Evaluate The Expression:${ [(18 \div 2 + 54 \div 9) \times 2] \times 2 }$

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Introduction

In mathematics, expressions are a fundamental concept that involves combining numbers and mathematical operations to obtain a result. Evaluating an expression means simplifying it to a single value. In this article, we will evaluate the given expression: $[(18 \div 2 + 54 \div 9) \times 2] \times 2$. We will break down the expression into smaller parts, apply the order of operations, and simplify it to obtain the final result.

Understanding the Order of Operations

The order of operations is a set of rules that dictate the order in which mathematical operations should be performed when there are multiple operations in an expression. The acronym PEMDAS is commonly used to remember the order of operations:

1. Parentheses: Evaluate expressions inside parentheses first.
2. Exponents: Evaluate any exponential expressions next.
3. Multiplication and Division: Evaluate multiplication and division operations from left to right.
4. Addition and Subtraction: Finally, evaluate any addition and subtraction operations from left to right.

Breaking Down the Expression

Let's break down the given expression into smaller parts:

$[(18 \div 2 + 54 \div 9) \times 2] \times 2$

We can see that there are two sets of parentheses, and we need to evaluate the expressions inside them first.

Evaluating the First Set of Parentheses

The first set of parentheses contains two division operations:

$18 \div 2 + 54 \div 9$

We need to evaluate these division operations first. Using the order of operations, we can rewrite the expression as:

$(18 \div 2) + (54 \div 9)$

Now, we can evaluate the division operations:

$18 \div 2 = 9$ $54 \div 9 = 6$

So, the expression becomes:

$9 + 6$

Now, we can add the two numbers:

$9 + 6 = 15$

Evaluating the Second Set of Parentheses

Now that we have evaluated the first set of parentheses, we can move on to the second set:

$(15 \times 2) \times 2$

We need to evaluate the multiplication operations first. Using the order of operations, we can rewrite the expression as:

$(15 \times 2) \times 2$

Now, we can evaluate the multiplication operations:

$15 \times 2 = 30$

So, the expression becomes:

$30 \times 2$

Now, we can evaluate the final multiplication operation:

$30 \times 2 = 60$

Conclusion

In this article, we evaluated the given expression: $[(18 \div 2 + 54 \div 9) \times 2] \times 2$. We broke down the expression into smaller parts, applied the order of operations, and simplified it to obtain the final result. The final result is:

$60$

We hope this article has provided a clear understanding of how to evaluate mathematical expressions and the importance of following the order of operations.

Frequently Asked Questions

• What is the order of operations? The order of operations is a set of rules that dictate the order in which mathematical operations should be performed when there are multiple operations in an expression.
• How do I evaluate an expression with multiple operations? To evaluate an expression with multiple operations, you need to follow the order of operations: parentheses, exponents, multiplication and division, and addition and subtraction.
• What is the final result of the given expression? The final result of the given expression is 60.

Further Reading

If you want to learn more about mathematical expressions and the order of operations, we recommend checking out the following resources:

• Khan Academy: Order of Operations
• Mathway: Order of Operations
• Wolfram Alpha: Order of Operations

We hope this article has provided a clear understanding of how to evaluate mathematical expressions and the importance of following the order of operations. If you have any further questions or need help with a specific problem, please don't hesitate to ask.

Introduction

Evaluating mathematical expressions is a fundamental concept in mathematics that involves simplifying expressions to obtain a single value. In our previous article, we evaluated the expression: $[(18 \div 2 + 54 \div 9) \times 2] \times 2$. In this article, we will provide a Q&A guide to help you understand how to evaluate mathematical expressions and address common questions and concerns.

Q&A Guide

Q: What is the order of operations?

A: The order of operations is a set of rules that dictate the order in which mathematical operations should be performed when there are multiple operations in an expression. The acronym PEMDAS is commonly used to remember the order of operations:

1. Parentheses: Evaluate expressions inside parentheses first.
2. Exponents: Evaluate any exponential expressions next.
3. Multiplication and Division: Evaluate multiplication and division operations from left to right.
4. Addition and Subtraction: Finally, evaluate any addition and subtraction operations from left to right.

Q: How do I evaluate an expression with multiple operations?

A: To evaluate an expression with multiple operations, you need to follow the order of operations:

1. Evaluate expressions inside parentheses first.
2. Evaluate any exponential expressions next.
3. Evaluate multiplication and division operations from left to right.
4. Finally, evaluate any addition and subtraction operations from left to right.

Q: What is the difference between multiplication and division?

A: Multiplication and division are both arithmetic operations that involve combining numbers. The main difference between the two is that multiplication involves repeated addition, while division involves sharing or grouping.

Q: How do I handle fractions in mathematical expressions?

A: Fractions are a type of mathematical expression that involves a numerator and a denominator. To handle fractions in mathematical expressions, you need to follow the order of operations and simplify the fraction by dividing the numerator by the denominator.

Q: What is the final result of the given expression: $[(18 \div 2 + 54 \div 9) \times 2] \times 2$?

A: The final result of the given expression is 60.

Q: How do I simplify complex mathematical expressions?

A: To simplify complex mathematical expressions, you need to follow the order of operations and break down the expression into smaller parts. This will help you to identify the operations that need to be performed and simplify the expression.

Q: What are some common mistakes to avoid when evaluating mathematical expressions?

A: Some common mistakes to avoid when evaluating mathematical expressions include:

• Not following the order of operations
• Not simplifying fractions
• Not handling parentheses correctly
• Not checking for errors in calculations

Conclusion

Evaluating mathematical expressions is a fundamental concept in mathematics that involves simplifying expressions to obtain a single value. In this article, we provided a Q&A guide to help you understand how to evaluate mathematical expressions and address common questions and concerns. We hope this article has provided a clear understanding of how to evaluate mathematical expressions and the importance of following the order of operations.

Frequently Asked Questions

• What is the order of operations? The order of operations is a set of rules that dictate the order in which mathematical operations should be performed when there are multiple operations in an expression.
• How do I evaluate an expression with multiple operations? To evaluate an expression with multiple operations, you need to follow the order of operations: parentheses, exponents, multiplication and division, and addition and subtraction.
• What is the difference between multiplication and division? Multiplication and division are both arithmetic operations that involve combining numbers. The main difference between the two is that multiplication involves repeated addition, while division involves sharing or grouping.
• How do I handle fractions in mathematical expressions? To handle fractions in mathematical expressions, you need to follow the order of operations and simplify the fraction by dividing the numerator by the denominator.

Further Reading

If you want to learn more about mathematical expressions and the order of operations, we recommend checking out the following resources:

• Khan Academy: Order of Operations
• Mathway: Order of Operations
• Wolfram Alpha: Order of Operations

We hope this article has provided a clear understanding of how to evaluate mathematical expressions and the importance of following the order of operations. If you have any further questions or need help with a specific problem, please don't hesitate to ask.