The document discusses basic rules of algebra. It recaps terms like algebraic expressions and equations from the previous class. It then explains that the rules of addition and subtraction of algebraic terms are similar to numerical addition and subtraction, but the terms must be "like" terms, meaning they have the same variables. Unlike terms, with different variables, cannot be added or subtracted. It provides several examples to illustrate how to combine like terms through addition and subtraction.

1. Algebra - Recap
In the last class you got to know about Terminologies of Algebra
• Any real number with unknown term
alphabets
Algebraic Terms
• Algebraic terms having same and
different coefficients
Like and Unlike Terms
• Having one or more than one
algebraic term combined with + or -
Algebraic Expressions
Equations • Two sides with = sign in between
In this class you will learn about Basic rules of algebra.
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2. Algebra – Class 3
Basic Rules of
Algebra
2
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3. 3
Algebra - Rules
addition subtraction
Let’s just brush up them…
6 + 3 = 9 15 - 8 = 7 14 + 17 = 31 835 - 583 = 252
Same thing continues here also.
But there are few rules to understand as we have
unknown terms!
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4. 4
Algebra - Addition
Do you remember
the Chocolate
example in the first
You had x
chocolates
class?
• You bought same
x chocolates
Now you have
x + x = 2x
chocolates
• Correct?
Let’s recall it
Then your friend
gives you 3x
chocolates
• So total is
• 2x + 3x = 5x
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5. 5
Algebra - Addition
So now you
got the idea,
right?
It is just adding
the numbers
Let’s see more examples
Then writing
literal coef.
with the
answer
2x + 4x = 6x 12y + 5y = 17y 6a + 15a = 21a
84m + 12m = 96m 52p + 32p = 84p 19c + 94c = 113c
241d + d = 242d 751k + 469k = 1220k 2135u + 135u = 2270u
53xy + 24xy = 77xy pqr + 29qpr = 30pqr abcd + abcd = 2abcd
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6. 6
Algebra - Subtraction
In subtraction also
the basic rules
remains the same.
Subtract the numbers and write the unknown
alphabet term in the answer with it
Let’s see few examples to understand
6x - 4x = 2x 12y - 5y = 7y 16a - 15a = a
86m - 22m = 64m x - x = 0 (0 x = 0) 198c - 94c = 104c
21d - d = 20d 651k - 262k = 389k 2135u - 135u = 2000u
63xy - 44yx = 19xy 2pqr - pqr = qpr abcd - abcd = 0
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7. Algebra – Observation
The literal coef. are to be same for both terms for addition and
subtraction.
• i.e. Addition and subtraction Only for like terms
You have learned in terminologies corollary that d=1d.
• So such single terms are to be taken as 1 for addition and subtraction.
Also you have learned ‘pqr’ = ‘qpr’ in algebra.
• So addition and subtraction is possible in such cases.
0z = 0 and 0abcd = 0 i.e whatever with 0 is 0 itself.
• No need to write the unknown term with 0
7
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8. 8
Algebra – Unlike Term Rules
What if the literal coeff. i.e. alphabets are not same? (unlike terms)
x Mangoes y Oranges x + y Mangoes
and Oranges
So we are not adding numbers because both are different fruits
It is common sense,
isn’t it?
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9. Algebra - Unlike Term Rules
So if the literal coeff. (alphabets) are not same (unlike) then
we can not add nor subtract numbers
Let’s familiarize them more clearly.
5x + 3y = 5x + 3y 41a + 12b = 41a + 12b
8pq+ 8pqr = 8pq + 8pqr 23qe – 5pe = 23qe – 5pe
9k – j = 9k – j p + q + r = p + q + r
Remember the Mango + Orange when you
see unlike terms
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10. 10
Algebra - Summary
Addition
Add the
numbers
Write the literal
coeff. with the
answer
Subtraction
Subtract the
numbers
Write the literal
coeff. with the
answer
Rules
Like terms can
be added and
subtracted
Unlike terms
can not be
added nor
subtracted.
Observations
0 has no value
so no need to
have unknown
term with it.
2x + 4y = 4y + 2x
Terms can be
interchanged but
sign should be
same
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