6 Math Chapter 11 Algebra

Chapter Notes and Summary
Algebra : Algebra is generalized arithmetic in which numbers are represented by letters, known as literal number of simply literals.
Operations on literals and numbers :
Addition :
(i) sum of a literal x and a number 5 is x + 5.
(ii) y more than x is written as x + y.
(iii) For any literals a, b, c, we have :
a + b = b + a; a + 0 = 0 + a = a and (a + b) + c = a + (b + c)
Subtraction :
(i) 5 less than a literal x is x – 5
(ii) y less than x is x – y.
Multiplication :
(i) 4 times x is 4 × x, written as 4x.
(ii) product of x and y is x × y, written as x y or xy.
(iii) For any literals a, b, c we have :
a × 0 = 0 × a = 0; a × 1 = 1 × a = a; a × b = b × a;
(ab) c = a (bc); a (b + c) = ab + ac.
Division :
(i) x divided by y is written as x y
(ii) x divided by 7 is x 7
(iii) 30 divided by x is 30 x
Variables and Constants : A symbol having a fixed numerical value is called a constant. And, a symbol which takes on various numerical values is known as a variable.
Remark :
In some situations literal numbers are also treated as constants. In such situations, it is presumed that particular literal number will only take a fixed value.
Algebraic Expression : A combination of constants and variables connected by any one or more of symbol +, – × and ÷ is called an algebraic expression.
The several parts of expression, separated by sign + or – are called terms of expression.
Using Algebraic Expression Practically Situation Variable Algebraic Expression
• Sarita has 10 more marbles than Ameena
• Vikas is twice as old as Raju
• How old was susan 4 year ago ?
• Let Ameena have x marbles
• Let Raju’s age be x years.
• Let y be susan’s present age in years.
• Sarita has (x + 10) marbles.
• Vikas’s age is 2 x years
• Four years ago, Susan was (y – 4) year old
Equation : A algebraic expression with a variable constants and sign of equality (=).
e.g., A number x increased by 9 is 17.
x + 9 = 17
Solution of an Equation : value of variable in an equation which satisfies equation. For getting solution of an equation, one method is trial and error method. In this method, we give some value to variable and check whether it satisfies equation. We go on giving this way different values to variable until we find right value which satisfies equation.

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