Calculate The Following Expression:$\[ (23 + 93) \times 7 + 29 = ? \\]A. 841 B. 801 C. \[$(76 + 24) \times 5\$\] D. \[$5 \times (76 + 5 + 24)\$\]

Introduction

In this article, we will be solving a mathematical expression that involves addition, multiplication, and parentheses. The expression is given as: $(23 + 93) \times 7 + 29$. Our goal is to simplify this expression and find its value. We will break down the solution into smaller steps, making it easier to understand and follow.

Step 1: Evaluate the Expression Inside the Parentheses

The first step is to evaluate the expression inside the parentheses: $23 + 93$. To do this, we simply add the two numbers together.

23 + 93 = 116

So, the expression now becomes: $116 \times 7 + 29$.

Step 2: Multiply 116 by 7

Next, we need to multiply 116 by 7. To do this, we can use the multiplication property of numbers.

116 × 7 = 812

Now, the expression becomes: $812 + 29$.

Step 3: Add 812 and 29

Finally, we need to add 812 and 29. To do this, we can simply add the two numbers together.

812 + 29 = 841

Therefore, the value of the expression $(23 + 93) \times 7 + 29$ is 841.

Comparing with the Options

Now that we have found the value of the expression, let's compare it with the options given:

• A. 841
• B. 801
• C. $(76 + 24) \times 5$
• D. $5 \times (76 + 5 + 24)$

As we can see, the value of the expression matches option A: 841.

Conclusion

In this article, we solved a mathematical expression that involved addition, multiplication, and parentheses. We broke down the solution into smaller steps, making it easier to understand and follow. We found the value of the expression to be 841, which matches option A.

Understanding the Options

Let's take a closer look at the options given:

• Option A: 841
• Option B: 801
• Option C: $(76 + 24) \times 5$
• Option D: $5 \times (76 + 5 + 24)$

We can see that option C and option D are expressions that involve addition and multiplication. However, they are not the same as the original expression.

Evaluating Option C

Let's evaluate option C: $(76 + 24) \times 5$. To do this, we need to follow the order of operations (PEMDAS):

1. Evaluate the expression inside the parentheses: $76 + 24 = 100$
2. Multiply 100 by 5: $100 \times 5 = 500$

Therefore, the value of option C is 500, which is not equal to the value of the original expression.

Evaluating Option D

Let's evaluate option D: $5 \times (76 + 5 + 24)$. To do this, we need to follow the order of operations (PEMDAS):

1. Evaluate the expression inside the parentheses: $76 + 5 + 24 = 105$
2. Multiply 5 by 105: $5 \times 105 = 525$

Therefore, the value of option D is 525, which is not equal to the value of the original expression.

Conclusion

In this article, we solved a mathematical expression that involved addition, multiplication, and parentheses. We broke down the solution into smaller steps, making it easier to understand and follow. We found the value of the expression to be 841, which matches option A. We also evaluated options C and D, and found that they are not equal to the value of the original expression.

Tips and Tricks

Here are some tips and tricks to help you solve mathematical expressions like this one:

• Follow the order of operations (PEMDAS): Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction.
• Evaluate expressions inside parentheses first.
• Multiply numbers in the correct order.
• Add numbers in the correct order.

By following these tips and tricks, you can become more confident and proficient in solving mathematical expressions like this one.

Final Answer

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Q: What is the order of operations (PEMDAS)?

A: The order of operations (PEMDAS) is a set of rules that tells us which operations to perform first when we have multiple operations in an expression. PEMDAS stands for:

1. Parentheses: Evaluate expressions inside parentheses first.
2. Exponents: Evaluate any exponential expressions next (e.g., 2^3).
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 evaluate expressions inside parentheses?

A: To evaluate expressions inside parentheses, simply follow the order of operations (PEMDAS) and perform the operations inside the parentheses first. For example, if we have the expression: $(2 + 3) \times 4$, we would first evaluate the expression inside the parentheses: $2 + 3 = 5$, and then multiply 5 by 4: $5 \times 4 = 20$.

Q: What is the difference between multiplication and division?

A: Multiplication and division are both operations that involve numbers, but they have different effects on the numbers. Multiplication involves adding a number a certain number of times, while division involves sharing a number into equal parts.

For example, if we have the expression: $4 \times 5$, we would multiply 4 by 5, which means adding 4 together 5 times: $4 + 4 + 4 + 4 + 4 = 20$. On the other hand, if we have the expression: $20 \div 5$, we would divide 20 into 5 equal parts: $20 \div 5 = 4$.

Q: How do I add and subtract numbers in the correct order?

A: When adding and subtracting numbers, it's essential to follow the order of operations (PEMDAS) and perform the operations from left to right. For example, if we have the expression: $3 + 2 - 1$, we would first add 3 and 2: $3 + 2 = 5$, and then subtract 1: $5 - 1 = 4$.

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

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

• Not following the order of operations (PEMDAS)
• Not evaluating expressions inside parentheses first
• Not multiplying numbers in the correct order
• Not adding numbers in the correct order
• Not checking for errors in the expression

Q: How can I practice solving mathematical expressions?

A: There are many ways to practice solving mathematical expressions, including:

• Working through practice problems in a textbook or online resource
• Using online tools or apps to generate random expressions to solve
• Creating your own expressions to solve and checking your work
• Joining a study group or working with a tutor to practice solving expressions together

Q: What are some real-world applications of solving mathematical expressions?

A: Solving mathematical expressions has many real-world applications, including:

• Calculating costs and prices in business and finance
• Determining the area and perimeter of shapes in architecture and engineering
• Modeling population growth and decline in biology and medicine
• Analyzing data and making predictions in statistics and data science

Conclusion

Solving mathematical expressions is a fundamental skill that has many real-world applications. By following the order of operations (PEMDAS) and practicing regularly, you can become more confident and proficient in solving expressions like this one. Remember to evaluate expressions inside parentheses first, multiply numbers in the correct order, and add numbers in the correct order. With practice and patience, you can master the art of solving mathematical expressions.