1. Patterns and Variables

Chapter 11

Algebra

Patterns and Variables

Introduction – Algebra
Algebra is the branch of Maths that uses alphabetical letters to find unknown numbers. These letters are also called variables. The values, which are known in the given expression similar as numbers, are called constants.
 

Algebra involves the simple operation of mathematics like addition, subtraction, addition, and division involving both constant as well as variables. For case, x +10 = 0.

Patterns
Number patterns
Still, again, its successor is (n +1); if a natural, number is denoted by n.
Case Successor of n = 10 is n +1 = 11.
Still, also 2n is an indeed number and (2n +1) is an odd number, If a natural number is denoted by n.
Illustration
If n = 10, further 2n = 20 is an even number and 2n +1 = 21 is an odd number.

Patterns using matchsticks/Ice candy sticks,
Matchstick Patterns
 No. of matchsticks used to make 1st square = 4
 No. of matchsticks used to make 2nd square = 7
 No. of matchsticks used to make 3rd square = 10
 Therefore, the pattern that we observe now is 3n +1
With this pattern, we can freely find the number of matchsticks needed in any number of squares.

 Illustration
How numerous matchsticks will be used in the 50th figure?

 Answer
 3n+ 1
 3 × 50 1
 = 151 matchsticks

More about variables,
Variable
A variable is an unknown volume that is prone to change with the environment of a situation.
Example In the expression 2x+5, x is the variable.
Examples on variables
Examples of Variables are:
3 + x = 2
X = 3
(a+b) ² = a² + b² + 2ab