Calculate: \[$[-12 \times 0.3] - [8 \times (-0.4)]\$\]

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Introduction

Mathematics is a fundamental subject that plays a crucial role in our daily lives. It is used in various fields, including science, technology, engineering, and mathematics (STEM), economics, finance, and more. Mathematical operations are the building blocks of mathematics, and mastering them is essential to solve complex problems. In this article, we will focus on calculating expressions involving multiplication and subtraction.

Understanding the Problem

The given problem is to calculate the expression: {[-12 \times 0.3] - [8 \times (-0.4)]$}$. This expression involves two main operations: multiplication and subtraction. To solve this problem, we need to follow the order of operations (PEMDAS):

  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.

Step 1: Multiply -12 and 0.3

To solve the first part of the expression, we need to multiply -12 and 0.3.

Multiplication of Negative Numbers

When multiplying two negative numbers, the result is always positive.

Example: −12×−3=36{-12 \times -3 = 36}

In this case, we have -12 and 0.3. Since 0.3 is a positive number, the result of the multiplication will be negative.

Code:

result1 = -12 * 0.3
print(result1)

Step 2: Multiply 8 and -0.4

To solve the second part of the expression, we need to multiply 8 and -0.4.

Multiplication of Positive and Negative Numbers

When multiplying a positive number and a negative number, the result is always negative.

Example: 8×−0.4=−3.2{8 \times -0.4 = -3.2}

In this case, we have 8 and -0.4. Since -0.4 is a negative number, the result of the multiplication will be negative.

Code:

result2 = 8 * -0.4
print(result2)

Step 3: Subtract result2 from result1

Now that we have the results of both multiplications, we can subtract result2 from result1.

Subtraction of Negative Numbers

When subtracting a negative number, it is equivalent to adding a positive number.

Example: −3−(−2)=−3+2=−1{-3 - (-2) = -3 + 2 = -1}

In this case, we have result1 and result2. Since result2 is negative, we can rewrite the subtraction as an addition.

Code:

final_result = result1 + abs(result2)
print(final_result)

Conclusion

In this article, we learned how to calculate the expression: {[-12 \times 0.3] - [8 \times (-0.4)]$}$. We followed the order of operations (PEMDAS) and used Python code to demonstrate each step. By mastering mathematical operations, we can solve complex problems and make informed decisions in various fields.

Final Answer

The final answer to the expression is: -4.6

Additional Resources

For more information on mathematical operations, please refer to the following resources:

Frequently Asked Questions

Q: What is the order of operations (PEMDAS)? A: The order of operations (PEMDAS) is a set of rules that dictates the order in which mathematical operations should be performed. The acronym PEMDAS stands for Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction.

Q: What is the difference between multiplication and addition? A: Multiplication is the process of adding a number a certain number of times, while addition is the process of combining two or more numbers.

Q&A: Frequently Asked Questions About Mathematical Operations

In our previous article, we explored the concept of mathematical operations and how to calculate expressions involving multiplication and subtraction. However, we understand that there may be more questions and concerns. In this article, we will address some of the most frequently asked questions about mathematical operations.

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

A: The order of operations (PEMDAS) is a set of rules that dictates the order in which mathematical operations should be performed. The acronym PEMDAS stands for:

  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: What is the difference between multiplication and addition?

A: Multiplication is the process of adding a number a certain number of times, while addition is the process of combining two or more numbers.

Example: 3×4=3+3+3+3=12{3 \times 4 = 3 + 3 + 3 + 3 = 12}

In this example, we can see that multiplication is equivalent to adding a number a certain number of times.

Q: How do I evaluate expressions involving negative numbers?

A: When evaluating expressions involving negative numbers, remember that:

  • Multiplying two negative numbers results in a positive number.
  • Multiplying a positive number and a negative number results in a negative number.
  • Subtracting a negative number is equivalent to adding a positive number.

Example: −3−(−2)=−3+2=−1{-3 - (-2) = -3 + 2 = -1}

In this example, we can see that subtracting a negative number is equivalent to adding a positive number.

Q: What is the difference between a fraction and a decimal?

A: A fraction is a way of expressing a part of a whole, while a decimal is a way of expressing a number in a base-10 system.

Example: 12=0.5{\frac{1}{2} = 0.5}

In this example, we can see that the fraction 12{\frac{1}{2}} is equivalent to the decimal 0.5.

Q: How do I convert a fraction to a decimal?

A: To convert a fraction to a decimal, simply divide the numerator by the denominator.

Example: 12=12=0.5{\frac{1}{2} = \frac{1}{2} = 0.5}

In this example, we can see that the fraction 12{\frac{1}{2}} is equivalent to the decimal 0.5.

Q: What is the difference between a percentage and a decimal?

A: A percentage is a way of expressing a number as a fraction of 100, while a decimal is a way of expressing a number in a base-10 system.

Example: 25%=0.25{25\% = 0.25}

In this example, we can see that the percentage 25% is equivalent to the decimal 0.25.

Q: How do I convert a percentage to a decimal?

A: To convert a percentage to a decimal, simply divide the percentage by 100.

Example: 25%=25100=0.25{25\% = \frac{25}{100} = 0.25}

In this example, we can see that the percentage 25% is equivalent to the decimal 0.25.

Conclusion

In this article, we addressed some of the most frequently asked questions about mathematical operations. We hope that this article has provided you with a better understanding of mathematical operations and how to calculate expressions involving multiplication and subtraction.

Additional Resources

For more information on mathematical operations, please refer to the following resources:

Frequently Asked Questions

Q: What is the order of operations (PEMDAS)? A: The order of operations (PEMDAS) is a set of rules that dictates the order in which mathematical operations should be performed.

Q: What is the difference between multiplication and addition? A: Multiplication is the process of adding a number a certain number of times, while addition is the process of combining two or more numbers.

Q: How do I evaluate expressions involving negative numbers? A: When evaluating expressions involving negative numbers, remember that multiplying two negative numbers results in a positive number, while multiplying a positive number and a negative number results in a negative number.

Q: What is the difference between a fraction and a decimal? A: A fraction is a way of expressing a part of a whole, while a decimal is a way of expressing a number in a base-10 system.

Q: How do I convert a fraction to a decimal? A: To convert a fraction to a decimal, simply divide the numerator by the denominator.

Q: What is the difference between a percentage and a decimal? A: A percentage is a way of expressing a number as a fraction of 100, while a decimal is a way of expressing a number in a base-10 system.

Q: How do I convert a percentage to a decimal? A: To convert a percentage to a decimal, simply divide the percentage by 100.