Learn about PEMDAS and step by step explanation of using the rules and applying through attempting the quiz

Last updated : 16 June 2024, Sunday

Verified for accuracy

## Introduction

In mathematics, when you encounter complex expressions or equations, it’s crucial to follow a specific order when performing operations. This ensures that you get the correct result. The order of operations is often remembered using acronyms like PEMDAS or BODMAS:

## PEMDAS

- Parentheses
- Exponents (Powers and Square Roots)
- Multiplication and Division (perform from left to right whichever comes first)
- Addition and Subtraction (perform from left to right whichever comes first)

## BODMAS

- Brackets (Parentheses)
- Orders (Exponents and Roots)
- Division and Multiplication ( perform from left to right whichever comes first)
- Addition and Subtraction ( perform from left to right whichever comes first)

## Step-by-step explanation of how to use the PEMDAS rules:

### Parentheses (Brackets):

- Begin by simplifying expressions inside parentheses or brackets. Evaluate what’s inside them first.

### Exponents (Orders):

- After simplifying the parentheses, work on any exponents (powers and square roots) present in the expression. Calculate these values.

### Multiplication and Division:

- Following the above steps, perform multiplication and division from left to right. If there’s a multiplication or division operation, do it before addition and subtraction.

### Addition and Subtraction:

- Finally, carry out addition and subtraction from left to right as they appear in the expression.

For example, consider the expression: 6 + 4 × (8 ÷ 2) – 7

**Using the order of operations (PEMDAS), you would evaluate it like this:**

- Parentheses: 6 + 4 × (4) – 7
- Multiplication: 6 + 16 – 7
- Addition and Subtraction: 22 – 7
- Final result: 15

By following the order of operations, you ensure that complex mathematical expressions are solved correctly and consistently. This is particularly important when dealing with equations, as the order in which you perform operations can affect the outcome.

## Applications of PEMDAS

The principles of PEMDAS, which dictate the order of operations in mathematics, have several real-world applications across various fields. Understanding and applying PEMDAS is crucial in many practical situations:

**Finance and Budgeting**: When calculating expenses, taxes, interest rates, and savings, the correct order of operations is essential. For example, in computing the interest on a savings account where you first need to add a deposit to the existing balance and then apply the interest rate, the order in which these operations are performed affects the final amount.**Construction and Engineering**: In construction and engineering, accurate measurements and calculations are vital. The order of operations is used in determining material quantities, costs, and structural load calculations. For instance, calculating the area of complex shapes or the volume of materials often requires the correct application of PEMDAS.**Computer Programming**: Computer algorithms often involve mathematical calculations where the order of operations is critical. Programming languages have built-in rules for the order of operations, closely following PEMDAS principles.**Science and Medicine**: In fields like chemistry, physics, and medicine, calculations often involve multiple steps and operators. For example, in pharmacology, determining the correct dosage of medication based on a person’s weight and the concentration of the medicine requires accurate application of the order of operations.**Cooking and Baking**: Recipes sometimes require mathematical adjustments, such as doubling ingredients or converting measurements. Correctly applying the order of operations ensures the right proportions are used.**Economics and Statistics**: In these fields, complex formulas are used to analyze data, predict trends, and make decisions. The correct application of the order of operations is essential for accurate analysis and predictions.**Education**: In teaching and learning, especially in math education, PEMDAS is a foundational concept that students must understand and apply correctly to solve mathematical problems.**Daily Decision Making**: For personal finances, such as calculating discounts or comparing loan interests, the order of operations helps in making informed financial decisions.

In all these examples, the correct application of PEMDAS ensures accurate results. Misapplying the order can lead to significant errors, affecting outcomes in sensitive areas like finance, health, and safety.