Algebra is that branch of mathematics that uses numbers and letters representing numbers. It uses symbols and rules to manipulate mathematical equations and expressions. The purpose of algebra is to find the unknown or to put variables of everyday life into mathematical equations and solve them. Matrixes, vectors, and real and complex numbers are all included in algebra. A mathematical equation is like a scale on which what is done on one side is also done on the other side, and numbers represent constants. 

Getting started with Algebra, it is necessary to be familiar with its basic terminology. Algebraic equations comprise four major components: variables, exponents, coefficients, operators, along with an equal sign. 

 

Consider the equation ax2 + bx + c = d. The term with the highest exponent is written first, and subsequently, the terms are written with reducing powers.

 

ax2+bx+c=d

 

Where;

• • a and b are coefficients
  • c and d are constants
  • 2 is the exponent
  • + is operator
  • X variable

 

The equation ax2 + bx + c = d has four terms. In algebra, terms can be like or unlike. Like terms in an equation are those with the same variables and exponents. Contrary to this, unlike terms in an equation represent different variables and exponents.

Variable is subject to change and can vary.

Say for Example: ____ + 5 = 9 

The answer is 4 in the place of blank, but in algebra, there is no such blank space, so we consider a letter x or y or any other letter in place of unknown values.

 Such that:

 x + 5 = 9

So, variables are unknown letters (such as the letter x). Variables may be letters from a to z. It is easier to find more unknown values by replacing unknown values with letters or by writing blank spaces instead of unknown values. A variable represents the unknown value as it changes continuously.

Constants are values that remain constant or symbols that have a fixed numeric value.

An algebraic expression comprises variables, constants, and mathematical operations.

There is no fixed value for variables; they have different values. Because they are numbers, they can be added, subtracted, multiplied, and divided.

Example:  5a+4

Equations in Algebra: In algebra, an equation is a collection of variables, constants, and mathematical operations, such as addition, subtraction, multiplication, and division balanced by the equal sign.

In an equation, the left-hand side (LHS) is the left side, while the right-hand side (RHS) is the right side. LHS and RHS are equal.

Example: x + 2 = 7, where x = 5.

Commonly used algebraic expressions

Addition, subtraction, multiplication, and division are the basic algebraic operations in Class 6 Algebra

Let x and y be two variables; we can write them as:

• • Addition: x + y
  • Subtraction: x– y
  • Multiplication: x*y or xy
  • Division: x/y or x÷y  

1. Addition has commutative property

Adding two variables in any order does not change the equation's sum. Where x and y are two variables, the commutative property states that x + y = y + x.

2. Commutativity of multiplication

The product remains the same when numbers are multiplied by distinct orders. If we consider variables x and y as in addition, we can express the commutativity of multiplication of two numbers as x*y = y*x

3. Multiplication distribution over the addition of numbers.

Consider x, y, and z as three variables, then

x × (y + z) = x × y + x × z.

The following guidelines and steps help simplify algebraic expressions:

Following is the order in which we perform algebraic operations:

• • Use brackets to perform all operations 
  • Perform root and exponent operations
  • All division and multiplication should be performed from left to right
  • Add and subtract from left to right

The easiest way to solve algebraic equations

• • Multiple factors to remove any grouping symbol, such as brackets.
  • Remove grouping if the terms contain exponents using the exponent rule.
  • By adding or subtracting like terms, combine them.
  • Put the constants together.

Q.  Algebraically express the following statements.

1. Kiran is younger than Ram by 2 years.

Answer: Let Ram’s age be x years

               Then the algebraic expression will be:

               Kiran's age is (x - 2) years

2. A kg of pulses costs 10 less than a kg of rice.

Answer: Let the price of rice be x Rs per kg

               Then the algebraic expression will be

               The price of pulses is (x-10)Rs per kg

3. Calculate the number left over after 10 is subtracted from 5 times a number is 40.

Answer: Let the number be x.

The expression for 10 is taken away from 5 times of a number is 40.

5x – 10 = 40

5x = 40 - 10

5x = 30

x = 30 / 5

x = 6.

This gives us the number 6.

 

4. Algebraic expressions for:

(a) 6 subtracted from a number x

(b) 4 is added to three times a number y

Answer:

(a) The expression is x–6

(b) The expression is 4 + 3y

1. What is the importance of algebra?

Answer:  Algebra is a crucial branch of mathematics. With the help of algebra, we can generalize any equation, which makes calculation easier. Using algebra, we can visualize an equation on a graph. The concepts of constants and variables are used in computer programming. We can also use it to solve computer-based games and puzzles. We use basic algebra in our everyday life to solve problems.

 

2. What is the name of the father of algebra?

Persian mathematician Muhammad ibn Musa al-Khwarizmi is known as the father of algebra. In his book Kitab Al-Jabr, he discusses algebra. Khwarizmi was one of the most renowned intellectuals of Bayt-al-Hikma, which dominated Baghdad's intellectual world. Apart from developing the concept of an algorithm in mathematics, he is also considered being the grandfather of computer science.

 

3. What are algebraic letters called?

Answer: In algebra, letters, called variables, are used to represent specific numbers. Algebraic variables can represent the unknown, the value being solved for, or known values.

 

4. Name the four basic properties of algebra?

Answer: Numbers have four basic properties: commutative, associative, distributive, and identity. As you progress through advanced math, such as algebra and calculus, it becomes increasingly important to understand these properties.

 

5. Can you tell me how many algebraic rules there are?

Answer: The three most commonly discussed laws are commutative, associative, and distributive. It is discovered that no matter what the order of numbers is when you add or multiply, the result will be the same.

 

6. The cadets are marching in a parade. Five cadets are lined up in a row. How can you calculate the number of cadets given in the number of rows?

Answer: Rows = n

The number of cadets in each row is 5

Thus, the total number of cadets is 5n.

 

7. Siddharth's score in mathematics is 15 more than two-fourths of his score in science. If he scores x marks in science, find his score in mathematics?

Solution:

Let us assume the score of science is x.

It is given that Siddharth’s score in mathematics is 2/4 th of x + 15

Siddharth's score in mathematics is 2/4 x + 15.

 

8. Anita and Manju are cousins. Anita is 8 years younger than Manju. Can you write about Anita’s age in terms of Manju’s age?

Answer:

Let’s take Manju’s age to be x years.

Anita is 8 years younger than Manju.

Then Anita’s age in terms of Manju’s age = (x–8) years.

 

9. How do you express the number of mangoes in terms of the number of boxes, 24 mangoes in a box? (Express it as b.)

Answer: The number of mangoes is 24b.

 

10. Eight less than two times of a has what algebraic representation?

Answer: 2a - 8 is a reasonable representation of the problem mentioned above.

You can develop your ability to think critically by learning algebra. Most professions, those in science and maths, require knowledge of algebra. You'll probably use algebra every day without even realizing it! 

Since in Class 6 the first introduction of the subject happens, students will need a lot of practice.