first,
<< 8 >> = square of 8 = 64
Step – 2 –: Taking Hundreds and Tens place digits,
<< 87 >> = 2 × ( 8 × 7 ) = 112
Step – 3 –: Taking Unit, Tens and Hundreds place digits,
<< 879 >> = 72 + 2 × (8 × 9) = 193,
Step – 4 –: Taking Tens and unit place digits,
<< 79 >> = 2 × ( 7 × 9 ) = 126
Step – 5 –: Taking Unit place digit,
<< 9 >> = square of 9 = 81
The required square is,
N = 81 + (126 × 10 ) + (193 × 100) + (112 ×1000) + (64 ×10000) = 772641.
Student practice the squaring process and you may save your time on solving the numerical.

Square of a Two Digit Number

Duplex of a number is another tool which reduces the arithmetical calculations in finding square of a number.

1. Square of 34 :-

Let N = square of 34
Step – 1 –: Taking Tens place digit first,
<< 3 >> = square of 3 =9
Step – 2 –: Taking Unit and Tens place digits,
<< 34 >> = 2 × ( 3 × 4 ) = 24
Step – 3 –: Taking Unit place digits,
<< 4 >> = square of 4 = 16
N = 16 + (24 × 10 )+ (9 × 100) = 1156.

2. Square of 87 :-

Let N = Square of 87
Step – 1 –: Taking Tens place digit first,
<< 8 >> = square of 8 = 64
Step – 2 –: Taking Unit and Tens Place digits,
<< 87 >> = 2 × ( 8 × 7 ) = 112
Step – 3 –: Taking Unit place digit
<< 7 >> = square of 7 = 49
The required square is,
N = 49 + ( 112 × 10 ) + ( 64 × 100) = 7569.
Student practice the squaring process and you may save your time on solving the numericals.