# Arithmetic Operations Calculator

## Evaluate Arithmetic Expressions using Order Of Operations rules with PEMDAS or BODMAS

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Simple Expression Solver

You can enter a valid Arithmetic expression in the text box below and get the result instantly. The processing is done locally

Valid operators are +, -, *, /, ^, % , (), [], {}

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## How to Use the Arithmetic Expressions Calculator?

This tool evaluates any valid arithmetic expression. It does not evaluate Algebraic expression or equations.
• In the text box labelled as 'Expression', you can copy paste your expression or type in a valid expression using the keypad.
• The result of the expression is automatically computed and shown in the output box instantly.
• You can enter numbers (decimal, real number, fraction).
• You can Use the following operators. Operators should be between the numbers except that of unary operators are supported +, - , / ,÷, * , x , %,^
You can enter * or x for multiplication and / or ÷ for division
• These expressions are also supported where there is no operator between number and parentheses. It is taken as multiplication for eg -2(3) is taken as -2 * (3)
• You can use any of the parenthese - flower bracket, round bracket or square bracket - (), {}, [] each opening parentheses or bracket must have a proper closing bracket
• If an invalid expression is entered, the output shows blank

## What is a Math Expression?

• A Math expression is a combination of numbers, variables and operators.
• The operators are in between the numbers and this is referred to as infix notation.
• An expression has at least a minimum of 2 numbers and an operator.
1 * 2 is an expression
• Math expressions can be classified into Arithmetic Expressions and Algebraic Expression.
• Arithmetic Expression contains only numbers and operators
All these are valid Arithmetic Expressions:
3 + 4
5 - 6 + 9 * 10
(8/4) * (7/3)

• Algebraic Expressions contain numbers with variables and operators.
Examples of algebraic expression:
2x + 3
5a + 3b + 20
Valid operators for a Math Expression are :
Subtraction (-)
Multiplication (*)
Division (/)
Exponents (^)
Modulo (%)
Square root ()
with Use of (), [], {}

## The Order of Operations Rules

• Examples of Arithmetic Expressions using infix notation

• (2 + 3) * 4 - 5
• 2 ^ 3 + 4 * 5 - 6
• 2 / (3 + 4) * 5 – 6
• (10 - 5) / 2 + 1
• 2 + 3 * 4 / 5 - 6

Valid operators for order of operations:

• Parentheses ( )
• Exponents (^)
• Multiplication (*)
• Division (/)
• Subtraction (-)

The order of operation rules goes like this:

• 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 more than one same level of operators, it is evaluated from left to right

• For example, to evaluate the expression (10 - 5) / 2 + 1,

• First evaluate the expression inside the parentheses, which is 10 - 5 = 5.
• Then, divide 5 by 2, which gives 2.5.
• Finally, add 1 to 2.5, which gives the final answer of 3.5.

## PEMDAS vs BODMAS

• BODMAS and PEMDAS both are acronyms for order of operation rules

• BODMAS: Brackets, Orders, Division, Multiplication, Addition, and Subtraction.

• PEMDAS: Parentheses, Exponents, Multiplication, Division, Addition, and Subtraction.

• 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. So both BODMAS and PEMDAS are the same

• To Evaluate the expression using BODMAS or PEMDAS , consider the expression : (2 + 3) * 4 - 5
• Evaluate inside the parentheses first: 2 + 3 = 5.
• Multiply 5 * 4 = 20.
• Subtract 5 from 20: 20 - 5 = 15.
• The order of operations can be used to create puzzles and challenges.
This is a popular puzzle : 8 / 2 * (2+2)

• Is the answer 16 or 1? Try it out with our Expression Solver!

## Example of math calculations using the PEMDAS rule

Consider the expression : 7 / (3 + 4) * 5 - 6
Step 1 : Evaluate Parentheses (3 + 4) = 7
Expression: 7 / 7 * 5 - 6
Step 2: There are no exponents, so skip.
Step 3: Evaluate from Left to Right - Division or Multiplication 7/7 = 1
Expression : 1 * 5 - 6
Step 4: Evaluate Multiplication - 1 * 5 = 5
Step 5: Evaluate Subtraction : 5 - 6 = -1
Result : -1

## Example of math calculations using the BODMAS rule

Consider the expression : 2 - 4 ^ 2 / 2 + ( 3 ^ 2) - 2 * 4 / 2
Step 1: Evaluate terms in Brackets ( 3 ^ 2) = 3 x 3 = 9
Expression: 2 - 4 ^ 2 / 2 + 9 - 2 * 4 / 2
Step 2: Evaluate Order(Exponent) = 4 ^ 2 = 4 x 4 = 16
Expression : 2 - 16 / 2 + 9 - 2 * 4 / 2
Step 3: Evaluate Division or Multiplication from left to right
16 / 2 = 8
Expression: 2 - 8 + 9 - 2 * 4 / 2
2 * 4 = 8
Expression : 2 - 8 + 9 - 8 / 2
8 / 2 = 4
Expression: 2 - 8 + 9 - 4
Step 4: Evaluate Addition or Subtraction from left to right
2 - 8 = -6
Expression : -6 + 9 -4
-6 + 9 = 3
Expression: 3 - 4 = -1
Result : -1

## Frequently Asked Questions on Arithmetic Operations Calculator

• BODMAS is a rule for simplification of Arithmetic expression.
BODMAS stands for 'Brackets Orders Division Multiplication Addition and Subtraction.
Consider an example to evaluate using BODMAS : 2 + 5 * (4 - 3) ^ 2
Evaluate Brackets first (4-3) = 1
Then Orders = (1)^ 2 = 1
Then multiplication 2 + 5 * 1 = 5
Then addition 2 + 5 = 7
Result = 7

• PEMDAS is a rule for simplification of Arithmetic expression.
PEMDAS stands for Parentheses, Exponents, Multiplication, Division, Addition, and Subtraction.
Multiplication/Division is evaluated equally based on whichever comes first from left to right.
Addition / Subtraction is evaluated equally based on whichever comes first from left to right.

• Yes, this calculator can handle complex Arithmetic expression but does not evaluate Algebraic expression whether simple or complex.
By complex Arithmetic expression we mean usage of many numbers and different operators with use of parentheses and exponents in different combinations

• They are different acronymns used for the same order of rules expressions and they are all similar.
PEDMAS - Parantheses, Exponent, Division & Multiplication, Addition & Subtraction.
Whether it is Division First or Multiplication, they are of the same priority and evaluated from Left to Right.
BEDMAS - Brackets, Exponents, Division, Multiplication, Addition , Subtraction Instead of 'Orders' it is Exponents here.
They are identical GEMDAS - Grouping, Exponents, Multiplication, Division, Addition, Subtraction Instead of Parentheses and Brackets, the term 'Groupinp' is used.
MDAS - Multiplication, Division, Addition and Subtraction.
It is a subset of the above acronyms.

• An Expression is a combination of numbers, variables with operator.
Example :
2 * 3 + 5
-5 -2 - 7
10x + 10x
An Equation has 2 expression statements separated by an = sign.
Example:
2x + 3 = 5
5 + 2 = 1 + 7
An expression is evaluated or simplified.
2 * 3 + 5 = 11
An Equation is usually solved
2x + 3 = 5 leads to x = 1

• Both PEMDAS and BODMAS evaluate Left to Right after evaluating terms within parentheses first and Orders/Exponents.
Consider expression: 16 / 4 / (1+1)
Step 1: Evaluate Parentheses (1+1) = 2
Expression becomes 16 / 4 / 2
Step2: Evaluate from left to right (division or multiplication) 16/4 = 4
Expression becomes 4 / 2
Step 3 : Evaluate 4 / 2 = 2
Result is 2

• To solve Arithmetic Expressions, follow the order of operation rules.
The order of operation rules are as follows:
1. Evaluate all expressions inside parentheses first.
2. Evaluate all exponents next.
3. Evaluate multiplication and division from left to right. Whichever comes first (* or /) is evaluated first .
4. Evaluate addition and subtraction from left to right. Whichever comes first (+ or -) is evaluated first.
5. If there are multiple operators of the same precedence, they are evaluated from left to right.