Select The Best Answer For The Question.7. Solve The Following: $32 \div 4 + 4 \times 8 = $?A. 42 B. 96 C. 40 D. 32

Mar 9, 2025 by ADMIN 119 views

**Solving Mathematical Expressions: A Step-by-Step Guide**

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Introduction

Mathematical expressions are a fundamental part of mathematics, and solving them requires a clear understanding of the order of operations. In this article, we will focus on solving a specific mathematical expression: $32 \div 4 + 4 \times 8 = ?$ . We will break down the solution step by step, using the correct order of operations to arrive at the correct answer.

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:

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

Solving the Mathematical Expression

Now that we have a clear understanding of the order of operations, let's apply it to the given mathematical expression: $32 \div 4 + 4 \times 8 = ?$ .

Step 1: Divide 32 by 4

The first operation in the expression is division. We need to divide 32 by 4.

$32 \div 4 = 8$

Step 2: Multiply 4 by 8

The next operation in the expression is multiplication. We need to multiply 4 by 8.

$4 \times 8 = 32$

Step 3: Add 8 and 32

The final operation in the expression is addition. We need to add 8 and 32.

$8 + 32 = 40$

Conclusion

In conclusion, the correct solution to the mathematical expression $32 \div 4 + 4 \times 8 = ?$ is 40. We arrived at this answer by following the order of operations, which dictates that we perform division and multiplication operations before addition and subtraction operations.

Answer Options

The answer options provided are:

A. 42 B. 96 C. 40 D. 32

Based on our solution, the correct answer is:

C. 40

Tips and Tricks

When solving mathematical expressions, it's essential to follow the order of operations to avoid errors. Here are some tips and tricks to help you:

Always evaluate expressions inside parentheses first.
Exponential expressions should be evaluated next.
Multiplication and division operations should be performed from left to right.
Addition and subtraction operations should be performed from left to right.

By following these tips and tricks, you'll be able to solve mathematical expressions with confidence and accuracy.

Practice Problems

To practice solving mathematical expressions, try the following problems:

$24 \div 3 + 5 \times 6 = ?$
$48 \div 6 + 2 \times 9 = ?$
$36 \div 4 + 3 \times 7 = ?$

Remember to follow the order of operations and use the tips and tricks provided to arrive at the correct answers.

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Introduction

Solving mathematical expressions can be a challenging task, especially when there are multiple operations involved. In this article, we will address some of the most frequently asked questions related to solving mathematical expressions.

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:

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

Q: How do I evaluate expressions inside parentheses?

A: When evaluating expressions inside parentheses, you should follow the order of operations within the parentheses. For example, if you have the expression $(2 + 3) \times 4$ , you should first evaluate the expression inside the parentheses: $2 + 3 = 5$ . Then, you can 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 result. Multiplication involves adding a number a certain number of times, while division involves finding the quotient of two numbers. For example, $4 \times 5 = 20$ (multiplication), while $20 \div 4 = 5$ (division).

Q: How do I evaluate expressions with exponents?

A: Exponents are a shorthand way of writing repeated multiplication. For example, $2^3$ means $2 \times 2 \times 2 = 8$ . When evaluating expressions with exponents, you should follow the order of operations and evaluate the exponent first.

Q: What is the difference between addition and subtraction?

A: Addition and subtraction are both operations that involve numbers, but they have different effects on the result. Addition involves finding the sum of two or more numbers, while subtraction involves finding the difference between two numbers. For example, $4 + 5 = 9$ (addition), while $9 - 4 = 5$ (subtraction).

Q: How do I evaluate expressions with multiple operations?

A: When evaluating expressions with multiple operations, you should follow the order of operations and evaluate the operations from left to right. For example, if you have the expression $4 + 3 \times 2$ , you should first evaluate the multiplication operation: $3 \times 2 = 6$ . Then, you can add 4 and 6: $4 + 6 = 10$ .

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
Evaluating expressions inside parentheses incorrectly
Not evaluating exponents correctly
Not following the order of operations when there are multiple operations
Not checking the result for errors

Conclusion

Solving mathematical expressions can be a challenging task, but by following the order of operations and avoiding common mistakes, you can arrive at the correct answer. Remember to always evaluate expressions inside parentheses first, then exponents, then multiplication and division, and finally addition and subtraction. With practice and patience, you can become proficient in solving mathematical expressions.

Practice Problems

To practice solving mathematical expressions, try the following problems:

$24 \div 3 + 5 \times 6 = ?$
$48 \div 6 + 2 \times 9 = ?$
$36 \div 4 + 3 \times 7 = ?$

Remember to follow the order of operations and use the tips and tricks provided to arrive at the correct answers.