Question

Explain simplification of numerical expression.

Answer 1

Hint: In this type of question we have to use the concept of numerical expression. A numerical expression is a mathematical statement that involves only numbers along with one or more operation symbols such as addition, subtraction, multiplication, division, radical and the absolute value symbol. Also we know that any mathematical word problem is solved by converting it into a numerical expression.

Complete step by step answer:
Now we have to discuss simplification of numerical expression.
We know that, A numerical expression is a mathematical statement that involves only numbers along with one or more operation symbols. So to simplify a numerical expression we have to follow the BODMAS rule.
The word BODMAS stands for
\[\begin{align}
  & \text{B }\to \text{ Brackets} \\
 & \text{O }\to \text{ Order} \\
 & \text{D }\to \text{ Division} \\
 & \text{M }\to \text{ Multiplication} \\
 & \text{A }\to \text{ Addition} \\
 & \text{S }\to \text{ Subtraction} \\
\end{align}\]
In this rule we have to solve operations in the order first bracket, followed by order, division, multiplication, addition and subtraction.
Now, we know that there are three types of brackets simple or round bracket \[\left( {} \right)\], curly bracket \[\left\{ {} \right\}\] and square bracket \[\left[ {} \right]\]. If two or more types of brackets are involved in the expression then they are simplified in the order \[\left( {} \right)\], \[\left\{ {} \right\}\]and lastly \[\left[ {} \right]\].
Let us consider an example of simplification of numerical expression
Solve- \[2000\div 10\times \left\{ \left( 12-6 \right)+\left( 36-18 \right) \right\}\]
Now we have to use simplification of numerical expressions for solving this. So we have to use the BODMAS rule.
First we will solve the round brackets
\[\Rightarrow \left( 12-6 \right)=6\And \left( 36-18 \right)=18\]
Thus the given expression becomes,
\[\Rightarrow 2000\div 10\times \left\{ 6+18 \right\}\]
Now we remove the curly bracket,
\[\Rightarrow \left\{ 6+18 \right\}=24\]
Hence we can rewrite the given expression as
\[\Rightarrow 2000\div 10\times 24\]
Now as per BODMAS rule we have to first perform division and then multiplication
\[\begin{align}
  & \Rightarrow 200\times 24 \\
 & \Rightarrow 480 \\
\end{align}\]
Hence, the final value is \[480\]i.e. \[2000\div 10\times \left\{ \left( 12-6 \right)+\left( 36-18 \right) \right\}=480\]

Note: In this type of question students have to remember that numerical expressions consist of only numbers while algebraic expressions consist of numbers along with variables. Also students have to note that the power is also termed as a numerical expression because \[{{5}^{6}}\] can be written as \[5\times 5\times 5\times 5\times 5\times 5\].