ALGEBRA SIMPLIFY : USE OF
BRACKETS AS GROUPING SYMBOLS
AND FOR PRIOROTIZING OPERATIONS

Please study Algebra Substitution before Algebra Simplify
if you have not already done so.

Brackets (or) Grouping Symbols

Need for Brackets in Algebra Simplify :

Suppose you want to subtract 3 from 9 (9 - 3 = 6)
and subtract the result from 20 (20 - 6 = 14).
How do you write it ?

If you write like 20 - 9 - 3,
it becomes wrong. why ?

Because it becomes subtracting 9 from 20 ( 20 - 9 = 11)
and then subtracting 3 from the result ( 11 - 3 = 8).
Instead of getting 14, you are getting 8.

To avoid this confusion, we write our
intended calculation as 20 - (9 - 3)
which conveys that we have to subtract
3 from 9 first and then subtract
the result from 20.

For the other way of calculating,
we may specify as (20 - 9) - 3.

Here we are using brackets (parentheses)
as grouping symbols and for priorotizing
the operation. (the operation in the
brackets is to be performed first).

Let us see one more example.

Suppose you want to add 5 and 8 (5 + 8 = 13)
and multiply the result with 4 ( 4 x 13 )
to get 52.

Writing this like 4 x 5 + 8 gives the result
as ( 4 x 5 = 20 and 20 + 8 = ) 28 which
is different from 52.

i.e. 4 x (5 + 8) = 4 x (13) = 52.
where as (4 x 5) + 8 = 20 + 8 = 28.

By using brackets, we specify how we
want to get the value of the expression.

Just as we use punctuation marks
in language to get correct
meaning of sentences, we use
brackets to get correct values
of expressions in mathematics.

From this discussion, it is clear that
In mathematical expressions
brackets usually convey two things :

(i) The operation in brackets is to be done first.
(ii) The expression in brackets is
to be treated as a single number.

Different types of Brackets and their order in Algebra Simplify

We may have to use more than
one bracket in an expression.

Then we use Small Brackets "( )" first,
Flower Brackets or Braces "{ }" as second
and Square Brackets "[ ]" as third.

While removing Brackets also,
the same order is followed.

First we remove Small Brackets "( )",
then Flower Brackets or Braces "{ }"
and then Square Brackets "[ ]".

Some people use Vinculum "¯"
as the first one folllowed by
Small Brackets "( )",
Flower Brackets or Braces "{ }"
and Square Brackets "[ ]"
in that order in putting and removing.

Vinculum "¯" is an over bar on the
entire expression which is to be
treated as a single unit.

For the Rules for Removal of Brackets
and the Rules for Inserting of Brackets,
and their application in solving problems
in Algebra Simplify, through Examples, Go to

Algebra Rules