Thursday, 23 February 2012

Properties of Numbers

Hello students, Previously we have discussed about fourier transform of sine and Today we are going to discuss properties of numbers which is an important part of ap secondary education board. The numbers systems are a part of mathematics. Number systems have some basic properties like: commutative, distributive, and associative.
Associative property: associative word means to associate or to group; this property is a rule that refers to grouping. For addition, the rule is x + (y + z) = (x + y) + z. This property can be understood with the help of example: 4+ (5+7) = (4+5) + 7.
For multiplication, the operation x(yz)=(xy)z. We will understand this operation with the help of example 3(4*5)=(3*4)5.
Commutative property: commutative word means to move around or to commute; the commutative property is one of the parts that stated that you can rearrange digits in an expression. For addition, the commutative property rule is x + y = y + x; this means 6 + 4 = 4 + 6.
For multiplication, the commutative property rule is xy = yx this means 4*5 = 5*4. For example, we use the commutative property to restate 4 * 6 * a: 6*4*a, 6*a*4, a*6*4, 4*a*6, and 4*6*a
Why is it true that 4(6a) = (6a)(4)?
This is true by commutative property. (We can see that 4(6a) = (6a)(4) = 24a)
Distributive property: this property is easy to remember, this property can be stated as: x(y + z) = xy + xz. This means 3(4 + 5) = 3*4 + 3*5.
Why is it truethat3(a + b) = 3a + 3b?
This is true by the distributive property. Distributive Property operations can be performed in the real numbers.(Know more about Properties of Numbers in broad manner, here,)
The example of the number system properties: 4x - 5y + 6z (this is original statement).
4x - 5y + 6x: this is commutative property, (4x+6x)-5y: this is the associative property, x(4+6)-5y: this is distributive property.
In the next topic we are going to discuss about Binary Numbers
and Read more maths topics of different grades such as Binomial Experiments in the upcoming sessions here and and You can visit our website for getting information about Negative Correlation Coefficient.

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