Mathematics is all around us, and understanding the right mathematical rules can greatly enhance our ability to solve problems efficiently. One pivotal rule in the realm of mathematics, especially when multiple operations are involved in an equation, is the **PEMDAS** rule.

You might be well-acquainted with basic operations like addition, division, subtraction, and multiplication, but how do you prioritize these when they appear together? **PEMDAS** is a fundamental rule used not only in solving complex mathematical problems but also extensively in computer programming.

**What is PEMDAS?**

PEMDAS is an acronym that helps us remember the order of operations to be followed while solving expressions with multiple operations. It stands for

**P** – Parentheses

**E** – Exponents

**M** – Multiplication

**D** – Division

**A** – Addition, and

**S** – Subtraction.

Different countries might use various acronyms to describe the order of operations. In Canada, for instance, it’s referred to as

**BEDMAS** (**B**rackets, Exponents, Division, Multiplication, Addition, and Subtraction)

Others may know it as

**B****ODMAS** (**B** – Brackets, **O** – Order (exponent or power) or **D**ivision, **M**ultiplication, **A**ddition, and **S**ubtraction)

GEMDAS (G – Grouping) and the rest of the letters representing each operation as above.

Illustrating **PEMDAS** Through Examples

Consider the following situation where two individuals, Tom and Jerry, solve the same mathematical expression, but each uses a different method:

Tom’s Method:

5 + 2 × 3

Tom adds the 5 and 2 together first, to obtain 7.

= 7 × 3

He then proceeds to multiply the 7 by 3.

= 21

Jerry’s Method:

5 + 2 × 3

Tom multiplies 2 by 3 first, to obtain 6.

= 5 + 6

He then adds 5 and 6, and gets 11

= 11

As you can see, Tom and Jerry arrived at different answers. In mathematics, there is only one correct answer for any given expression (unless you’re solving trigonometric functions). Using PEMDAS, we can determine the right solution.

**PEMDAS Rules in Action**

Let’s follow the **PEMDAS** rules: We start with Parentheses, then Exponents. Following that, we perform Multiplication and Division from left to right, and finally, Addition and Subtraction from left to right. Following this order ensures the correct answer.

Here’s another example to deepen your understanding:

Expression:

4 + 3[8 – 2(6 – 3)] ÷ 2

Steps:

- Solve the innermost parentheses first: 6−3=3, making the expression: 4+3[8−2(3)]÷2

- Perform the multiplication within the brackets: 2(3)=6, resulting in: 4+3[8−6]÷2

- Solve the expression in the brackets: 8−6=2, thus: 4+3×(2)÷2

- Multiply: 3×2=6, now our expression is: 4+6÷2

- Divide: 6÷2=3, and the equation becomes: 4+3

- Finally, add: 4+3=7

By following **PEMDAS **strictly, you ensure that all calculations are performed in the correct order, leading to accurate results.

Using **PEMDAS** to Excel in Math

**PEMDAS** isn’t just a rule but a crucial strategy that, when applied correctly, can help you excel in your mathematics classes and beyond. Understanding and practicing this rule can simplify complex problems and increase your efficiency in solving them.

**Explaining the BODMAS rule**, which is a mnemonic similar to **PEMDAS** for remembering the order of operations in mathematics. **BODMAS** stands for Brackets, Order, Divide, Multiply, Add, and Subtract.

**BODMAS** Explained:

P – Parentheses

- B
**– Brackets**: Solve expressions inside brackets or parentheses first. This is the innermost part of any mathematical problem involving multiple operations. - O –
**Order**: This refers to indices in some regions, which means you handle exponents (powers and roots, for example) after brackets. - D –
**Divide**: and**Multiply**(M): These operations are at the same level of priority and are performed from left to right. Division is not prioritized over multiplication or vice versa; the one that appears first as you read from left to right is the one to do first. - A –
**Add (A)**and S –**Subtract (S):**Lastly, you perform addition and subtraction, also from left to right, depending on which comes first in the expression.

The order is crucial because performing these operations out of sequence can lead to incorrect results. The left-to-right rule for operations at the same level (like Divide and Multiply, Add and Subtract) is important and is a common feature shared with **PEMDAS**.

**PEMDAS**, on the other hand, stands for Parentheses, Exponents, Multiplication, Division, Addition, and Subtraction. While it may seem that Multiplication comes before Division and Addition before Subtraction in **PEMDAS**, the operations at each level (Multiplication and Division, Addition and Subtraction) are actually carried out from left to right, similar to **BODMAS**.

Example Using BODMAS:

Let’s apply BODMAS to the same example used previously for PEMDAS to show they are equivalent:

Expression:

4+3[8−2(6−3)]÷2

Steps:

**Brackets**: Solve the innermost part first: 6−3=3, so we update the expression to 4+3[8−2(3)]÷2

**Order**: There are no exponents to deal with here, so we move on.

**Divide**and**Multiply**: Solve these as they appear from left to right. First, 2×3=6, updating to 4+3[8−6]÷2. Then 8−6=2, updating to 4+3×2÷2. Next, 3×2=6, updating to 4+6÷2.

**Divide**: Now, 6÷2=3, updating to 4+3.

**Add**and**Subtract**: Finally, 4+3=7.

So, whether you use **BODMAS** or **PEMDAS**, the correct order of operations will guide you to the right answer. In this case, the final result is 7.

Keep practicing and applying the **BODMAS** or **PEMDAS** rule to different problems you encounter in your studies or in everyday life, and watch your proficiency in mathematics grow!

Until next time, happy calculating!

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