# Order of Operations (PEMDAS) Calculator

## Evaluate expressions using PEMDAS step by step

The calculator will evaluate the given expression showing the order of operations using PEMDAS.

If the calculator did not compute something or you have identified an error, or you have a suggestion/feedback, please write it in the comments below.

Our Order of Operation Calculator is your assistant that evaluates complex mathematical expressions following a specific order of operations. The order in which you evaluate math expressions is critical to finding the correct answer. By using our tool, you are guaranteed to get accurate results.

## How to Use the Order of Operations (PEMDAS) Calculator?

• ### Input

Begin by typing or pasting the mathematical expression you wish to evaluate into the provided input field. While you input, remember the PEMDAS sequence: parentheses, exponents, multiplication, division, addition, and subtraction. Don't worry if you can't remember because the calculator will automatically adhere to this rule during the computation.

• ### Calculation

Once you've entered your expression, click the "Calculate" button below the input field.

• ### Result

The calculator will display a step-by-step breakdown of the process, demonstrating how the PEMDAS rule was applied to arrive at the final answer. This feature is handy for those looking to understand the underlying process.

## What Is PEMDAS?

PEMDAS is an acronym used to remember the order of operations for evaluating mathematical expressions. Each letter in PEMDAS stands for a specific operation, and the sequence of the letters indicates the order in which these operations should be performed. Here's a breakdown:

• P: Parentheses – This refers to evaluating expressions enclosed within parentheses (or brackets) first. For example, in the expression $3\times(4+5)$, you would first add $4$ and $5$ because they are inside parentheses.
• E: Exponents – Once parentheses have been resolved, the next step is calculating powers or square roots. For instance, in $3^2$, the number $3$ is raised to the power of $2$, which equals $9$.
• MD: Multiplication and Division – After exponents, perform multiplication and division operations from left to right as they appear in the expression.
• AS: Addition and Subtraction – The last operations to be performed are addition and subtraction, done from left to right.

It's worth noting that PEMDAS is also known by other acronyms depending on the region or curriculum, such as BODMAS (Brackets, Orders, Division/Multiplication, Addition/Subtraction) or BEDMAS (Brackets, Exponents, Division/Multiplication, Addition/Subtraction). Regardless of the acronym, the principle remains the same: it ensures that mathematical expressions are evaluated in a consistent and correct manner.

## What Are the Rules for Adding, Subtracting, Multiplying, and Dividing Two Numbers?

Addition $(+)$

During addition, the sum of two or more numbers or values is calculated. The result of addition is called the sum.

The formula for addition is

$$a+b=c,$$

where $a$ and $b$ are the numbers being added (also called addends) and $c$ is the sum.

For example:

• Positive + Positive gives Positive: $5+3=8$.
• Negative + Negative is negative: $-4+(-6)=-10$.
• Positive + Negative can be both Positive or Negative: $9+(−3)=6$ or $5+(-8)=-3$.

Subtraction $(-)$

Subtraction is the operation of finding the difference of two numbers.

The formula for subtraction is

$$a-b=c,$$

where $a$ is the minuend, $b$ is the subtrahend, and $c$ is the difference.

For example:

• Positive - Positive can be either Positive or Negative: $9-4=5$ or $6-7=-1$.
• Negative - Negative can be both Positive and Negative: $-7-(-3)=-4$ or $-1-(-2)=1$.
• Positive - Negative is Positive: $8-(-5)=13$.
• Negative - Positive gives Positive: $-5-7=-12$.

Multiplication $(\times)$

Multiplication is the process of repeatedly adding a number to itself a certain number of times.

The formula for multiplication is

$$a\times b=c,$$

where $a$ and $b$ are the numbers being multiplied (also called factors) and $c$ is the product.

For example:

• Positive × Positive is Positive: $4\times3=12$.
• Negative × Negative gives Positive: $-4\times(-3)=12$.
• Positive × Negative gives Negative: $5\times(-2)=-10$.

Division $(\div)$

Division is the process of finding how many times one number (divisor) is contained in another (dividend).

The formula for division is

$$a\div b=c,$$

where $a$ is the dividend, $b$ is the divisor, and $c$ is the quotient.

For example:

• Positive ÷ Positive gives Positive: $8\div2=4$.
• Negative ÷ Negative gives Positive: $-10\div(-2)=5$.
• Positive ÷ Negative is Negative: $12\div(-3)=-4$.

## Why Is the Order of Operations Needed?

An established order of operations, like PEMDAS, ensures consistent and accurate mathematical results. It prevents confusion. Whether in daily life or complex fields like science and finance, this order maintains reliability and prevents errors.

## Why Choose Our Order of Operations (PEMDAS) Calculator?

• ### Precision in Calculations

Our calculator adheres strictly to the PEMDAS rule, ensuring accurate and correct results for your mathematical expressions.

• ### Step-by-Step Solutions

For those seeking a deeper understanding, our calculator provides a detailed breakdown of each operation, promoting understanding and learning.

• ### Handling of Integers with Ease

Specifically designed to handle integer computations, our calculator evaluates expressions that contain both positive and negative numbers.

• ### Fast and Convenient

Quickly evaluate complex expressions without the need for manual calculations, saving valuable time and effort.

• ### User-Friendly Interface

With an intuitive design, our calculator is suitable for users of all skill levels, making it accessible to both students and professionals.

### FAQ

#### What is the Order of Operations (PEMDAS)?

The Order of Operations, often remembered as PEMDAS (parentheses, exponents, multiplication, division, addition, and subtraction), defines the order in which mathematical operations should be performed to ensure correct results.

#### Why is the Order of Operations important?

The Order of Operations maintains consistency and prevents ambiguity in mathematical expressions. It guarantees uniformity in calculations and prevents errors.

#### Can I use the calculator for negative numbers?

Absolutely. Our calculator handles both positive and negative numbers, ensuring accurate solutions for a wide range of expressions.

#### Does the calculator support step-by-step solutions?

Yes, our calculator provides a detailed, step-by-step breakdown of each operation, allowing users to understand and learn from the process.