Because if numerical expressions were simplified in any old order, then different orders would give different answers.
For example,
2+3*5 = 2 + 15 = 17
But if you did it as 2+3*5 = 5*5 = 25
The rules are there to ensure that the same everyone arrives at the same answer every time.
order of operations
They both use PEMDAS or Order of Operation
When you replace the variable with a number and perform the operations, you evaluate an expression. This process involves substituting the numerical value for the variable and simplifying the expression according to the given operations. Evaluation is a fundamental concept in mathematics and is used to determine the value of the expression under specific conditions.
Numerical expressions solely include numbers, while algebraic expressions may contain a variable like x. An example of a numerical expression is 1+2 and an example of an algebraic expression is 2x+3y=0.
A pair of parentheses consists of two round brackets, typically written as "(" and ")". They are used in writing to enclose additional information, clarify meaning, or indicate a separate thought. In mathematics, parentheses denote the order of operations, indicating which calculations should be performed first. Overall, they serve to add clarity and structure to both written language and numerical expressions.
Simplifying an expression is getting rid of any brackets or parentheses, performing as many operations as you can - including combining like terms. To evaluate an expression you would substitute the numerical values of all the variables, carry out all the operations (addition, multiplication etc) in the expression to reach the answer - the numerical value of the expression.
numerical expression
order of operations
the order of operations
In mathematics, to evaluate means to find the numerical value of an expression or equation. This involves substituting given values into the expression and simplifying it to obtain a single numerical result. Evaluation is a fundamental process in mathematics used to determine the outcome of mathematical operations and expressions.
In mathematics, "calculate" typically refers to performing specific operations, such as addition, subtraction, multiplication, or division, to find a numerical result. On the other hand, "evaluate" involves determining the value of a mathematical expression by substituting specific values for variables and simplifying the expression to obtain a numerical answer. While calculating focuses on the process of arithmetic operations, evaluating involves analyzing and simplifying mathematical expressions to find their values.
A combination of numbers and operations is called a Numerical Expression.
what mathematicians agreed on an so that numercial expressions would have only one value?
The four basic operations that can be used in math expressions in Alice are addition (+), subtraction (-), multiplication (*), and division (/). These operations allow you to perform calculations and manipulate numerical values in Alice programming.
It is a collection of numerical values along which are combined using arithmetic operations such as powers, addition, subtraction, multiplication and division.
It is: 245,510,000,000
None of the expressions on that list is a numerical one.