Algebra for Class 6 Notes - Concepts, Formulas & Examples

Algebra for Class 6

CBSE Class 6 Maths Chapter 11 Algebra Notes –

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Algebra for Class 6 Notes

Algebra is a branch of mathematics that 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 need basic knowledge of algebra. Some of the important concepts of algebra include:

• 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
• Using the slope-intercept formula and point-slope form, how to draw the graph of the lines
• How to solve the equation to find the roots using the quadratic formula

Algebra for Class 6 Notes - Concepts, Formulas & Examples

Algebra Class 6 Concepts

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

Algebra is the study of the use of letters, and 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. In this article, we are going to discuss the basic concepts involved in algebra for class 6 along with its formula and example.

Algebra Formulas for Class 6

The list of important algebra formulas for class 6 is given. Before that, you will get to know about the basic concepts covered in algebra for class 6.

• 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 × Y = XY
  • Example 5 × X = 5X
• a × a × a ×….× 11 times = a11 times
• In x9, 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
    $\begin{array}{l}\frac{x}{y}\end{array}$
    or
    $\begin{array}{l}y\sqrt{x}\end{array}$
• 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 division and multiplication 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

ax2 + bx + c = 0

Where a is the coefficient of x2

b is the coefficient of x

c is a constant term

To find the variable x, the quadratic equation is,

$\begin{array}{l}x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}\end{array}$

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

Algebra Class 6 Examples

Question 1:

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

Solution:

Let ‘a ‘ be the number.

Given: 18 is taken away from the 6 times of a number is 30.

6a – 18 = 30

Adding 18 on both sides,

6a = 30 + 18

6a = 48

Dividing by 6 on both sides,

6a/6 = 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)a

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.

Practice Questions

1. The length of a rectangular hall is 4 meters less than 3 times the breadth of the hall. What is the length, if the breadth is b meters?
2. Give expressions in the following cases.
   (a) 11 added to 2m
   (b) 11 subtracted from 2m
   (c) 5 times y to which 3 is added
   (d) 5 times y from which 3 is subtracted

3. To find sum of three numbers 14, 27 and 13, we can have two ways:
   (a) We may first add 14 and 27 to get 41 and then add 13 to it to get the total sum 54 or
   (b) We may add 27 and 13 to get 40 and then add 14 to get the sum 54. Thus, (14 + 27) + 13 = 14 + (27 + 13)