Calculating Hair Length After a Haircut

Oct 13, 2025 by miodeya.com 86 views

Introduction

Florencia's hair length is a classic example of a percentage decrease problem in mathematics. In this article, we will explore how to calculate the length of Florencia's hair after she got a haircut on Tuesday. We will also examine which expression could represent the new length of her hair.

Calculating Hair Length After a Haircut

Let's assume that Florencia's hair was $$h$$ centimeters long on Monday. After getting a haircut on Tuesday, her hair was only $$75%$$ of the length it was on Monday. To calculate the new length of her hair, we need to multiply the original length by $$75%$$ or $$0.75$$.

The new length of Florencia's hair can be calculated as follows:

\text{New Length} = h \times 0.75

This can be rewritten as:

\text{New Length} = 0.75h

Which Expression Could Represent the New Length of Her Hair?

Now, let's examine which expression could represent the new length of Florencia's hair. We have two options:

$0.75h$
$\frac{3}{4}h$

Both expressions are equivalent and can represent the new length of Florencia's hair. However, the second expression is more intuitive and easier to understand.

Why is the Second Expression More Intuitive?

The second expression, $$\frac{3}{4}h$$, is more intuitive because it represents the fraction of the original length that Florencia's hair is after the haircut. Since $$75%$$ is equivalent to $$\frac{3}{4}$$, this expression clearly shows that Florencia's hair is $$\frac{3}{4}$$ of its original length.

Conclusion

In conclusion, the expression $$\frac{3}{4}h$$ could represent the new length of Florencia's hair after she got a haircut on Tuesday. This expression is more intuitive and easier to understand than the first expression, $$0.75h$$. By using fractions, we can clearly see that Florencia's hair is $$\frac{3}{4}$$ of its original length.

Real-World Applications

This problem has real-world applications in various fields, such as:

Finance: When calculating interest rates or investment returns, we often need to multiply a value by a percentage or fraction.
Science: In physics and chemistry, we often need to calculate percentages or fractions of a value to understand a phenomenon or predict an outcome.
Business: In business, we often need to calculate percentages or fractions of a value to understand sales, profits, or losses.

Tips and Tricks

Here are some tips and tricks to help you solve percentage decrease problems like this one:

Understand the problem: Before solving the problem, make sure you understand what is being asked.
Identify the percentage: Identify the percentage or fraction that is being applied to the original value.
Multiply or divide: Multiply or divide the original value by the percentage or fraction to get the new value.
Check your units: Make sure your units are consistent and match the units of the original value.

Common Mistakes

Here are some common mistakes to avoid when solving percentage decrease problems like this one:

Not understanding the problem: Failing to understand the problem can lead to incorrect solutions.
Not identifying the percentage: Failing to identify the percentage or fraction can lead to incorrect solutions.
Not multiplying or dividing correctly: Failing to multiply or divide correctly can lead to incorrect solutions.
Not checking units: Failing to check units can lead to incorrect solutions.

Conclusion

$In conclusion, the expression $$\frac{3}{4}h$$ could represent the new length of Florencia's hair after she got a haircut on Tuesday. This expression is more intuitive and easier to understand than the first expression, $$0.75h$$. By using fractions, we can clearly see that Florencia's hair is $$\frac{3}{4}$$ of its original length.<br/> **Frequently Asked Questions (FAQs)**$

Q: What is the formula for calculating the new length of Florencia's hair after a haircut?

A: The formula for calculating the new length of Florencia's hair after a haircut is:

\text{New Length} = h \times 0.75

\text{New Length} = 0.75h

Q: Why is the second expression, $$\frac{3}{4}h$$, more intuitive than the first expression, $$0.75h$$?

A: The second expression, $$\frac{3}{4}h$$, is more intuitive because it represents the fraction of the original length that Florencia's hair is after the haircut. Since $$75%$$ is equivalent to $$\frac{3}{4}$$, this expression clearly shows that Florencia's hair is $$\frac{3}{4}$$ of its original length.

Q: Can I use other expressions to represent the new length of Florencia's hair?

A: Yes, you can use other expressions to represent the new length of Florencia's hair. For example, you can use:

\text{New Length} = \frac{3}{4}h

\text{New Length} = 0.75h \times 100\%

\text{New Length} = 75\% \times h

Q: How do I calculate the new length of Florencia's hair if the haircut is $$80%$$ instead of $$75%$$?

A: To calculate the new length of Florencia's hair if the haircut is $$80%$$ instead of $$75%$$, you can use the formula:

\text{New Length} = h \times 0.8

\text{New Length} = 0.8h

Q: Can I use this formula to calculate the new length of Florencia's hair if the haircut is $$90%$$ instead of $$75%$$?

A: Yes, you can use this formula to calculate the new length of Florencia's hair if the haircut is $$90%$$ instead of $$75%$$. You can simply replace $$0.75$$ with $$0.9$$ in the formula:

\text{New Length} = h \times 0.9

\text{New Length} = 0.9h

Q: What if I want to calculate the new length of Florencia's hair if the haircut is $$50%$$ instead of $$75%$$?

A: To calculate the new length of Florencia's hair if the haircut is $$50%$$ instead of $$75%$$, you can use the formula:

\text{New Length} = h \times 0.5

\text{New Length} = 0.5h

Q: Can I use this formula to calculate the new length of Florencia's hair if the haircut is $$25%$$ instead of $$75%$$?

A: Yes, you can use this formula to calculate the new length of Florencia's hair if the haircut is $$25%$$ instead of $$75%$$. You can simply replace $$0.75$$ with $$0.25$$ in the formula:

\text{New Length} = h \times 0.25

\text{New Length} = 0.25h

Conclusion

In conclusion, the formula for calculating the new length of Florencia's hair after a haircut is:

\text{New Length} = h \times 0.75

\text{New Length} = 0.75h

You can use this formula to calculate the new length of Florencia's hair if the haircut is $$80%$$, $$90%$$, $$50%$$, or $$25%$$ instead of $$75%$$.