Get The Best Grades With the Least Amount of Effort : Algebra Simplify
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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.
Thus, brackets play a prominent role in Algebra Simplify.
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.
Thus we use brackets in Algebra Simplify.
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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
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