Calculate The Following Expression: − 3 × 4 + ( − 7 ) × 9 -3 \times 4 + (-7) \times 9 − 3 × 4 + ( − 7 ) × 9
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Introduction
Mathematical expressions are a fundamental part of mathematics, and solving them is an essential skill for students and professionals alike. In this article, we will focus on calculating the expression . We will break down the solution into manageable steps, making it easy to understand and follow.
Understanding the Expression
The given expression is . To solve this expression, we need to follow the order of operations, which is Parentheses, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right). In this case, we have two multiplication operations and one addition operation.
Step 1: Multiply -3 and 4
The first step is to multiply -3 and 4. When multiplying two numbers, we simply multiply the numbers together and keep the sign of the first number. In this case, the product of -3 and 4 is -12.
result1 = -3 * 4
print(result1) # Output: -12
Step 2: Multiply -7 and 9
The next step is to multiply -7 and 9. Again, we multiply the numbers together and keep the sign of the first number. In this case, the product of -7 and 9 is -63.
result2 = -7 * 9
print(result2) # Output: -63
Step 3: Add the Results
The final step is to add the results of the two multiplication operations. We add -12 and -63 together to get the final result.
final_result = result1 + result2
print(final_result) # Output: -75
Conclusion
In this article, we solved the mathematical expression by following the order of operations. We broke down the solution into manageable steps, making it easy to understand and follow. By multiplying -3 and 4, then multiplying -7 and 9, and finally adding the results, we arrived at the final answer of -75.
Tips and Tricks
- When solving mathematical expressions, always follow the order of operations.
- Use parentheses to group numbers and operations when necessary.
- Multiply numbers together and keep the sign of the first number.
- Add or subtract numbers from left to right.
Real-World Applications
Solving mathematical expressions is an essential skill in many real-world applications, including:
- Science and engineering: Mathematical expressions are used to model and solve problems in physics, chemistry, and other scientific fields.
- Finance: Mathematical expressions are used to calculate interest rates, investments, and other financial metrics.
- Computer programming: Mathematical expressions are used to write algorithms and solve problems in computer science.
Common Mistakes
- Failing to follow the order of operations.
- Not using parentheses to group numbers and operations.
- Multiplying numbers incorrectly.
- Adding or subtracting numbers incorrectly.
Conclusion
Solving mathematical expressions is a fundamental skill that is essential in many real-world applications. By following the order of operations and breaking down the solution into manageable steps, we can arrive at the final answer with confidence. Remember to use parentheses to group numbers and operations, multiply numbers together and keep the sign of the first number, and add or subtract numbers from left to right. With practice and patience, you will become proficient in solving mathematical expressions and tackle even the most complex problems with ease.
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Introduction
Solving mathematical expressions can be a challenging task, especially for those who are new to mathematics. In this article, we will address some of the most frequently asked questions about solving mathematical expressions. Whether you are a student, teacher, or simply someone who wants to improve their math skills, this article is for you.
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:
- 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: To evaluate expressions inside parentheses, we need to follow the order of operations. We start by evaluating any exponential expressions, then any multiplication and division operations, and finally any addition and subtraction operations.
For example, consider the expression: 2 × (3 + 4)
To evaluate this expression, we start by evaluating the expression inside the parentheses: 3 + 4 = 7
Then, we multiply 2 by 7: 2 × 7 = 14
Therefore, the final answer is 14.
Q: What is the difference between multiplication and division?
A: Multiplication and division are both operations that involve numbers, but they have different meanings.
Multiplication is a repeated addition operation. For example, 3 × 4 means 3 + 3 + 3 + 3 + 3 + 3 + 3 + 3 + 3 + 3 = 30
Division, on the other hand, is a sharing operation. For example, 30 ÷ 3 means sharing 30 into 3 equal groups.
Q: How do I evaluate expressions with multiple operations?
A: To evaluate expressions with multiple operations, we need to follow the order of operations. We start by evaluating any expressions inside parentheses, then any exponential expressions, and finally any multiplication and division operations.
For example, consider the expression: 2 × 3 + 4
To evaluate this expression, we start by multiplying 2 and 3: 2 × 3 = 6
Then, we add 4 to 6: 6 + 4 = 10
Therefore, the final answer is 10.
Q: What is the difference between addition and subtraction?
A: Addition and subtraction are both operations that involve numbers, but they have different meanings.
Addition is a combining operation. For example, 3 + 4 means combining 3 and 4 to get 7
Subtraction, on the other hand, is a taking away operation. For example, 7 - 3 means taking away 3 from 7.
Q: How do I evaluate expressions with negative numbers?
A: To evaluate expressions with negative numbers, we need to follow the order of operations. We start by evaluating any expressions inside parentheses, then any exponential expressions, and finally any multiplication and division operations.
For example, consider the expression: -2 × 3 + 4
To evaluate this expression, we start by multiplying -2 and 3: -2 × 3 = -6
Then, we add 4 to -6: -6 + 4 = -2
Therefore, the final answer is -2.
Conclusion
Solving mathematical expressions can be a challenging task, but with practice and patience, you can become proficient in solving even the most complex expressions. Remember to follow the order of operations, evaluate expressions inside parentheses first, and use parentheses to group numbers and operations when necessary. With these tips and tricks, you will be able to tackle even the most challenging math problems with ease.
Tips and Tricks
- Always follow the order of operations.
- Use parentheses to group numbers and operations when necessary.
- Evaluate expressions inside parentheses first.
- Use the correct order of operations for multiplication and division.
- Use the correct order of operations for addition and subtraction.
Real-World Applications
Solving mathematical expressions is an essential skill in many real-world applications, including:
- Science and engineering: Mathematical expressions are used to model and solve problems in physics, chemistry, and other scientific fields.
- Finance: Mathematical expressions are used to calculate interest rates, investments, and other financial metrics.
- Computer programming: Mathematical expressions are used to write algorithms and solve problems in computer science.
Common Mistakes
- Failing to follow the order of operations.
- Not using parentheses to group numbers and operations.
- Evaluating expressions incorrectly.
- Not using the correct order of operations for multiplication and division.
- Not using the correct order of operations for addition and subtraction.