Calculate The Result Of The Following Expression: ${ 12 \frac{3}{4} - 6 \frac{1}{10} - 8.4 }$

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Understanding Mixed Numbers and Decimal Numbers

In mathematics, mixed numbers and decimal numbers are two different ways to represent fractions. A mixed number is a combination of a whole number and a fraction, while a decimal number is a way to represent a fraction using the base-10 number system. In this article, we will learn how to calculate the result of the expression ${ 12 \frac{3}{4} - 6 \frac{1}{10} - 8.4 }$.

Converting Mixed Numbers to Decimal Numbers

To calculate the result of the expression, we need to convert the mixed numbers to decimal numbers. We can do this by dividing the numerator by the denominator and adding the result to the whole number.

For example, let's convert the mixed number 123412 \frac{3}{4} to a decimal number.

1234=12+34{ 12 \frac{3}{4} = 12 + \frac{3}{4} }

To convert the fraction to a decimal number, we can divide the numerator by the denominator.

34=0.75{ \frac{3}{4} = 0.75 }

Now, we can add the result to the whole number.

12+0.75=12.75{ 12 + 0.75 = 12.75 }

Similarly, let's convert the mixed number 61106 \frac{1}{10} to a decimal number.

6110=6+110{ 6 \frac{1}{10} = 6 + \frac{1}{10} }

To convert the fraction to a decimal number, we can divide the numerator by the denominator.

110=0.1{ \frac{1}{10} = 0.1 }

Now, we can add the result to the whole number.

6+0.1=6.1{ 6 + 0.1 = 6.1 }

Converting Decimal Numbers to Decimal Numbers

Now that we have converted the mixed numbers to decimal numbers, we can subtract the decimal numbers.

12.75−6.1−8.4{ 12.75 - 6.1 - 8.4 }

Calculating the Result

To calculate the result, we need to follow the order of operations (PEMDAS).

  1. Subtract 6.1 from 12.75.

12.75−6.1=6.65{ 12.75 - 6.1 = 6.65 }

  1. Subtract 8.4 from 6.65.

6.65−8.4=−1.75{ 6.65 - 8.4 = -1.75 }

Therefore, the result of the expression ${ 12 \frac{3}{4} - 6 \frac{1}{10} - 8.4 }$ is -1.75.

Conclusion

In this article, we learned how to calculate the result of the expression ${ 12 \frac{3}{4} - 6 \frac{1}{10} - 8.4 }$. We converted the mixed numbers to decimal numbers and then subtracted the decimal numbers. The result of the expression is -1.75.

Tips and Tricks

  • When converting mixed numbers to decimal numbers, make sure to divide the numerator by the denominator.
  • When subtracting decimal numbers, make sure to follow the order of operations (PEMDAS).
  • Practice converting mixed numbers to decimal numbers and subtracting decimal numbers to become more comfortable with the process.

Common Mistakes

  • Forgetting to convert mixed numbers to decimal numbers.
  • Forgetting to follow the order of operations (PEMDAS) when subtracting decimal numbers.
  • Making mistakes when dividing the numerator by the denominator.

Real-World Applications

  • Calculating the result of the expression ${ 12 \frac{3}{4} - 6 \frac{1}{10} - 8.4 }$ can be applied to real-world situations such as calculating the cost of goods or services.
  • Converting mixed numbers to decimal numbers and subtracting decimal numbers can be applied to real-world situations such as calculating the total cost of a project.

Final Thoughts

In conclusion, calculating the result of the expression ${ 12 \frac{3}{4} - 6 \frac{1}{10} - 8.4 }$ requires converting mixed numbers to decimal numbers and subtracting decimal numbers. By following the order of operations (PEMDAS) and practicing converting mixed numbers to decimal numbers and subtracting decimal numbers, you can become more comfortable with the process and apply it to real-world situations.

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Understanding Mixed Numbers and Decimal Numbers

In our previous article, we learned how to calculate the result of the expression ${ 12 \frac{3}{4} - 6 \frac{1}{10} - 8.4 }$. In this article, we will answer some frequently asked questions about calculating mixed numbers and decimal numbers.

Q&A

Q: What is the difference between a mixed number and a decimal number?

A: A mixed number is a combination of a whole number and a fraction, while a decimal number is a way to represent a fraction using the base-10 number system.

Q: How do I convert a mixed number to a decimal number?

A: To convert a mixed number to a decimal number, you need to divide the numerator by the denominator and add the result to the whole number.

Q: What is the order of operations (PEMDAS) when subtracting decimal numbers?

A: The order of operations (PEMDAS) when subtracting decimal numbers is:

  1. Subtract the decimal numbers from left to right.
  2. Make sure to follow the order of operations (PEMDAS) when subtracting decimal numbers.

Q: What are some common mistakes to avoid when calculating mixed numbers and decimal numbers?

A: Some common mistakes to avoid when calculating mixed numbers and decimal numbers include:

  • Forgetting to convert mixed numbers to decimal numbers.
  • Forgetting to follow the order of operations (PEMDAS) when subtracting decimal numbers.
  • Making mistakes when dividing the numerator by the denominator.

Q: How can I practice converting mixed numbers to decimal numbers and subtracting decimal numbers?

A: You can practice converting mixed numbers to decimal numbers and subtracting decimal numbers by:

  • Using online calculators or worksheets to practice converting mixed numbers to decimal numbers and subtracting decimal numbers.
  • Working with real-world examples, such as calculating the cost of goods or services.
  • Creating your own practice problems and solving them.

Q: What are some real-world applications of calculating mixed numbers and decimal numbers?

A: Some real-world applications of calculating mixed numbers and decimal numbers include:

  • Calculating the cost of goods or services.
  • Calculating the total cost of a project.
  • Calculating the result of a mathematical expression.

Tips and Tricks

  • Make sure to follow the order of operations (PEMDAS) when subtracting decimal numbers.
  • Practice converting mixed numbers to decimal numbers and subtracting decimal numbers to become more comfortable with the process.
  • Use online calculators or worksheets to practice converting mixed numbers to decimal numbers and subtracting decimal numbers.

Common Mistakes

  • Forgetting to convert mixed numbers to decimal numbers.
  • Forgetting to follow the order of operations (PEMDAS) when subtracting decimal numbers.
  • Making mistakes when dividing the numerator by the denominator.

Real-World Applications

  • Calculating the result of the expression ${ 12 \frac{3}{4} - 6 \frac{1}{10} - 8.4 }$ can be applied to real-world situations such as calculating the cost of goods or services.
  • Converting mixed numbers to decimal numbers and subtracting decimal numbers can be applied to real-world situations such as calculating the total cost of a project.

Final Thoughts

In conclusion, calculating mixed numbers and decimal numbers requires converting mixed numbers to decimal numbers and subtracting decimal numbers. By following the order of operations (PEMDAS) and practicing converting mixed numbers to decimal numbers and subtracting decimal numbers, you can become more comfortable with the process and apply it to real-world situations.