Order of Operations Calculator

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Operations Order Calculator

The order of operations calculator is used to solve the mathematical expressions with the correct order of operation. In solving mathematical problems, it is very critical to apply the correct order of operations to get the right answer. Order of operations in math should be the most important consideration, especially when you are working on complex mathematical equations. This calculator evaluates your input with the exact order of operations and also shows you each and every order of operation for the given expression.

We will discuss PEMDAS meaning when it is used, and some examples to solve expressions with PEMDAS order of operations.

How to use our Order of Operations Calculator?

This online PEMDAS calculator makes the order of operations very simple to execute. To use this calculator:

  1. Enter a mathematical expression in the textbox above
  2. Press the calculate
  3. See the result on the right side.

It will give you the step by evaluation of the order of operations it has implemented on your mathematical expression. You can follow each step to understand the process. These steps can also be used to solve further expressions for your next test or exam. Follow the steps that are shown in results and practice them on paper to master the PEMDAS order of operations.

What is PEMDAS?

PEMDAS is an acronym for an operating order convention to solve complex mathematical problems. The PEMDAS stands for:

  • Parenthesis
  • Exponents
  • Multiplication
  • Division
  • Addition
  • Subtraction

This acronym is actually the PEMDAS rules which specify the exact order in which operations should be executed. You can remember this acronym by using a customized string such as “Please Eat MDonut And Salad” or whatever you can remember conveniently.

The PEMDAS acronym convention implies grouping (parenthesis) first, then exponents, multiplication, division, and then addition and subtraction. Multiplication and division have the same importance and are left to right associated with each other, so you just solve them in the order they are represented in left to right.

Addition and subtraction also have the same importance and are both linked left to right, so you also resolve them when they are represented in left to right.

Exponents are connected from right to left and are resolved from right to left when the exponents appear next to one another. For \(2^3^2)\), we will first solve (3^2) and then (2^9). They are solved in the order they appear from left to right when they do not appear next to each other. For \((2^3 + 3^2)\), we will solve it as \((8 + 9)\).

When to use PEMDAS?

When mathematical expressions are written in ambiguous form, the PEMDAS convention is required. For examples, there is no doubt what the operations are to be done in the following expression:

\(4 + (3 \times 5)\)

If the parentheses are omitted, the expression may generate more than one answer without a convention depending on the order of the operations.

\(4 + 3 = 7 \times 5 = 35\)

\(3 \times 5 = 15 + 4 = 19\)

So everyone who solves the expression will be given the same result of 19 (multiplication is carried out before addition) by solving it according to the PEMDAS order of operations convention.

PEMDAS Problems

The following examples illustrate how the PEMDAS Convention addresses unclear mathematical problems.

Example 1:   \(\dfrac{10}{2} \times (3 + 2)\)

Step 1: First, solve the parenthesis.

\(= \dfrac{10}{2} \times (3 + 2)\)

\(= \dfrac{10}{2} \times (5)\)

Step 2: Eliminate the parenthesis that is solved and solve the remainder expression from the highest priority to the lowest priority.

\(= \dfrac{10}{2} \times 5\)

Step 3: Since the same precedence is given to multiplication and division, address them in the order they appear from left to right. We will solve the division first because it has appeared first from left to right.

\(= \dfrac{10}{2} \times 5\)

\(= 5 \times 5\)

Step 4: Solve the remaining expression.

\(= 5 \times 5\)

\(= 25\)

So,  \(\dfrac{10}{2} \times (3 + 2) = 25\)

Example 2:   \(6 \times (4^2 - 3)\)

Step 1: Solve expressions from highest precedence to lowest precedence within the parenthesis first. As exponents are above subtraction in precedence, solve 4^2 first.

\(= 6 \times (4^2 - 3)\)

\(= 6 \times (16 - 3)\)

Step 2: Now, solve the parenthesis. Here parenthesis contains an expression with subtraction.

\(= 6 \times (16 - 3)\)

\(= 6 \times (13)\)

Step 3: Now, we have only one expression. Solve the expression after removing the parenthesis.

\(= 6 \times 13\)

\(= 78\)

So, \(6 \times (4^2 - 3) = 78\)

PEMDAS Worksheet

The worksheet below contains ten different mathematical expressions. These expressions are comprised of basic math operations (addition, subtraction, multiplication, and division), exponents, and parenthesis. Students can use it for practice, whereas teachers and parents can use this worksheet to test the knowledge of their students and children, respectively.

You can use the above calculator to solve the expressions in the worksheet. Just copy an expression and paste it in the above text box. You will get all the steps and the final answer, which you can use to understand the PEMDAS problems.

Question Answer
\(\dfrac{(15 + 39 – 2^2 )}{( 6 + 4)}\)

((15+39)−2^2)÷(6+4)

(54−2^2)÷(6+4)

(54−4)÷(6+4)

50÷(6+4)

50÷10

5

\(\dfrac{( 8 + 55 - 3)}{3 – 2^2}\)

((8+55)−3)÷3−2^2

(63−3)÷3−2^2

60÷3−2^2

20−2^2

20−4

16

\(2 \times  ( 7 \times 8 + 4 2 ) - 5\)

2×(7×8+4^2)−5

2×(56+4^2)−5

2×(56+16)−5

2×72−5

144−5

139

\(\dfrac{(12 + 42 - 6)}{12 – 6^2}\)

((12+42)−6)÷12−6^2

(54−6)÷12−6^2

48÷12−6^2

4−6^2

4−36

-32

\((10 - 3)^2 + (15 +\dfrac{16}{2})\)

(10−3)^2+(15+16÷2)

7^2+(15+16÷2)

49+(15+16÷2)

49+(15+8)

49+23

72

\((13 + 4) \times (13 - 2) + 5^2\)

(13+4)×(13−2)+5^2

17×(13−2)+5^2

17×11+5^2

187+5^2

187+25

212

\(\dfrac{( 8 + 56 – 4^2 )}{( 12 - 4)}\)

((8+56)−4^2)÷(12−4)

(64−4^2)÷(12−4)

(64−16)÷(12−4)

48÷(12−4)

48÷8

6

\((10 - 2)^2 + ( 9 + \dfrac{20}{10})\)

(10−2)^2+(9+20÷10)

8^2+(9+20÷10)

64+(9+20÷10)

64+(9+2)

64+11

75

\(4 \times ( 9 \times 9 + 7^2 ) - 10\)

4×(9×9+7^2)−10

4×(81+7^2)−10

4×(81+49)−10

4×130−10

520−10

510

\((16 - 8) \times ( 9 + 6) + 2^2\)

(16−8)×(9+6)+2^2

8×(9+6)+2^2

8×15+2^2

120+2^2

120+4

124

PEMDAS or BOMDAS

PEMDAS and BOMDAS are the same things. Both of them refer to the mnemonic for the logical order of operations for the mathematical expressions. The acronym is different because some countries (such as the US) refer to brackets are parentheses, and orders as exponents.

Both acronyms are different because of the demographical difference in terms. In the USA, brackets are referred to parenthesis while in the UK, they use the term brackets instead of parenthesis. It is the same case for the term exponent. Exponent is referred to orders in the UK. BODMAS stands for Brackets, Orders, Division, Multiplication, Addition, Subtraction, while PEMDAS stands for Parenthesis, Exponents, Division, Multiplication, Addition, Subtraction.

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