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How to Evaluate Arithmetic Expression using Order of Operations
Examples of Arithmetic Expressions
- (2 + 3) * 4 - 5
- 2 ^ 3 + 4 * 5 - 6
- 2 / (3 + 4) * 5 – 6
- (10 - 5) / 2 + 1
- 2 + 3 * 4 / 5 - 6
The expressions are written in infix notation, which is the most common way to write arithmetic expressions. In infix notation, the operators are written between the operands
Valid operators for order of operations:
- Parentheses ( )
- Exponents (^)
- Multiplication (*)
- Division (/)
- Addition (+)
- Subtraction (-)
The order of operation rules are as follows:
- Evaluate all expressions inside parentheses first.
- Evaluate all exponents next.
- Evaluate multiplication and division from left to right.
- Evaluate addition and subtraction from left to right.
If there are multiple operators of the same precedence, they are evaluated from left to right.
For example, to evaluate the expression (10 - 5) / 2 + 1,
- You must first evaluate the expression inside the parentheses, which is 10 - 5 = 5.
- Then, you must divide 5 by 2, which gives you 2.5.
- Finally, you must add 1 to 2.5, which gives you a final answer of 3.5.
PEMDAS vs BODMAS
BODMAS and PEMDAS are two different acronyms for the same order of operations rules
BODMAS: Brackets, Orders, Division, Multiplication, Addition, and Subtraction.
PEMDAS: Parentheses, Exponents, Multiplication, Division, Addition, and Subtraction.
The origin of PEMDAS is unclear, but it is thought to have been developed in the early 20th century. The acronym BODMAS is thought to have originated in the United Kingdom, but it is now used in many other countries as well.
Both PEMDAS and BODMAS are widely used in mathematics education and in many scientific and engineering fields. They are important for ensuring that everyone will get the same answer when evaluating an expression, even if they use different calculators or software programs
The only difference between the two acronyms is the word used for exponents. In the UK, exponents are called orders, while in the US, they are called exponents.
Therefore, BODMAS and PEMDAS are essentially the same thing. They both describe the order in which operations should be performed in an arithmetic expression.
Here is an example of how to use the BODMAS/PEMDAS rules to evaluate an expression: (2 + 3) * 4 - 5
- Evaluate the expression inside the parentheses first: 2 + 3 = 5.
- Multiply 5 * 4 = 20.
- Subtract 5 from 20: 20 - 5 = 15.
- Therefore, the final answer is 15.
The order of operations was first developed in the 17th century by the German mathematician Gottfried Wilhelm Leibniz.
The order of operations is important because it ensures that everyone will get the same answer when evaluating an expression, even if they use different calculators or software programs.
The order of operations can be used to create expressions that have different values depending on which operations are performed first. For example, the expression 2 * 3 + 4 can have the value of 10 or 22, depending on whether you multiply 2 * 3 or add 2 + 4 first.
The order of operations can be used to create puzzles and challenges. For example, the following puzzle is a classic example of a tricky order of operations expression: 8 / 2 * (2+2)
- The answer is 16 or 1? Try it out with the expression solver above!
The order of operations is not universal. There are some variations in the order of operations that are used in different countries and in different fields of mathematics.
There are other order of operations besides BODMAS and PEMDAS.
- One example is the Reverse Polish Notation (RPN) order of operations. In RPN, the operands are written before the operators. For example, the expression 2 + 3 would be written as 2 3 + in RPN.
- Another example is the Polish Notation (PN) order of operations. In PN, the operators are written before the operands. For example, the expression 2 + 3 would be written as + 2 3 in PN.
- RPN and PN are often used in computer programming, but they are not as commonly used in mathematics education.
Note: The above content has inputs from Bard, the AI Model from Google
The acronyms stand for:
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