Math Equation Solver | Order of Operations (2024)

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)
rRoots (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:

  1. 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
  2. Exponents and Roots - working left to right in the equation, calculate all exponential and root expressions second
  3. 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.
  4. 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 "Parentheses, Exponents, Multiplication and Division, Addition and Subtraction"

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 "Brackets, Exponents, Division and Multiplication, Addition and Subtraction"

BEDMAS is similar to BODMAS.

BODMAS stands for "Brackets, Order, Division and Multiplication, Addition and Subtraction"

GEMDAS stands for "Grouping, Exponents, Division and Multiplication, Addition and Subtraction"

MDAS is a subset of the acronyms above. It stands for "Multiplication, and Division, Addition and Subtraction"

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.

(-) + (-) = (-)

(+) + (+) = (+)

-21 + -9 = - 30

(+7) + (+13) = (+20)

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

(-Large) + (+Small) = (-)

(-Small) + (+Large) = (+)

(-13) + (+5) = (-8)

(-7) + (+9) = (+2)

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.

(-) - (-) =

(-) - (+) =

(+) - (-) =

(-15) - (-7) =

(-5) - (+6) =

(+4) - (-3) =

(-15) + (+7) = (-8)

(-5) + (-6) = (-11)

(+4) + (+3) = (+7)

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.

(-) * (-) = (+)

(+) * (+) = (+)

(+) * (-) = (-)

(-) * (+) = (-)

-10 * -2 = 20

10 * 2 = 20

10 * -2 = -20

-10 * 2 = -20

(-) × (-) = (+)

(+) × (+) = (+)

(+) × (-) = (-)

(-) × (+) = (-)

-10 × -2 = 20

10 × 2 = 20

10 × -2 = -20

-10 × 2 = -20

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.

(-) / (-) = (+)

(+) / (+) = (+)

(+) / (-) = (-)

(-) / (+) = (-)

-10 / -2 = 5

10 / 2 = 5

10 / -2 = -5

-10 / 2 = -5

(-) ÷ (-) = (+)

(+) ÷ (+) = (+)

(+) ÷ (-) = (-)

(-) ÷ (+) = (-)

-10 ÷ -2 = 5

10 ÷ 2 = 5

10 ÷ -2 = -5

-10 ÷ 2 = -5

Math Equation Solver | Order of Operations (2024)

FAQs

What is the order of operations in solving algebraic equations? ›

What is the order of operations in math? The order of operations are the rules that tell us the sequence in which we should solve an expression with multiple operations. The order is PEMDAS: Parentheses, Exponents, Multiplication, and Division (from left to right), Addition and Subtraction (from left to right).

How to solve order of operations math problem? ›

The order of operations can be remembered by the acronym PEMDAS, which stands for: parentheses, exponents, multiplication and division from left to right, and addition and subtraction from left to right. First, simplify what is in parentheses. Then, do any exponents. Next, multiply and divide from left to right.

How to remember order of operations? ›

In the USA the mnemonic is PEMDAS, where 'P' denotes parentheses, along with the phrase "Please Excuse My Dear Aunt Sally". In the UK the mnemonic BIDMAS is used, where I stands for indices. Other variations include BODMAS, POMDAS or PODMAS, where O stands for Order.

What is the best equation solver? ›

Wolfram|Alpha is a great tool for finding polynomial roots and solving systems of equations. It also factors polynomials, plots polynomial solution sets and inequalities and more.

What are the 4 order of operations in math? ›

The order of operations (PEMDAS) is essential for solving complex math problems. PEMDAS stands for Parentheses, Exponents, Multiplication and Division (same level), and Addition and Subtraction (same level).

Do you multiply or divide first? ›

PEMDAS (“Parentheses, exponents, ...”) and BEDMAS are also used in the USA and Australia. Returning to the above example, the correct answer would be the first answer as it follows the rules of BODMAS: division can be done before multiplication and must be done before addition, and multiplication comes before addition.

What is the acronym for the order of operations in math? ›

PEMDAS is an acronym used to mention the order of operations to be followed while solving expressions having multiple operations. PEMDAS stands for P- Parentheses, E- Exponents, M- Multiplication, D- Division, A- Addition, and S- Subtraction.

How do you simplify equations using order of operations? ›

When simplifying mathematical expressions perform the operations in the following order:
  1. Parentheses and other Grouping Symbols. Simplify all expressions inside the parentheses or other grouping symbols, working on the innermost parentheses first.
  2. Exponents. ...
  3. Multiplication and Division. ...
  4. Addition and Subtraction.

What is the PEMDAS rule? ›

PEMDAS is an acronym for the words parenthesis, exponents, multiplication, division, addition, subtraction. Given two or more operations in a single expression, the order of the letters in PEMDAS tells you what to calculate first, second, third and so on, until the calculation is complete.

What are gems instead of PEMDAS? ›

GEMS stands for Groupings, Exponents, Multiplication or Division, Subtraction or Addition. Groupings refers to all grouping symbols – parentheses, brackets, braces, etc. GEMS is a new acronym that has been introduced to replace PEMDAS. These can be used interchangeably.

Why is PEMDAS wrong? ›

PEMDAS is shortsighted. It ignores mathematical properties (that is, laws), which take precedence over order of operations like PEMDAS (an accepted convention, not a law or property). I would suggest the “P” in PEMDAS should not only stand for Properties first, but secondarily for Parentheses.

How to solve the order of operations? ›

Applying the Order of Operations (PEMDAS)

The order of operations says that operations must be done in the following order: parentheses, exponents, multiplication, division, addition, and subtraction.

What's the hardest math equation you know? ›

x3+y3+z3=k, with k being all the numbers from one to 100, is a Diophantine equation that's sometimes known as "summing of three cubes."

What is the easiest way to solve equations? ›

The following steps provide a good method to use when solving linear equations.
  1. Simplify each side of the equation by removing parentheses and combining like terms.
  2. Use addition or subtraction to isolate the variable term on one side of the equation.
  3. Use multiplication or division to solve for the variable.
Sep 7, 2021

What are the 4 operations of algebraic terms? ›

The four operations of mathematics are mathematical functions which take input values (that is, numbers) and convert them into output values (again, that's another number). They are: addition, subtraction, multiplication, and division.

What is the PEMDAS in algebraic equations? ›

Lesson Summary. PEMDAS is an acronym for the words parenthesis, exponents, multiplication, division, addition, subtraction. For any expression, all exponents should be simplified first, followed by multiplication and division from left to right and, finally, addition and subtraction from left to right.

What is the order of operations to be used in solving each mathematical expression? ›

In order to evaluate expressions using order of operations, you would use PEMDAS:
  1. Solve any calculations within parentheses.
  2. Solve for any exponents.
  3. Solve any division and multiplication calculations.
  4. Solve any addition and subtraction calculations.

What is the order of operations for simplifying algebraic expressions? ›

Order of Operations
  • When simplifying mathematical expressions perform the operations in the following order: Parentheses and other Grouping Symbols.
  • Exponents.
  • Multiplication and Division.
  • Addition and Subtraction.

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