Understanding the Order of Operations with PEMDAS/BODMAS: A Comprehensive Guide

The order of operations, often remembered by the acronyms PEMDAS or BODMAS, is a fundamental concept in mathematics that ensures consistency in solving mathematical problems. In this article, we'll explore how the expression 2×22×10-222 can be solved using these principles, providing a step-by-step guide for clarity and accuracy.

What is the Order of Operations?

The Order of Operations is a set of rules that dictate the sequence in which mathematical operations should be performed to ensure that expressions are evaluated correctly. The acronym PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction) and BODMAS (Brackets, Orders, Division and Multiplication, Addition and Subtraction) both convey the same sequence of operations, just with different terminology.

Applying PEMDAS/BODMAS to Solve the Expression: 2×22×10-222

Let's break down the expression 2×22×10-222 step by step, following the PEMDAS/BODMAS rules:

Multiplication Addition and Subtraction

The expression can be rewritten as:

2×22×10-222

First, we perform the multiplication:

2×2 4 2×10 20

Substituting back into the expression, we get:

420 - 222

Next, we perform the subtraction from left to right:

420 - 222 198

Therefore, the final answer is:

198

A Step-by-Step Breakdown

Let's break it down further using the PEMDAS/BODMAS principle:

First, we address the multiplications: 2×2 4 2×10 20 Now, the expression simplifies to 420 - 222 We then perform the subtraction from left to right: 420 - 222 198

Further Examples and Practice

To better understand the application of PEMDAS/BODMAS, let's look at a few more examples:

Example 1

Solve: 3 6×(5 4)

According to PEMDAS/BODMAS:

Perform the operations within the parentheses first: 5 49 Multiplication next: 6×954 Finally, addition: 3 5457

Example 2

Solve: (12÷3)×2 4

According to PEMDAS/BODMAS:

Division first: 12÷34 Multiplication next: 4×28 Finally, addition: 8 412

Conclusion

Mastering the order of operations is crucial for solving mathematical expressions accurately. By adhering to the principles of PEMDAS/BODMAS, you can simplify complex equations into manageable steps. Whether it's basic arithmetic or advanced formulas, understanding these rules ensures your calculations are both correct and efficient.

Ready to Test Your Knowledge?

Try solving the following expression using PEMDAS/BODMAS:

8 6×(2 1)÷3

Post your answers in the comments section for discussion.

Related Keywords

PEMDAS BODMAS Order of Operations