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# Numerical Expression

There are two types of expressions defined in algebra. Numerical expression and algebraical expression. A numerical expression contains numbers separated by algebraic operations, while algebraic expression may contain numbers and variables separated by algebraic operations.

By algebraic operations, we refer addition, subtraction, multiplication, division, exponentiation etc. So, Numerical expressions are combinations of numerical values and algebraic operations.

Few examples of numerical expression are:

1. $3 + 14 - 9 \times 2$

2. $\frac{5^{2}}{3}$ + $\frac{7}{3}-8$

3.
$18 \times 5 + 12 - 3 \times 15$

4.
$11 - 4 + 17$

In order to solve numerical expression, we use the rule of PEMDAS which states that:
P: First perform parenthesis operation.
E: Secondly perform all exponentiation and root operations.
M
: After that perform multiplication
D: Then division
A:
S: Finally perform
subtraction from left to right.
The example problems based on numerical expression are given below:

Example 1: Calculate $10+7(6+3)\div 9-8$.
Solution:
$10+7(6+3)\div 9-8$
= $10+7\times9\div 9-8$
= $10+63\div 9-8$
= $10+7-8$
= $17-8$
= $11$

Example 2:
Evaluate the numerical expression $100\div (13+3\times9)-2$.
Solution:
$100\div (13+3\times9)-2$
= $100\div (13+27)-2$
= $100\div 40-2$
= $2.5-2$
= 0.5

Example 3: Evaluate $3^{2}-(2+3)\div 5$.
Solution:
$3^{2}-(2+3)\div 5$
= $9-5\div 5$
= $9-1$
= 8

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