# Math Equation Solver

## Calculator Use

Solve math problems using order of operations like PEMDAS, BEDMAS and BODMAS. 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

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

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

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:

- Parentheses - solve expressions in parentheses first; innermost to outermost
- Exponents and Roots - calculate exponential and root expressions second
- Multiplication and Division - solve these expressions next
- Addition and Subtraction - do these calculations last

**PEMDAS** means you should solve equations in this order, first to last: "**P**arentheses
**E**xponents **M**ultiplication **D**ivision
**A**ddition **S**ubtraction"

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

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

BEDMAS is similar to BODMAS.

**BODMAS **stands for "**B**rackets **O**rder
**D**ivision **M**ultiplication **A**ddition
**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.

**Cite this content, page or calculator as:**

Furey, Edward "Math Equation Solver"; from *https://www.calculatorsoup.com* - Online Calculator Resource.