Select All Of The Expressions That Could Be Used To Find 80 % 80 \% 80% Of X X X . Be Prepared To Explain Your Reasoning.- 8 100 ⋅ X \frac{8}{100} \cdot X 100 8 ​ ⋅ X - 80 100 ⋅ X \frac{80}{100} \cdot X 100 80 ​ ⋅ X - 4 10 ⋅ X \frac{4}{10} \cdot X 10 4 ​ ⋅ X - $\frac{8}{5}

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Introduction

In mathematics, finding a percentage of a number is a common operation that involves multiplying the number by a fraction that represents the percentage. In this article, we will explore the different expressions that can be used to find 80% of a number, and we will examine the reasoning behind each expression.

Understanding Percentages

Before we dive into the expressions, let's review what a percentage is. A percentage is a way of expressing a value as a fraction of 100. For example, 80% is equal to 80/100, which can be simplified to 4/5.

The Expressions

Now, let's examine the expressions that can be used to find 80% of a number.

8100⋅x\frac{8}{100} \cdot x

This expression can be used to find 80% of a number. To see why, let's break it down. The fraction 8/100 represents 8% of 100, which is equal to 80/100. When we multiply this fraction by x, we are essentially finding 80% of x.

80100⋅x\frac{80}{100} \cdot x

This expression is also a valid way to find 80% of a number. The fraction 80/100 represents 80% of 100, which is equal to 4/5. When we multiply this fraction by x, we are essentially finding 80% of x.

410⋅x\frac{4}{10} \cdot x

This expression can be used to find 80% of a number. To see why, let's break it down. The fraction 4/10 represents 40% of 10, which is equal to 80/100. When we multiply this fraction by x, we are essentially finding 80% of x.

85⋅x\frac{8}{5} \cdot x

This expression is not a valid way to find 80% of a number. The fraction 8/5 represents 160% of 5, which is not equal to 80% of 100. When we multiply this fraction by x, we are essentially finding 160% of x, not 80% of x.

Conclusion

In conclusion, the expressions 8100⋅x\frac{8}{100} \cdot x, 80100⋅x\frac{80}{100} \cdot x, and 410⋅x\frac{4}{10} \cdot x can be used to find 80% of a number. However, the expression 85⋅x\frac{8}{5} \cdot x is not a valid way to find 80% of a number.

Why is 85⋅x\frac{8}{5} \cdot x not a valid expression?

The reason why 85⋅x\frac{8}{5} \cdot x is not a valid expression is that it represents 160% of 5, not 80% of 100. When we multiply this fraction by x, we are essentially finding 160% of x, not 80% of x.

Why are 8100⋅x\frac{8}{100} \cdot x, 80100⋅x\frac{80}{100} \cdot x, and 410⋅x\frac{4}{10} \cdot x valid expressions?

The reason why 8100⋅x\frac{8}{100} \cdot x, 80100⋅x\frac{80}{100} \cdot x, and 410⋅x\frac{4}{10} \cdot x are valid expressions is that they represent 80% of 100, which is equal to 4/5. When we multiply these fractions by x, we are essentially finding 80% of x.

Real-World Applications

Finding 80% of a number is a common operation in real-world applications, such as:

  • Calculating discounts: If a product is on sale for 80% off, you can find the discount by multiplying the original price by 80/100.
  • Calculating tips: If you want to leave a 20% tip at a restaurant, you can find the tip by multiplying the total bill by 20/100.
  • Calculating interest rates: If you want to find the interest rate on a loan, you can multiply the principal amount by the interest rate as a decimal.

Conclusion

Q: What is the formula for finding 80% of a number?

A: The formula for finding 80% of a number is to multiply the number by the fraction 80/100, which can be simplified to 4/5.

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

A: To convert a percentage to a decimal, divide the percentage by 100. For example, 80% can be converted to a decimal by dividing 80 by 100, which equals 0.8.

Q: Can I use a calculator to find 80% of a number?

A: Yes, you can use a calculator to find 80% of a number. Simply enter the number and multiply it by 0.8 (or 80/100).

Q: What if I want to find 80% of a negative number?

A: To find 80% of a negative number, multiply the negative number by the fraction 80/100, which can be simplified to 4/5. The result will be a negative number.

Q: Can I use a percentage to find a percentage of a number?

A: Yes, you can use a percentage to find a percentage of a number. For example, if you want to find 80% of 120%, you can multiply 120% by 80/100, which equals 96%.

Q: How do I find 80% of a decimal number?

A: To find 80% of a decimal number, multiply the decimal number by the fraction 80/100, which can be simplified to 4/5. The result will be a decimal number.

Q: Can I use a calculator to find 80% of a decimal number?

A: Yes, you can use a calculator to find 80% of a decimal number. Simply enter the decimal number and multiply it by 0.8 (or 80/100).

Q: What if I want to find 80% of a fraction?

A: To find 80% of a fraction, multiply the fraction by the fraction 80/100, which can be simplified to 4/5. The result will be a fraction.

Q: Can I use a calculator to find 80% of a fraction?

A: Yes, you can use a calculator to find 80% of a fraction. Simply enter the fraction and multiply it by 0.8 (or 80/100).

Q: How do I find 80% of a mixed number?

A: To find 80% of a mixed number, convert the mixed number to an improper fraction, multiply the improper fraction by the fraction 80/100, which can be simplified to 4/5, and then convert the result back to a mixed number.

Q: Can I use a calculator to find 80% of a mixed number?

A: Yes, you can use a calculator to find 80% of a mixed number. Simply enter the mixed number and multiply it by 0.8 (or 80/100).

Conclusion

In conclusion, finding 80% of a number is a common operation that involves multiplying the number by a fraction that represents the percentage. By understanding the formula and how to convert percentages to decimals, you can easily find 80% of a number using a calculator or by hand.