Understanding the Order of Operations: A Step-by-Step Guide to Solving 12 × 56 - 8 ÷ 2

When solving mathematical expressions, it’s crucial to follow a consistent and systematic method. This ensures accurate results and helps prevent common errors. In this guide, we will explore the order of operations using the well-known rules, PEMDAS and BODMAS. We will walk you through the process of solving the expression 12 × 56 - 8 ÷ 2, ultimately leading to the correct answer.

The Order of Operations: PEMDAS and BODMAS

The order of operations is a set of rules that dictate the sequence in which mathematical operations should be performed. Two common acronyms used to remember these rules are PEMDAS and BODMAS. Both acronyms stand for similar operations, although the order of division and multiplication, as well as addition and subtraction, can be slightly different in their interpretations depending on the region.

PEMDAS: Parentheses, Exponents, Multiplication and Division (left to right), Addition and Subtraction (left to right)

Following the PEMDAS rule involves several steps. Each letter in the acronym stands for a specific operation:

Parentheses: Solve any expressions within parentheses first. Exponents: Solve any exponents. Multiplication and Division: Perform multiplication and division from left to right. Addition and Subtraction: Finally, perform addition and subtraction from left to right.

BODMAS: Brackets, Orders, Division and Multiplication (left to right), Addition and Subtraction (left to right)

Similarly, BODMAS stands for the following operations:

Brackets: Solve any expressions within brackets first. Orders: Solve any exponents. Division and Multiplication: Perform division and multiplication from left to right. Addition and Subtraction: Finally, perform addition and subtraction from left to right.

Solving the Expression: 12 × 56 - 8 ÷ 2

Let’s break down the expression 12 × 56 - 8 ÷ 2 using both PEMDAS and BODMAS.

Using PEMDAS

First, we look for parentheses or brackets. There are none in this expression. No exponents to solve, so we move to the next step. Next, we perform multiplication and division from left to right.

We start with multiplication: 12 × 56 672

Then we move to division: 8 ÷ 2 4

Now we perform addition and subtraction from left to right.

We perform the subtraction: 672 - 4 668

Note: The provided solution of 12 × 56 - 8 ÷ 2 yielding 62 seems incorrect based on the given expression. The correct application of PEMDAS should yield 668.

Using BODMAS

First, we look for brackets. There are none in this expression. No orders to solve, so we move to the next step. Next, we perform division and multiplication from left to right.

We start with division: 8 ÷ 2 4

Then we move to multiplication: 12 × 56 672

Now we perform addition and subtraction from left to right.

We perform the subtraction: 672 - 4 668

As in the PEMDAS method, the correct answer using BODMAS is 668.

Conclusion

It’s important to remember that the order of operations is crucial in solving mathematical expressions. The acronyms PEMDAS and BODMAS help to ensure that the operations are performed in the correct sequence. By following these rules, you can solve complex expressions and avoid errors. Remember, multiplication and division are performed from left to right, as are addition and subtraction.

Key Takeaways

PEMDAS: Parentheses, Exponents, Multiplication and Division, Addition and Subtraction. BODMAS: Brackets, Orders, Division and Multiplication, Addition and Subtraction. The order of operations ensures accurate results when solving mathematical expressions.

Further Reading

For more detailed information on order of operations, you can refer to the following resources:

Math is Fun: Order of Operations Math Planet: The Order of Operations

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