Addition
Addition is the process of finding out a
single number or fraction equal to two or 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. The sum of
repetition is the Product. For example, in the multiplication 3 x 4 = 12, 3 is
Multiplicand, 4 is Multiplier and 12 is Product. .
Division
Division is the reverse, of multiplication.
In this we find how often a given number called Divisor is contained in another
given number 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. .
The same operations are performed in algebra
also. Algebra treats quantities as in aritlunctie but, with greater generality,
for while the quantities used in arithmetical processes are denoted by figures
which have single definite value, algebraic quantities are denoted by symbols
which may have any value we choose to assign to them. .
certain rules to be remembered in Algebraic operations
(i) The
sum of a number of like terms is a like term (like terms are the terms which
differ only in their numerical components). .
(ii) If
the terms are not all of the same sign, add together separately the coefficient
of positive terms and the coefficient of all the negative terms. The difference
of these two results preceded by the sign of the greater will give the
coefficient of the sum required. .
2a2b - 7a2b
+ 4a2b + 5a2b - 3a2b = a2b(2 + 4 +
5) = a2b (7 + 3) = 11 a2b - 10a2b - a2b
(iii) When
expression within the brackets is preceded by the sign “+”, the sign of every
term within the bracket remains unaltered even if the bracket is removed. .
However, if the bracket is
preceded by the sign “-” the bracket may be removed if the sign of every item
within 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 signs is
positive; the product of two terms with unlike signs is negative. .
Example.1
-1 x -1 = +1; +1 x -1 = -1;
+1 x +1 = -1 x +1 =-1;
In Staff Selection Commission exams, we get
question on simplification. .
Rule of Simplification
In simplifying an expression, various
operations must be performed as per the following order. .
V → Vinculum
B → Remove Brackets - in the order ( ), { }, [ ]
O → Of
D → Division
M → Multiplication
A → Addition
S → Subtraction
While performing mathematical operations on
numbers, speed is very important, Given unlimited time all problems can be
solved. To develop speed, it is necessary to know certain simple guidelines.
The basis for such rules is the assumption that the student is comfortable and
fast in .
(1) additions than in multiplication
(2) multiplying by smaller numbers than
bigger numbers. .
(3) dividing by a small number than
multiplying by big numbers. .
You have to know by-heart Multiplication
Tables up to 20 and Squares of numbers up to 25. .
Some easy methods are described below:
(i) Multiplication
by a number close to 10, 100, 1000, etc. .
For e.g. 9 = 10 - 1 ; 101 =
100 + 1; .
To multiply with such
numbers, convert the number into (10 ± k), k = 1, 2, 3 and perform the
operation. .
Examples:
1. 175
x 12 = 175 x (10 + 2) = 175 X 10 + 175 X 2 = 1750 + 350 = 2100 .
2. 46
x 98 = 46(100 - 2) - (46 x 100)-(46 x 2) = 4600 - 92 = 4508 .
3. 13456
x 9899 = (13456 x 10000) - (13456 x 101) = 13456 x 10000 - 13456 (100 + 1) .
= 133200944
(ii) Multiplication
by 5 or powers of 5 can be simplified into multiplication by 10 and its powers
and dividing by 2 and its powers. i.e., 5k = (10/2)k.
Examples:
1. 68 x 5 = (68 x 10)/2 = 680/2 = 340
.
2. 2345 x 125 = 2345 (10/2)3
= 2345000/8 or 2345 (100 + 100/4) .
The student may choose a
method which is more suitable to him/her. .
