Algebra Class 6 Maths Notes - Chapter 11

Algebra is a branch of mathematics that can substitute letters for numbers to find the unknown. It can also be defined as putting real-life variables into equations and then solving them. The word ‘algebra’ is derived from Arabic “al-jabr”, which means the reunion of broken parts. Below are some algebra problems for students to practice.

Introduction to Algebra

Variable

A variable is an unknown quantity that is prone to change with the context of a situation.
Example: In the expression $2x+5$, x is the variable.

Constant

Constant is a quantity which has a fixed value. In the given example $2x+5$, $5$ is the constant.

Terms of an Expression

Parts of an expression which are formed separately first and then added or subtracted, are known as terms.
In the above-given example, terms $2x$ and $5$ are added to form the expression $(2x+5)$.

Factors of a Term

Parts of an expression which are formed separately first and then added or subtracted, are known as terms.

• Factors of a term are quantities which cannot be further factorised.
• In the above-given example, factors of the term 2x are 2 and x.

Coefficient of a Term

The numerical factor of a term is called the coefficient of the term.
In the above-given example, 2 is the coefficient of the term 2x.
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Like and Unlike Terms

Like Terms

Terms having the same variables are called like terms.>
Example: 8xy and 3xy are like terms.

Unlike Terms

Terms having different variables are called, unlike terms.
Example: 7xy and -3x are unlike terms.
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Monomial, Binomial, Trinomial and Polynomial Terms

To know more about Polynomials, visit here.

Formation of Algebraic Expressions

Combinations of variables, constants and operators constitute an algebraic expression.

Example: $2x+3$, $3y+4xy$, etc.

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Addition and Subtraction of Algebraic Expressions

Addition and Subtraction of Like Terms

Sum of two or more like terms is a like term.

Its numerical coefficient will be equal to the sum of the numerical coefficients of all the like terms.
Example:  $8y+7y=?$

  8y
+7y
___________
(8+7)y = 15y
____________

Difference between two like terms is a like term.

Its numerical coefficient will be equal to the difference between the numerical coefficients of the two like terms.
Example: $11z-8z=?$

$11z$

$-8z\; \_\_\_\_\_\_\_\_\_\_\; (1-8)z\; =\; 3z\; \_\_\_\_\_\_\_\_\_\_\_$

Addition and Subtraction of Unlike Terms

• For adding or subtracting two or more algebraic expressions, like terms of both the expressions are grouped together and unlike terms are retained as it is.
• Addition of $-5x^2+12xy$ and $7x^2+xy+7x$ is shown below:

−5x²+12xy
7x²+xy+7x
__________
2x²+13xy+7x
__________

• Subtraction of $-5x^2+12xy$ and $7x^2+xy+7x$ is shown below:

−5x²+12xy
−7x²+xy+7x
__________

12x²+11xy−7x
__________

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Algebra as Patterns

For more information on Algebra as a Pattern, watch the below video

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Number Patterns

• If a natural number is denoted by n, then its successor is (n + 1).
  Example: Successor of $n=10$ is $n+1=11$.
• If a natural number is denoted by n, then 2n is an even number and (2n+1) is an odd number.
  Example: If $n=10$, then $2n=20$ is an even number and $2n+1=21$ is an odd number.

For more information on Number Patterns, watch the below video

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Patterns in Geometry

• Some geometrical figures follow patterns which can be represented by algebraic expressions.
  Example: Number of diagonals we can draw from one vertex of a polygon of n sides is (n – 3) which is an algebraic expression.

Algebraic Expressions in Perimeter and Area Formulae

• Algebraic expressions can be used in formulating perimeter of figures.
  Example: Let L be the length of one side then, the perimeter of :

1. An equilateral triangle = 3L.
2. A square = 4L.
3. A regular pentagon = 5L.

• Algebraic expressions can be used in formulating area of figures.
  Example: Area of :

1. Square = l2 where l is the side length of the square.
2. Rectangle = l * b, where l and b are lengths and breadth of the rectangle.
3. Triangle = 1/2 b * h where b and h are base and height of the triangle.

For more information on Perimeter and Area, watch the below video

What Is the Equation?

An equation is a condition on a variable which is satisfied only for a definite value of the variable.

• The left-hand side(LHS) and right-hand side(RHS) of an equation are separated by an equality sign. Hence LHS = RHS.
• If LHS is not equal to RHS, then it is not an equation.

Solving an Equation

Value of a variable in an equation which satisfies the equation is called its solution.

• One of the simplest methods of finding the solution of an equation is the trial and error method.

For more information on Solving an Equation, watch the below video

To know more about Linear Equations, visit here.
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