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Order of Operations Calculator

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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, fractions and exponents. You can also include parentheses and numbers with exponents or roots in your equations. (See PEMDAS Note below.)

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)
() [] {} Parentheses and Brackets

You can copy equations from other sources and paste them in the calculator. If they use ÷ for division and × for multiplication this equation calculator will try to convert them to / and * respectively. 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

Fractions in Equations

If you want an entry such as 1/2 to be treated as a fraction then enter it with parentheses as (1/2). For the equation 4 divided by ½ you must enter 4/(1/2). The fraction division 1/2 = 0.5 is calculated first because it's in parentheses, and 4/0.5 = 8 is calculated next. So 4 divided by ½ = 8.

If you enter the same equation, 4/1/2 without parentheses then the calculation proceeds from left to right. 4/1 = 4, and then 4/2 = 2. So your answer is different if you do not enclose the fraction 1/2 in parentheses.

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 typically 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 - 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
  3. Multiplication and Division - next, solve multiplication AND division expressions, working left to right in the equation
  4. Addition and Subtraction - next, solve addition AND subtraction expressions, working left to right in the equation

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.

After solving for parentheses, exponents and radicals you will solve multiplication and division proceeding from left to right in the equation. Solve addition and subtraction last, again working from left to right to add and subtract.

PEMDAS Note

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 rank in the order of operations and are solved after parentheses and exponents. If your equation has several multiplication and division signs, just solve them one-by-one from left to right. So the equation 4/2*2 equals 4; it does not equal 1.

The same confusion can happen with "AS" however, addition and subtraction have the same rank in the order of operations and are solved after multiplication and division. If your equation has several addition and subtraction signs, just solve them one-by-one from left to right. So the equation 8-3+7 = 12; it does not equal -2.

Order of Operations Acronyms

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

PEMDAS stands for "Parentheses, Exponents, Multiplication and Division, Addition and Subtraction"

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

BEDMAS is similar to BODMAS.

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

Special Case: When to Solve From Right to Left

If you have multiple exponents or roots together in part of your equation you need to work from right to left and solve those before moving on and working from left to right for the remainder of the solution.

Example: 100000 - 4^3^2 / 16

  1. First solve the part of the equation that has multiple exponents, working from right to left: 4^3^2
  2. 3^2 = 3 raised to the 2nd power = 9
  3. 4^9 = 4 raised to the 9th power = 262144
  4. Plug that number back into the equation to get 100000 - 262,144 / 16
  5. Follow order of operations and do the division next: 262144 / 16 = 16384
  6. Do the subtraction next: 100000 - 16384 = 83616

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


 

Cite this content, page or calculator as:

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

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