Hello everyone can you all tell what comes
in to your mind as soon as you hear the word
mathematics.
Some might say numbers..some say addition
subtraction .. Shapes like circle, triangle
etc.
Yes! You all are right...but math is much
more than this.
Math is part of our everyday life. For example
when we wake up in the morning, our first
action is to look at our clock. Then when
we go for breakfast ask for 2 slices of bread
We will again be using maths if we dial number
to phone. We all love shopping and here too
maths plays an important role say if there's
a discount then you can see how much it would
be if it was maybe 20% off or something. So
like this there are many incidents where math
is used & hence is so important to learn and
understand.
But do we really know what mathematics is?
Is it only about numbers & shapes?
No.
There are many more interesting things that
we can learn as the word mathematics itself
means the things that are learned
One of the very first things that we learnt
in our childhood is numbers and its counting.
We ve also learnt some basic operations that
we apply on them.
Like addition of numbers.subtraction multiplication
& division the answers that we get are called
sum, difference, product & quotient.
Now the area of mathematics where numbers
are combined with some basic operations & their
calculation s����.. forms a different
branch in math called arithmetic, the operations
are called arithmetic operations.
The word arithmetic itself means number.
Now as time passes we gain more knowledge.
So in this session we are going to learn one
of the most important branches of math known
as algebra which is the foundation for many
other topics & a great subject for getting
your brain to think differently and sharply.
So what is algebra? Is it same as arithmetic?
Lets understand it.
We know that in arithmetic we can easily say
8+2=10 & 7-5=2 but suppose someone asks the
same question in some other way i.e. how much
amount do we add to 8 to get total of 10?
Or how much should we remove from 7 to get
balance of 2.
Look at this 8 + ___ . 10
7 - ___ .. 2 okay so the answers for these
blank place are 2 & 5 resp � right.
Here what we are actually doing?
We are finding the value of the empty place
which we don�t know yet hence this empty
place also called as unknown.
But every time we cannot use words like empty
place or unknown.
Hence in algebra we denote this unknown value..i.e.
this empty place by an alphabet & it can be
any letter a..b..cor xyso on.
So instead of keeping it
So, Algebra simply means finding the value
of unknown numbers
I am sure you have now understood the difference
between arithmetic and algebra
Lets take an example to learn few more things
in it.
Suppose, you have a small stationary shop,
where you sell one pencil for 3 bucks.
Customer1 comes and asks for 5 pencils, costomer2
asks for 7 pencils customer3 directly gives
you 12 bucks and asks to give as many pencils
as you can for 12 bucks.
Price of 1 pencil no of pencil amount
3 5 ___
3 7 ___
3 ___ 12
Friends here price for a pencil is a fixed
amount and what is unknown to us is either
no. of pencils or total amount for the same.
Let us first find the unknown values.
Now, can you tell what should be the total
amount for 5 pencils in case of customer 1.
It is 3*5 = 15 right? Similarly for 7 pencils
the amount will be 21 bucks.
So what did we do exactly? We have multiplied
price of a pencil with number of pencils sold
to get the unknown total amount
But for 3rd customer .in 12 bucks what will
be the number of pencil?
How to find that, all we have to do is divide
the total amount 12 by price of a pencil i.e.
3 and that will give us 4.
Observe the table and understand that here
cost of pencil is a constant value while the
number of pencils purchased by each customer
varies and as a result their total amount
is also different.
So if we denote num of pencils by x & total
amount as y
��������in general we can
write it as 3x = y
Friends 3x simply means that 3 multiplied
by x or sometimes 3 dot x, dot also represents
multiplication.
Now note that here x & y are unknowns whose
value is not fixed & its varying hence in
algebra unknown numbers are also known as
variables.
And the fixed number here price for a pencil
is known as constant.
Now if we concentrate only on 3x, we can see
that we have constant 3 & the variable x&
both are combined with an operation.. multiplication.
So such type of expressions that involve variables
and constants & are combined with the fundamental
operations, it is called as algebraic expression.
Therefore 3x is an algebraic expression and
y is also an alg exp as y is a variable and
can be written as 1* y
And when such algebraic expressions are equated
i.e. we put an equal to sign between them
, then this whole thing is called an equation.
Lets have some more examples of algebraic
expression:
I had some money I gave 16 bucks to one of
my friend now I have 56 bucks left.
How can we form an algebraic expression of
this statement?
Here the money I had is unknown 
so this is the equation and this is expression.
These are some examples of equations and expressions
match them correctly.
Sum of 2 numbers is 15
X = y + 3
Mr. x is 3 years elder than Mr. y
7y
I had some mango & gave
3 to my brother
X - 3
Price for one chocolate y bucks
Price for 7chocolates is X + y = 15
Friends in our upcoming sessions we ll be
learning in detail about the algebraic expressions
and equations.
So thats all for this session in our next
session well learn more on algebra. But if
you have any doubts or anything for this session
do let us know in the common below. Also like
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by sharing the same.
