Numerical Expression vs Algebraic Expression
Numerical expression and algebraic expression are a set of symbols and numbers that are formed to represent a certain number once they have been evaluated. They contain constants, variables, operations and relations and are used in simple or complex arithmetic operations.
Numerical Expression
A numerical expression involves purely numbers and mathematical operations. Also, it is a set of numerical values that are separated by the four mathematical operations, addition, subtraction, multiplication and division. The numbers may be positive or negative. Also, when evaluating numerical expressions, we need to evaluate them using the PODMAS or BODMAS method. Start with parenthesis (bracket), order (exponent), then dividing or multiplying, and lastly adding or subtracting.
Algebraic Expressions
Algebraic expressions, on the other hand, involve letters (pronumerals) as well as numbers and mathematical operations. Numbers are called constants while letters are called variables. Even though the equation uses letters they still represent a certain number. In this case, though, the number they represent changes whenever you change the value of the variable. They still use the PODMAS method of evaluating expressions.
Difference between Numerical Expression and Algebraic Expression
So what are the differences between the numerical expressions and algebraic expressions? Well, to start, the latter uses letters as well as numbers. And therein lays the key difference. While numerical expressions are of fixed value, algebraic expressions can change depending on what you use for the variables. They are still solved using the same method, but algebraic expressions give you certain flexibility in juggling the equation. Also, to qualify as an expression, numerical or algebraic, the equation must be wellformed. That means, at the very least, everything must be in its correct place. For example, * 2/3 + is not a valid expression.
Algebraic expressions and numerical expressions are the cornerstones of our mathematical knowledge, as well as they are the basics of math itself. All those complex equations start from these simple terms and our understanding of what they are is crucial for their further study.
In brief: • Numerical expressions are expressions containing numbers and math operations only. Numbers may be positive or negative while the operations are limited to addition, subtraction, multiplication and division. • Algebraic expressions use letters as well as math operations. The letters are termed as variables while the numbers are called constants.

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