Simplification:
Addition:
Addition is the process of finding out a single number or fraction equal to two are more quantities
taken together.
Subtraction:
Subtraction is the process of finding out the quantity left when a smaller quantity (number/fraction)
is reduced from a larger one.
Multiplication:
multiplication signifies repeated addition.
If a number has to be repeatedly added then that number is the multiplicand.
The number of times the addition is to be done is the multiplier.
For example in the multiplication 3 * 4=12,3 is multiplicand,4 is multiplier and 12 is product.
Division:
Division is the revers of multiplication.In this we find how often a given number is called Divisor is contained in another given number is called Dividend.
The number expressing this is called the Quotient and the excess of the dividend over the product of the divisor and the quotient is called the Remainder.
For example,In the division 32/5,32 is the Dividend,5 is the Divisor,6 is the Quotient and 2 is the Remainder.
Certain rules to be remembered in Algebraic operations:
1)The sum of a number of like term(Like term are the terms which differ only in their numerical components).
2)If the terms are not all of the same sign,add together separately he coefficient of positive terms and the coefficient of all the negative terms.The difference of
two results preceded by the sign of the greater will give the coefficient of the sum required.
3)When the expressions with in the bracket is preceded by the sign "+" ,the sign of the every term within the bracket remains unaltered even if the bracket is removed
However,If the bracket is preceded by sign "-",the bracket maybe removed if the sign of every item with in the bracket is changed.
a+(b-c+d)=a+b-c+d;
a-(b-c+d)=a-b+c-d.
Rule of signs:
The product of two terms with like sign is positive;
The product of two terms with unlike sign is negative,
Example:-1 * -1 =+1
+1 * -1 =-1
+1 * +1 =+1
-1 * +1 =-1
Rule of simplification:
1)BODMAS Rule:
This rule depicts the correct sequence in which the operations are to be executed, so as to find out the value of given expression.
Here B - Bracket,
O - of,
D - Division,
M - Multiplication,
A - Addition and
S - Subtraction
Thus, in simplifying an expression, first of all the brackets must be removed, strictly in the order (), {} and ||.
After removing the brackets, we must use the following operations strictly in the order:
(i) of (ii) Division (iii) Multiplication (iv) Addition (v) Subtraction.
Modulus of a Real Number:
Modulus of a real number a is defined as
|a| = a, if a > 0
-a, if a < 0
Thus, |5| = 5 and |-5| = -(-5) = 5.
Virnaculum (or Bar):
When an expression contains Virnaculum, before applying the 'BODMAS' rule, we simplify the expression under the Virnaculum.
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