What Is $ -% $ Of $ 16 $?A. 0.012 B. 0.12 C. 1.2 D. 12

by ADMIN 58 views

What is $ -% $ of $ 16 $?

Understanding the Concept of Percentage

In mathematics, a percentage is a way to express a value as a fraction of 100. It is denoted by the symbol "%". To find a percentage of a given number, we multiply the number by the percentage value. For example, to find 25% of 100, we multiply 100 by 0.25 (which is 25% expressed as a decimal).

Calculating $ -% $ of $ 16 $

The given problem asks us to find $ -% $ of $ 16 $. To solve this, we need to first convert the percentage value to a decimal. Since the percentage value is negative, we will also need to consider the sign of the result.

Converting Percentage to Decimal

To convert a percentage value to a decimal, we divide the percentage value by 100. In this case, we have $ -% $, which is equivalent to $ -\frac{1}{100} $.

Multiplying by the Decimal Value

Now that we have the decimal value, we can multiply it by the given number, $ 16 $. This will give us the result of $ -% $ of $ 16 $.

$ -% $ of $ 16 $ = $ -\frac{1}{100} \times 16 $

To simplify this expression, we can multiply the numerator and denominator by 16.

$ -% $ of $ 16 $ = $ -\frac{16}{100} $

Simplifying the Fraction

We can simplify the fraction by dividing both the numerator and denominator by their greatest common divisor, which is 4.

$ -% $ of $ 16 $ = $ -\frac{4}{25} $

Converting the Fraction to a Decimal

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

$ -% $ of $ 16 $ = $ -\frac{4}{25} $ = $ -0.16 $

Rounding the Result

Since the result is a negative decimal value, we can round it to two decimal places.

$ -% $ of $ 16 $ ≈ $ -0.16 $

Comparing the Result to the Options

Now that we have the result, we can compare it to the given options.

A. 0.012 B. 0.12 C. 1.2 D. 12

The result we obtained is $ -0.16 $, which is closest to option A. However, we need to consider the sign of the result. Since the result is negative, we can conclude that the correct answer is option A.

Conclusion

In this problem, we were asked to find $ -% $ of $ 16 $. To solve this, we converted the percentage value to a decimal, multiplied it by the given number, and simplified the result. The final answer is $ -0.16 $, which is closest to option A.

Key Takeaways

  • To find a percentage of a given number, we multiply the number by the percentage value.
  • To convert a percentage value to a decimal, we divide the percentage value by 100.
  • When multiplying a decimal value by a number, we can simplify the result by dividing both the numerator and denominator by their greatest common divisor.
  • When comparing the result to the options, we need to consider the sign of the result.

Practice Problems

  1. Find 25% of 100.
  2. Find 50% of 200.
  3. Find 75% of 300.

Answer Key

  1. 25
  2. 100
  3. 225
    Frequently Asked Questions (FAQs) About Calculating Percentages

Q: What is a percentage?

A: A percentage is a way to express a value as a fraction of 100. It is denoted by the symbol "%". For example, 25% is equal to 25/100 or 0.25.

Q: How do I calculate a percentage of a given number?

A: To calculate a percentage of a given number, you multiply the number by the percentage value. For example, to find 25% of 100, you multiply 100 by 0.25 (which is 25% expressed as a decimal).

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

A: A percentage is a way to express a value as a fraction of 100, while a decimal is a way to express a value as a fraction with a denominator of 10. To convert a percentage to a decimal, you divide the percentage value by 100.

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

A: To convert a percentage to a decimal, you divide the percentage value by 100. For example, to convert 25% to a decimal, you divide 25 by 100, which equals 0.25.

Q: What is the formula for calculating a percentage of a given number?

A: The formula for calculating a percentage of a given number is:

Percentage = (Number x Percentage Value) / 100

For example, to find 25% of 100, you would use the formula:

25% of 100 = (100 x 0.25) / 100 = 25

Q: How do I calculate a negative percentage of a given number?

A: To calculate a negative percentage of a given number, you multiply the number by the negative percentage value. For example, to find -25% of 100, you multiply 100 by -0.25 (which is -25% expressed as a decimal).

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

A: A percentage is a way to express a value as a fraction of 100, while a proportion is a way to express a relationship between two values. For example, 25% is equal to 25/100, while 25% of 100 is equal to 25.

Q: How do I calculate a percentage of a percentage?

A: To calculate a percentage of a percentage, you multiply the two percentage values together. For example, to find 25% of 50%, you multiply 0.25 (25% expressed as a decimal) by 0.5 (50% expressed as a decimal).

Q: What is the formula for calculating a percentage of a percentage?

A: The formula for calculating a percentage of a percentage is:

Percentage of Percentage = (Percentage Value 1 x Percentage Value 2) / 100

For example, to find 25% of 50%, you would use the formula:

25% of 50% = (0.25 x 0.5) / 100 = 0.125

Q: How do I calculate a percentage increase or decrease?

A: To calculate a percentage increase or decrease, you use the formula:

Percentage Increase or Decrease = ((New Value - Old Value) / Old Value) x 100

For example, to find the percentage increase from 100 to 120, you would use the formula:

Percentage Increase = ((120 - 100) / 100) x 100 = 20%

Q: What is the difference between a percentage increase and a percentage decrease?

A: A percentage increase is a way to express a value as a fraction of the original value, while a percentage decrease is a way to express a value as a fraction of the original value. For example, a 20% increase from 100 to 120 is equal to 20/100 or 0.2, while a 20% decrease from 100 to 80 is equal to -20/100 or -0.2.

Q: How do I calculate a percentage of a percentage increase or decrease?

A: To calculate a percentage of a percentage increase or decrease, you multiply the percentage increase or decrease by the percentage value. For example, to find 25% of a 20% increase, you multiply 0.25 (25% expressed as a decimal) by 0.2 (20% expressed as a decimal).

Q: What is the formula for calculating a percentage of a percentage increase or decrease?

A: The formula for calculating a percentage of a percentage increase or decrease is:

Percentage of Percentage Increase or Decrease = (Percentage Value x Percentage Increase or Decrease)

For example, to find 25% of a 20% increase, you would use the formula:

25% of 20% increase = (0.25 x 0.2) = 0.05

Conclusion

In this article, we have covered frequently asked questions about calculating percentages. We have discussed the difference between a percentage and a decimal, how to convert a percentage to a decimal, and how to calculate a percentage of a given number. We have also covered how to calculate a negative percentage of a given number, a percentage of a percentage, and a percentage increase or decrease. We hope that this article has been helpful in answering your questions about calculating percentages.