# Algebra for Class 6

Algebra is a branch of mathematics deals with symbols and rules for manipulating those symbols. Algebra involves algebraic expressions or manipulating equations. Studying algebra helps you to think logically and critically to solve many problems both in studies and in real life situations. It opens up the other subject. Most of the subjects needs a basic knowledge of algebra. Algebra for class 6 will help to get a basic knowledge like

- How to add, subtract, multiply and divide integers, decimals and fractional values.
- How to calculate powers and roots
- How to simplify the expressions with exponents
- How to solve the single variable and multivariable equations
- How to solve the inequalities of variables
- By using slope- intercept formula and point-slope form, how to graph the lines
- How to solve the equation to find the roots using the quadratic formula.

Algebra is the study of the use of letters it is useful to solve the problems. Using pictorial and graphical representation in class 6 algebra makes the chapter more interesting and the concepts are in a comprehensive manner.

## Algebra Formulas for Class 6

The list of important algebra formulas for class 6 are given. Before that you will get to know about the basic characteristics of algebra.

**Variable**: A letter or symbol that represents any member of a collection of two or more numbers is called a variable.**Constant**: A letter or a symbol that represents a specific number is called a constant or else a symbol having a fixed numerical value is called a constant.- The letters which are used to represent numbers are called literals or literal numbers
- Multiplication Property : X x Y = XY
- Example 5 x X = 5X

- a x a x a x….x 11 times = a
^{11 }times - In x
^{9}, where 9 is called the index or exponent and x is called the base. - The operations used in algebra are addition, subtraction, multiplication and division
- Addition : x + y
- Subtraction : x – y
- Multiplication :It is represented in either of the forms such as xy or x.y or x(y) or (x)(y)
- Division : x/y or x÷y or \(\frac{x}{y}\) or \(y\sqrt{x}\)

**Order of operations:**The order of operation in algebra is given as follows- Perform all the operations inside the brackets
- Perform the operations on roots and exponents
- Perform all the multiplication and division operations moving from left to right
- Perform all the addition and subtraction operations from left to right.

### Basic Algebra Formula:

The simple quadratic equation is given by

ax^{2}+bx+c = 0

Where, a is the coefficient of \(x^{2}\)

b is the coefficient of x^{2}

c is a constant term

To find the variable x, the quadratic equation is,

\(x=\frac{-b\pm \sqrt{b^{2}-4ac}}{2a}\)

Some of the topics that are covered in class 6 algebra are as follows:

- Introduction to Algebra
- Matchstick Problems
- The idea of a variable
- Use of variables in common rules
- Rules from Geometry
- Rules from arithmetic

- Expressions with variables
- Practical applications of expressions
- What is the equation?
- A solution of an equation

The basic topics which are covered in algebra for class 6 like writing expressions using variables, evaluating the expressions using single variables, two variables will build a strong foundation for the further concepts in higher studies.

## Sample Example

### Question :

Find the number if 18 is taken away from the 6 times of a number is 30.

### Solution :

Let ‘a ‘ be the number.

Given : 16 is taken away from the 6 times of a number is 30.

6a – 18 = 30

6a = 30 + 18

6a = 48

a=48 / 6

a=8

Therefore, the number is 8.

### Question 2 :

Solve the equation given below and find the value of x and y

X + y = 3

X – y = 1

### Solution:

Given, x + y = 3 …(1)

x – y = 1 …..(2)

By solving two equations, we get

2x = 4

X = 4/2

x= 2

Substitute x= 2 in equation (1), we get

2 + y =3

Y = 3 – 2

Y = 1

Therefore, x = 2 and y =1