Solving Complex Arithmetic Expressions Using PEMDAS/BODMAS

Understanding the correct order of operations is crucial when solving complex arithmetic expressions. The acronyms PEMDAS and BODMAS both represent the same set of rules but are used in different parts of the world. This article will guide you through each step, utilizing the expression 49×7 - 3÷9 4 as an example, to help you master these concepts.

Understanding PEMDAS and BODMAS

PEMDAS and BODMAS are mnemonics used to remember the order in which to perform mathematical operations.

P/Brackets - parentheses or brackets first (do all the calculations within them) E/Orders - exponents or orders (i.e., powers and square roots, etc.) Multiplication and Division - next in order, from left to right, are performed equally Addition and Subtraction - finally, from left to right, are performed equally

Solving the Expression: 49×7 - 3÷9 4

Let's break down the expression 49×7 - 3÷9 4 using the order of operations (PEMDAS/BODMAS).

Multiplication: 49×7 Division: 3÷9

Step-by-step Solution:

Step 1: Perform the multiplication first. 49×7 343 Step 2: Perform the division next. 3÷9 3/9 1/3 Step 3: Convert the fraction to a decimal for easier operations. 1/3 ≈ 0.3333 Step 4: Subtract the decimal from the result of the multiplication. 343 - 0.3333 342.6667 Then multiply the result by 4. 342.6667 4 346.6667

Alternative Solutions

Here are a few different solutions for the expression 497–3÷94, each using BODMAS:

Step 1: 497 - 3÷94 Step 2: 497 - 0.334 Step 3: 343 - 0.334 342.666 Step 4: 342.666 4 346.666 Step 1: 497 - 3÷94 Step 2: 497 - 0.334 Step 3: 343 - 0.334 342.666 Step 4: 342.666 4 346.666

Conclusion and Further Reading

Mastering the order of operations is essential for solving complex arithmetic expressions and equations. The expressions like 49×7 - 3÷9 4 can often be simplified and solved using the principles of BODMAS/PEMDAS. For further reading, you can explore more complex expressions or delve into algebraic equations.

Keywords: PEMDAS, BODMAS, Order of Operations, Arithmetic Expressions