# Math Equation Solver | Order of Operations

## Calculator Use

Solve math problems using order of operations like PEMDAS, BEDMAS, BODMAS, GEMDAS and MDAS. (PEMDAS Caution) This calculator solves math equations that add, subtract, multiply and divide positive and negative numbers and exponential numbers. You can also include parentheses and numbers with exponents or roots in your equations.

Use these math symbols:

**+** Addition

**-** Subtraction

***** Multiplication

**/** Division

**^** Exponents (2^5 is 2 raised to the power of 5)

**r** Roots (2r3 is the 3rd root of 2)

**() [] {}** Brackets or Grouping

You can try to copy equations from other printed sources and paste them here and, if they use ÷ for division and × for multiplication, this equation calculator will try to convert them to / and * respectively but in some cases you may need to retype copied and pasted symbols or even full equations.

If your equation has fractional exponents or roots be sure to enclose the fractions in parentheses. For example:

- 5^(2/3) is 5 raised to the 2/3
- 5r(1/4) is the 1/4 root of 5 which is the same as 5 raised to the 4th power

### Entering fractions

If you want an entry such as 1/2 to be treated as a fraction then enter it as (1/2). For example, in the equation 4 divided by ½ you must enter it as 4/(1/2). Then the division 1/2 = 0.5 is performed first and 4/0.5 = 8 is performed last. If you incorrectly enter it as 4/1/2 then it is solved 4/1 = 4 first then 4/2 = 2 last. 2 is a wrong answer. 8 was the correct answer.

## Math Order of Operations - PEMDAS, BEDMAS, BODMAS, GEMDAS, MDAS

PEMDAS is an acronym that may help you remember order of operations for solving math equations. PEMDAS is typcially expanded into the phrase, "Please Excuse My Dear Aunt Sally." The first letter of each word in the phrase creates the PEMDAS acronym. Solve math problems with the standard mathematical order of operations, working left to right:

- Parentheses, Brackets, Grouping - working left to right in the equation, find and solve expressions in parentheses first; if you have nested parentheses then work from the innermost to outermost
- Exponents and Roots - working left to right in the equation, calculate all exponential and root expressions second
- Multiplication and Division - next, solve both multiplication AND division expressions as they occur, working left to right in the equation. For the MDAS rule, you'll start with this step.
- Addition and Subtraction - next, solve both addition AND subtraction expressions as they occur, working left to right in the equation

### PEMDAS Caution

Multiplication DOES NOT always get performed before Division. Multiplication and Division are performed as they occur in the equation, from left to right.

Addition DOES NOT always get performed before Subtraction. Addition and Subtraction are performed as they occur in the equation, from left to right.

The order "MD" (DM in BEDMAS) is sometimes confused to mean that Multiplication happens before Division (or vice versa). However, multiplication and division have the same precedence. In other words, multiplication and division are performed during the same step from left to right. For example, 4/2*2 = 4 and 4/2*2 does not equal 1.

The same confusion can also happen with "AS" however, addition and subtraction also have the same precedence and are performed during the same step from left to right. For example, 5 - 3 + 2 = 4 and 5 - 3 + 2 does not equal 0.

A way to remember this could be to write PEMDAS as PE(MD)(AS) or BEDMAS as BE(DM)(AS).

### Order of Operations Acronyms

The acronyms for order of operations mean you should solve equations in this order always working left to right in your equation.

**PEMDAS** stands for "**P**arentheses, **E**xponents,
**M**ultiplication *and* **D**ivision, **A**ddition
*and* **S**ubtraction"

You may also see BEDMAS, BODMAS, and GEMDAS as order of operations acronyms. In these acronyms, "brackets" are the same as parentheses, and "order" is the same as exponents. For GEMDAS, "grouping" is like parentheses or brackets.

**BEDMAS **stands for "**B**rackets, **E**xponents,
**D**ivision *and* **M**ultiplication, **A**ddition
*and* **S**ubtraction"

BEDMAS is similar to BODMAS.

**BODMAS **stands for "**B**rackets, **O**rder,
**D**ivision *and* **M**ultiplication, **A**ddition
*and* **S**ubtraction"

**GEMDAS **stands for "**G**rouping, **E**xponents,
**D**ivision *and* **M**ultiplication, **A**ddition
*and* **S**ubtraction"

**MDAS ** is a subset of the acronyms above. It stands for "**M**ultiplication,
*and* **D**ivision, **A**ddition *and* **S**ubtraction"

### Operator Associativity

Multiplication, division, addition and subtraction are left-associative. This means that when you are solving multiplication and division expressions you proceed from the left side of your equation to the right. Similarly, when you are solving addition and subtraction expressions you proceed from left to right.

Examples of left-associativity:

- a / b * c = (a / b) * c
- a + b - c = (a + b) - c

Exponents and roots or radicals are right-associative and are solved from right to left.

Examples of right-associativity:

- 2^3^4^5 = 2^(3^(4^5))
- 2r3^(4/5) = 2r(3^(4/5))

For nested parentheses or brackets, solve the innermost parentheses or bracket expressions first and work toward the outermost parentheses. For each expression within parentheses, follow the rest of the PEMDAS order: First calculate exponents and radicals, then multiplication and division, and finally addition and subtraction.

You can solve multiplication and division during the same step in the math problem: after solving for parentheses, exponents and radicals and before adding and subtracting. Proceed from left to right for multiplication and division. Solve addition and subtraction last after parentheses, exponents, roots and multiplying/dividing. Again, proceed from left to right for adding and subtracting.

## Adding, Subtracting, Multiplying and Dividing Positive and Negative Numbers

This calculator follows standard rules to solve equations.

### Rules for Addition Operations (+)

If signs are the same then keep the sign and add the numbers.

If signs are different then subtract the smaller number from the larger number and keep the sign of the larger number.

### Rules for Subtraction Operations (-)

Keep the sign of the first number. Change all the following subtraction signs to addition signs. Change the sign of each number that follows so that positive becomes negative, and negative becomes positive then follow the rules for addition problems.

### Rules for Multiplication Operations (* or ×)

Multiplying a negative by a negative or a positive by a positive produces a positive result. Multiplying a positive by a negative or a negative by a positive produces a negative result.

### Rules for Division Operations (/ or ÷)

Similar to multiplication, dividing a negative by a negative or a positive by a positive produces a positive result. Dividing a positive by a negative or a negative by a positive produces a negative result.