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Simplify \[100(100 - 3) - (100 \times 100 - 3)\].

Last updated date: 29th May 2024
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Hint: In the given question, we have to solve the equation by giving priority to the arithmetic operators. We have to follow the BODMAS rule in order to answer such a question. The means that in the given case, the brackets will be solved first, then multiplication and finally subtraction.

Complete step by step solution:
One of the most fundamental tasks of arithmetic is the evaluation of a numerical expression. When an expression includes addition (\[ + \]), subtraction (\[ - \]), multiplication (\[ \times \]), division (\[ \div \]), bracket (), and Of (of), the “BODMAS rule” determines the order of operation and simplification.
The full form of BODMAS is:
$\bullet$ Brackets (Parts of a calculation inside the bracket always come first).
 Precedence of brackets are: [{(bar)}]. Round brackets will be solved first, then curly and at last square braces.
$\bullet$ Orders (powers and square roots)
$\bullet$ Division
$\bullet$ Multiplication
$\bullet$ Addition
$\bullet$ Subtraction
The first letter of each operator is represented by each letter of the name. The precedent is from left to right in an expression involving two or more identical operators that occur in succession. We can analyse an expression in the proper order of precedence by using BODMAS.
We can now solve the given sum as follows:
\[ = 100(100 - 3) - (100 \times 100 - 3)\]
Solving the braces first, we get,
\[ = 100(97) - (10000 - 3)\] (Multiplication will take precedence over subtraction in \[100 \times 100 - 3\])
\[ = 100(97) - (9997)\]
Opening the braces, we get,
\[ = 100 \times 97 - 9997\]
Now multiplication will take precedence over subtraction and we will get,
\[ = 9700 - 9997\]
\[ = - 297\]
Thus, \[100(100 - 3) - (100 \times 100 - 3) = - 297\].

It is important to use the BODMAS rule in such questions because every operation is not associative- addition and multiplication are associative but division and subtraction are not.
Sometimes, numbers can be grouped. The symbol used for grouping the value is a bar. Grouped symbols are treated as a single expression.