By using a simple technique from Vedic Math, I help you to remember Multiplication Table. You need to just remember some basic multiplication facts (2 times table upto 8 x 2; 3 times table upto 7 x 3; 4 times table upto 6 x 4; 5 times table upto 5 x 5;). Using these basic multiplication facts, we can arrive at all other values.The method is easy to follow, learn and apply.
To remember Multiplication Table, consider the sum of multiplicand and multiplier.
Remember the values for the sum < 10 (2 times table upto 8 x 2; 3 times table upto 7 x 3; 4 times table upto 6 x 4; 5 times table upto 5 x 5;).
We may call these basic Multiplication facts to be remembered.
Using these basic Multiplication facts, We arrive at the values for the sum > 10 (all other values of the multiplication Table) using simple technique from Vedic Mathematics.
The method we follow, here, is very simple to understand and very easy to follow.
The method is based on "Nikhilam" sutra of vedic mathematics.
The method will be clear from the following examples.
Example 1 :
Suppose, we have to find 9 x 6.
First we write one below the other.
9
6
Then we subtract the digits from 10 and write the values (10-9=1; 10-6=4) to the right of the digits with a '-' sign in between.
9 - 1
6 - 4
The product has two parts. The first part is the cross difference (here it is 9 - 4 = 6 - 1 = 5).
The second part is the vertical product of the right digits (here it is 1 x 4 = 4).
We write the two parts seperated by a slash.
9 - 1
6 - 4
-----
5/4
-----
So, 9 x 6 = 54.
Let us see one more example.
Example 2 :
Suppose, we have to find 8 x 7.
First we write one below the other.
8
7
Then we subtract the digits from 10 and write the values (10-8=2; 10-7=3) to the right of the digits with a '-' sign in between.
8 - 2
7 - 3
The product has two parts. The first part is the cross difference (here it is 8 - 3 = 7 - 2 = 5).
The second part is the vertical product of the right digits (here it is 2 x 3 = 6).
We write the two parts seperated by a slash.
8 - 2
7 - 3
-----
5/6
-----
So, 8 x 7 = 56.
Let us see one more example.
Example 3 :
Suppose, we have to find 9 x 9.
First we write one below the other.
9
9
Then we subtract the digits from 10 and write the values (10-9=1; 10-9=1) to the right of the digits with a '-' sign in between.
9 - 1
7 - 1
The product has two parts. The first part is the cross difference (here it is 9 - 1 = 9 - 1 = 8).
The second part is the vertical product of the right digits (here it is 1 x 1 = 1).
We write the two parts seperated by a slash.
9 - 1
9 - 1
-----
8/1
-----
So, 9 x 9 = 81.
In the next examples, the second part has two digits.
Let us see how to handle the issue.
Example 4:
To find 7 x 6
First we write one below the other.
7
6
Then we subtract the digits from 10 and write the values (10-7=3; 10-6=4) to the right of the digits with a '-' sign in between.
7 - 3
6 - 4
The product has two parts. The first part is the cross difference (here it is 7 - 4 = 6 - 3 = 3).
The second part is the vertical product of the right digits (here it is 3 x 4 = 12).
We write the two parts seperated by a slash.
7 - 3
6 - 4
-----
3/12
-----
The second part, here, has two digits.
we retain the units' digit (2) and carry over the other digit (1) to the left.
7 - 3
6 - 4
--------------
(3+1)/2 = 4/2
-------------
So, the answer becomes (3+1)/2 = 4/2
Thus, 7 x 6 = 42.
Example 5 :
To find 8 x 3
By following the above procedure, we may write as follows.
8 - 2
3 - 7
-----
2/14
-----
The first part = 8 - 7 = 3 - 2 = 1.
The second part here is 2x7 = 14.
It has two digits. we retain the units' digit (4) and carry over the other digit (1) to the left.
8 - 2
3 - 7
--------------
(1+1)/4 = 2/4
-------------
So, the answer becomes (1+1)/4 = 2/4
Thus, 8 x 3 = 24.
let us see one last example.
Example 6 :
To find 6 x 5
By following the above procedure, we may write as follows.
6 - 4
5 - 5
-----
1/20
-----
The first part = 6 - 5 = 5 - 4 = 1.
The second part here is 4x5 = 20.
It has two digits. we retain the units' digit (0) and carry over the other digit (2) to the left.
6 - 4
5 - 5
--------------
(1+2)/0 = 3/0
-------------
So, the answer becomes (1+2)/0 = 3/0
Thus, 6 x 5 = 30.
Thus, we can arrive at any values upto 10 x 10.
For multiplication of one and two digit numbers, go to,
http://www.math-help-ace.com/Multiplication-Table.html
Greatest Common Factor : Finding Made Easy - Lucid Explanation of an Efficient Method With Examples
Finding the largest positive integer that divides two or more numbers without remainder (G.C.F.) is an important topic in Elementary Number Theory. One way of finding the G.C.F. is by prime factorizations of the numbers. The second method based on the Euclidean algorithm, is more efficient and is discussed here. We provide lucid explanation of the method with a number of solved Examples.Quadratic Formula : Lucid Explanation of Its Derivation and Application in Solving Problems
We explain lucidly, the derivation of Quadratic formula and applying it in finding the roots, Relation between roots and coefficients, Nature of the roots, finding Quadratic Equation whose roots are given, with Examples.Unveiling the Binary Number System: A Comprehensive Guide to Conversions with Decimal
Discover the intricacies of the binary number system, the language of computers, and learn how to effortlessly convert between binary and decimal systems. This guide provides a clear and detailed explanation, complete with examples, to demystify the process of working with binary numbers.