Simplify The Expression: $\[ (24 \div 3 + 10) - 14 \div 2 \\]

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Introduction

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In mathematics, simplifying expressions is a crucial skill that helps us evaluate complex mathematical problems. It involves breaking down the expression into smaller parts, following the order of operations, and simplifying each part to obtain the final result. In this article, we will simplify the expression: $(24 \div 3 + 10) - 14 \div 2$. We will break down the expression into smaller parts, follow the order of operations, and simplify each part to obtain the final result.

Understanding the Order of Operations

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Before we simplify the expression, it's essential to understand the order of operations. The order of operations is a set of rules that tells us which operations to perform first when we have multiple operations in an expression. The order of operations is often remembered using the acronym PEMDAS, which stands for:

1. Parentheses: Evaluate expressions inside parentheses first.
2. Exponents: Evaluate any exponential expressions next.
3. Multiplication and Division: Evaluate any 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

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Now that we understand the order of operations, let's break down the expression: $(24 \div 3 + 10) - 14 \div 2$. We can see that the expression contains several operations, including division, addition, and subtraction. To simplify the expression, we need to follow the order of operations.

Step 1: Evaluate Expressions Inside Parentheses

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The first step is to evaluate the expressions inside the parentheses. In this case, we have two expressions inside the parentheses: $24 \div 3$ and $10$. We can evaluate these expressions separately.

• $24 \div 3 = 8$
• $10$ remains the same.

So, the expression inside the parentheses becomes: $8 + 10$.

Step 2: Evaluate Exponential Expressions

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There are no exponential expressions in this expression, so we can move on to the next step.

Step 3: Evaluate Multiplication and Division Operations

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The next step is to evaluate any multiplication and division operations from left to right. In this case, we have two operations: $14 \div 2$ and $8 + 10$. We can evaluate these operations separately.

• $14 \div 2 = 7$
• $8 + 10 = 18$

So, the expression becomes: $18 - 7$.

Step 4: Evaluate Addition and Subtraction Operations

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The final step is to evaluate any addition and subtraction operations from left to right. In this case, we have one operation: $18 - 7$. We can evaluate this operation to obtain the final result.

• $18 - 7 = 11$

Conclusion

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In this article, we simplified the expression: $(24 \div 3 + 10) - 14 \div 2$. We broke down the expression into smaller parts, followed the order of operations, and simplified each part to obtain the final result. The final result is: $11$. We hope this article has helped you understand how to simplify mathematical expressions and evaluate complex mathematical problems.

Frequently Asked Questions

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Q: What is the order of operations?

A: The order of operations is a set of rules that tells us which operations to perform first when we have multiple operations in an expression. The order of operations is often remembered using the acronym PEMDAS, which stands for:

1. Parentheses: Evaluate expressions inside parentheses first.
2. Exponents: Evaluate any exponential expressions next.
3. Multiplication and Division: Evaluate any 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 simplify a mathematical expression?

A: To simplify a mathematical expression, you need to follow the order of operations. First, evaluate any expressions inside parentheses. Then, evaluate any exponential expressions. Next, evaluate any multiplication and division operations from left to right. Finally, evaluate any addition and subtraction operations from left to right.

Q: What is the final result of the expression: $(24 \div 3 + 10) - 14 \div 2$?

A: The final result of the expression: $(24 \div 3 + 10) - 14 \div 2$ is: $11$.

Further Reading

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If you want to learn more about simplifying mathematical expressions and evaluating complex mathematical problems, we recommend the following resources:

• Khan Academy: Simplifying Expressions
• Mathway: Simplifying Expressions
• Wolfram Alpha: Simplifying Expressions

We hope this article has helped you understand how to simplify mathematical expressions and evaluate complex mathematical problems. If you have any questions or need further clarification, please don't hesitate to ask.

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Introduction

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In our previous article, we simplified the expression: $(24 \div 3 + 10) - 14 \div 2$. We broke down the expression into smaller parts, followed the order of operations, and simplified each part to obtain the final result. In this article, we will answer some frequently asked questions about simplifying mathematical expressions and evaluating complex mathematical problems.

Q&A

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Q: What is the order of operations?

A: The order of operations is a set of rules that tells us which operations to perform first when we have multiple operations in an expression. The order of operations is often remembered using the acronym PEMDAS, which stands for:

1. Parentheses: Evaluate expressions inside parentheses first.
2. Exponents: Evaluate any exponential expressions next.
3. Multiplication and Division: Evaluate any 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 simplify a mathematical expression?

A: To simplify a mathematical expression, you need to follow the order of operations. First, evaluate any expressions inside parentheses. Then, evaluate any exponential expressions. Next, evaluate any multiplication and division operations from left to right. Finally, evaluate any addition and subtraction operations from left to right.

Q: What is the difference between simplifying and evaluating an expression?

A: Simplifying an expression involves breaking down the expression into smaller parts, following the order of operations, and simplifying each part to obtain the final result. Evaluating an expression involves substituting values into the expression and calculating the final result.

Q: How do I handle negative numbers when simplifying an expression?

A: When simplifying an expression with negative numbers, you need to follow the order of operations. First, evaluate any expressions inside parentheses. Then, evaluate any exponential expressions. Next, evaluate any multiplication and division operations from left to right. Finally, evaluate any addition and subtraction operations from left to right.

Q: Can I simplify an expression with variables?

A: Yes, you can simplify an expression with variables. To simplify an expression with variables, you need to follow the order of operations. First, evaluate any expressions inside parentheses. Then, evaluate any exponential expressions. Next, evaluate any multiplication and division operations from left to right. Finally, evaluate any addition and subtraction operations from left to right.

Q: How do I handle fractions when simplifying an expression?

A: When simplifying an expression with fractions, you need to follow the order of operations. First, evaluate any expressions inside parentheses. Then, evaluate any exponential expressions. Next, evaluate any multiplication and division operations from left to right. Finally, evaluate any addition and subtraction operations from left to right.

Q: Can I simplify an expression with multiple operations?

A: Yes, you can simplify an expression with multiple operations. To simplify an expression with multiple operations, you need to follow the order of operations. First, evaluate any expressions inside parentheses. Then, evaluate any exponential expressions. Next, evaluate any multiplication and division operations from left to right. Finally, evaluate any addition and subtraction operations from left to right.

Tips and Tricks

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Tip 1: Use the Order of Operations

The order of operations is a set of rules that tells us which operations to perform first when we have multiple operations in an expression. The order of operations is often remembered using the acronym PEMDAS, which stands for:

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

Tip 2: Break Down the Expression

To simplify a mathematical expression, you need to break down the expression into smaller parts. This will help you follow the order of operations and simplify each part to obtain the final result.

Tip 3: Use a Calculator

If you are having trouble simplifying a mathematical expression, you can use a calculator to help you. However, be careful not to rely too heavily on the calculator, as this can lead to mistakes.

Conclusion

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In this article, we answered some frequently asked questions about simplifying mathematical expressions and evaluating complex mathematical problems. We also provided some tips and tricks to help you simplify mathematical expressions. We hope this article has been helpful in your understanding of simplifying mathematical expressions and evaluating complex mathematical problems.

Further Reading

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If you want to learn more about simplifying mathematical expressions and evaluating complex mathematical problems, we recommend the following resources:

• Khan Academy: Simplifying Expressions
• Mathway: Simplifying Expressions
• Wolfram Alpha: Simplifying Expressions

We hope this article has been helpful in your understanding of simplifying mathematical expressions and evaluating complex mathematical problems. If you have any questions or need further clarification, please don't hesitate to ask.