The word algebra comes from an Arabic Book called compendious book on calculation and balancing written by a famous mathematician who lived in Baghdad. Algebra means, restoration and completion.
Why do we use letters in Algebra?
You use letters to represent different numbers. This makes it easier when you are doing the same operation over and over. Rather than coming up with a new equation each time, you get one equation and just put in different numbers for the letter.
In our daily life even in the syllabus of higher classes up to university Level only Algebra leads to the remaining mathematics.
It general say that if you learn mathematics then must learn Algebra. Algebra is the super set.
First of all we comes to know that what is Algebra? Who invent it? What is the logic behind this name (Algebra)? How we teach Algebra? How we learn Algebra? Etc. etc.
In 830AD a book named al-Kitab al-mukhtasar fi hisab al-jabr wa'l-muqabala , in Arabic was written by Muhammad ibn Musa al-Khwarizmi, Khwarizm was a city near Baghdad the capital of Iraq.
It was the first time that a word Al- gabr was introduced by a mathematitian. In a meeting of Mathematitian a question asked to Muhammad ibn Musa al-Khwarizmi, that what is the meaning of Al-gabr then he said that the meaning of al-gabr is Equating both side.
Now-a-day al-gabr becomes Algebra and we teach algebra from the very beginning to the learners from elementary level.
See an equation
x + 2 = 4
(It is called 'equation' because = sign is there otherwise simply x + 2 is called an expression.)
Here ‘x’ is called variable (whose values vary time to time)
If we write this equation in statement form then we can say that “ when we add 2 to a number then it gives us 4.
In simple way in a physical balance one pan occupy x+2 and other pan contains 4.
How we calculate ‘x’?
x + 2 = 4
subtract from each pan
x + 2 - 2 = 4 – 2
(Equating both side so we call it Algebra)
x + (2 – 2) = (4 – 2)
x + (0) = (2)
x = 2
so unknown no. is nothing but 2.
Let us see another example:
3y = 21
Mean when we multiply an unknown number by 3 it gives us 21.
What is this number?
Now we calculate the desire Number as
3y = 21
Divide both side by 3 (Algebra means equating both sides)
3y/3 = 21/3
y = 7.
So 7 is the required Number, which satisfy the given condition.
Take another example
3x +7 = 19
This means that ‘if we add 7 to the thrice of a number then this gives 19’
How we solve it.
3x +7 = 19.
To solve this type of problems we use always rules of Algebra i.e. equating both sides.
Overall we draw the value of x so we should remove all the numbers surrounding ‘x’
3x +7 = 19
Subtract 7 from both sides
3x +7 - 7 = 19 – 7
3x +(7 – 7) = (19 – 7)
3x +(0) = (12)
3x = 12
Divide both side by 3
3x/3 = 12/3
x = 4
So the required number is 4.
Let's check in a bit detail what variables and expressions are in next chapter.