Operations ## An introduction to order of operations: Definition, Rules, and Examples

**How Can an Order of Operations Calculator Help You?** The order of operations is widely used in mathematics to calculate the problems of math expression perfectly. This form allows using of a sequence of mathematical symbols such as multiply, divide, addition, & subtraction.

It is usually used all over the world to get a similar result by applying the correct sequence of operations in math expression problems. In this article, we will cover all the general basics of the order of **operations calculator** along with solved examples.

In mathematics, the order that is used to solve the mathematical expression correctly is known as the order of operations. Also, It provides a sequence of operations that are applied to the math expressions to get the correct result.

The following are two well-known techniques of the order of operations that are frequently used all over the world.

- PEMDAS Rule
- BODMAS Rule

In western countries (United States, United Kingdom, Canada, etc.), the PEMDAS rule is used to solve math expression problems. While in Asian countries (India, Pakistan, Sri Lanka, etc.), the BODMAS rule is used.

Here is a brief introduction to both techniques of the order of operations.

The PEMDAS rule is widely used in western and European countries for solving the expressions of mathematics in a perfect sequence. The PEMDAS stands for:

- P for
**P**arentheses “( )” - E for
**E**xponent “^” - M for
**M**ultiplication “* or x” - D for
**D**ivision “/” - A for
**A**ddition “+” - S for
**S**ubtraction “-”

The BODMAS rule is widely used in Asian countries for solving the expressions of mathematics in a perfect sequence. The BODMAS stands for:

- B for
**B**rackets (brackets can be braces or parenthesis) - O for
**O**rder of (exponent “^”) - D for
**D**ivision “/” - M for
**M**ultiplication “* or x”, - A for
**A**ddition “+” - S for
**S**ubtraction “-”.

The problems of the math expression can be solved easily with the help of the PEMDAS and the BODMAS rules. Below are a few steps to solve the problems of PEMDAS and the BODMAS rules.

- Firstly, evaluate the parenthesis, brackets, and braces that are present in the given math expression. Evaluate the leftmost parenthesis or braces first if there is more than one parenthesis or braces.
- After that evaluate the power, exponent, or order of the terms that are present in the math expression. Evaluate the leftmost exponent or order term first if there is more than one exponent or order.
- Then evaluate the division and multiplication terms of the math expression from left to right.
- Lastly, evaluate the addition and subtraction operations from left to right.

Following are a few examples of the order of operations.

Evaluate 6^{3} + (112 – 8) * 4^{4} – 40/8 + (43 + 17) – 2 (16 * 4) – 8 by using the PEMDAS rule.

**Solution**

6^{3} + (112 – 8) * 4^{4} – 40/8 + (43 + 17) – 2 (16 * 4) – 8

6^{3} + (**104**) * 4^{4} – 40/8 + (43 + 17) – 2 (16 * 4) – 8

6^{3} + 104 * 4^{4} – 40/8 + (**60**) – 2 (16 * 4) – 8

Also, 6^{3} + 104 * 4^{4} – 40/8 + 60 – 2 (**64**) – 8

6^{3} + 104 * 4^{4} – 40/8 + 60 – **128** – 8

(6 x 6 x 6) + 104 * 4^{4} – 40/8 + 60 – 128 – 8

**216** + 104 * 4^{4} – 40/8 + 60 – 128 – 8

216 + 104 * (4 x 4 x 4 x 4) – 40/8 + 60 – 128 – 8

Also, 216 + 104 * **256** – 40/8 + 60 – 128 – 8

216 + 104 * 256 – 40/8 + 60 – 128 – 8

216 + **26624** – 40/8 + 60 – 128 – 8

Also, 216 + 26624 – **5** + 60 – 128 – 8

**26840 **– 5 + 60 – 128 – 8

**26835** + 60 – 128 – 8

**26895** – 128 – 8

**26767** – 8

**26759**

6^{3} + (112 – 8) * 4^{4} – 40/8 + (43 + 17) – 2 (16 * 4) – 8 = 26759

To avoid such a large number of steps to solve the math expression, use a PEMDAS calculator.

Follow the steps below to solve math expressions using a calculator.

**Step i:** Write the given math expression into the required input field.

**Step ii:** Click the calculate button below the input field.

Also, **Step iii:** The result will show in a fraction of a second with steps.

**Step iv:** Hit the show more button to view the solution with steps.

Solve 12 – (7 + 11) * 6 + 9^{3} – 40/5 – (60 * 3 + 12) + 5 (2 * 14) / 4^{4} by using the BODMAS rule.

**Solution**

12 – (7 + 11) * 6 + 9^{3} – 40/5 – (60 * 3 + 12) + 5 (2 * 14) / 4^{4}

12 – (7 + 11) * 6 + 9^{3} – 40/5 – (60 * 3 + 12) + 5 (2 * 14) / 4^{4}

12 – (**18**) * 6 + 9^{3} – 40/5 – (60 * 3 + 12) + 5 (2 * 14) / 4^{4}

Also, 12 – 18 * 6 + 9^{3} – 40/5 – (**180** + 12) + 5 (2 * 14) / 4^{4}

12 – 18 * 6 + 9^{3} – 40/5 – (**192**) + 5 (2 * 14) / 4^{4}

12 – 18 * 6 + 9^{3} – 40/5 – 192 + 5 (**28**) / 4^{4}

Maybe, 12 – 18 * 6 + 9^{3} – 40/5 – 192 + **140** / 4^{4}

12 – 18 * 6 + 9^{3} – 40/5 – 192 + 140 / 4^{4}

12 – 18 * 6 + (9 x 9 x 9) – 40/5 – 192 + 140 / 4^{4}

Also, 12 – 18 * 6 + (**729**) – 40/5 – 192 + 140 / (4 x 4 x 4 x 4)

12 – 18 * 6 + 729 – 40/5 – 192 + 140 / **256**

12 – 18 * 6 + 729 – 40/5 – 192 + 140 / 256

12 – **108 **+ 729 – 40/5 – 192 + 140 / 256

Also, 12 – 108+ 729 – **8** – 192 + 140 / 256

12 – 108+ 729 – 8 – 192 + **0.55**

12 – 108+ 729 – 8 – 192 + 0.55

**-96 **+ 729 – 8 – 192 + 0.55

**633** – 8 – 192 + 0.55

**625** – 192 + 0.55

**433** + 0.55

**433.55**

**Step VI:** Write the given math expression with the result.

12 – (7 + 11) * 6 + 9^{3} – 40/5 – (60 * 3 + 12) + 5 (2 * 14) / 4^{4} = 433.55

Now you are witnessed that solving the problems of math expression by using the PEMDAS and BODMAS is not a difficult task, as well as the order of operations calculator. You have to follow the sequence of operations to get the correct result.

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