Using Division to Simplify

Oct 13, 2025 by recoveryshake.com 25 views

Rewrite $\frac{\frac{1}{5} \text{ barrel }}{\frac{1}{2} \text{ hour }}$ as a Unit Rate

Understanding Unit Rates

A unit rate is a rate with a denominator of 1. It is a way to express a rate or ratio in a simpler form. In this article, we will focus on rewriting a given expression as a unit rate.

The Given Expression

The given expression is $\frac{\frac{1}{5} \text{ barrel }}{\frac{1}{2} \text{ hour }}$ . This expression represents the rate at which barrels are being filled or used per hour.

Rewriting the Expression

To rewrite the expression as a unit rate, we need to simplify it. We can do this by dividing the numerator by the denominator.

$\frac{\frac{1}{5} \text{ barrel }}{\frac{1}{2} \text{ hour }} = \frac{1}{5} \div \frac{1}{2}$

Using Division to Simplify

When we divide a fraction by another fraction, we can multiply the first fraction by the reciprocal of the second fraction.

$\frac{1}{5} \div \frac{1}{2} = \frac{1}{5} \times \frac{2}{1}$

Multiplying the Fractions

Now, we can multiply the numerators and denominators.

$\frac{1}{5} \times \frac{2}{1} = \frac{1 \times 2}{5 \times 1}$

Simplifying the Result

The result is $\frac{2}{5}$ .

Conclusion

Therefore, the unit rate is $\frac{2}{5}$ barrel/hour.

Answer

The correct answer is B. $\frac{2}{5}$ barrel/hour.

Why is this Important?

Understanding unit rates is important in many real-world applications, such as finance, science, and engineering. It allows us to compare rates and ratios in a simpler and more meaningful way.

Real-World Applications

Unit rates are used in many real-world applications, such as:

Calculating interest rates on loans and investments
Determining the cost of goods and services
Measuring the efficiency of machines and processes
Analyzing data and making informed decisions

Tips and Tricks

Here are some tips and tricks for working with unit rates:

Always simplify fractions by dividing the numerator and denominator by their greatest common divisor (GCD)
Use the reciprocal of a fraction to divide it by another fraction
Multiply the numerators and denominators when dividing fractions
Simplify the result by dividing the numerator and denominator by their GCD

Common Mistakes

Here are some common mistakes to avoid when working with unit rates:

Failing to simplify fractions
Not using the reciprocal of a fraction when dividing
Not multiplying the numerators and denominators when dividing fractions
Not simplifying the result by dividing the numerator and denominator by their GCD

Conclusion

In conclusion, rewriting $\frac{\frac{1}{5} \text{ barrel }}{\frac{1}{2} \text{ hour }}$ as a unit rate is a simple process that involves dividing the numerator by the denominator and simplifying the result. By following the tips and tricks outlined in this article, you can become proficient in working with unit rates and apply them to real-world applications.
Unit Rate Q&A

Frequently Asked Questions About Unit Rates

In this article, we will answer some frequently asked questions about unit rates.

Q: What is a unit rate?

A: A unit rate is a rate with a denominator of 1. It is a way to express a rate or ratio in a simpler form.

Q: Why is it important to understand unit rates?

A: Understanding unit rates is important in many real-world applications, such as finance, science, and engineering. It allows us to compare rates and ratios in a simpler and more meaningful way.

Q: How do I rewrite a rate as a unit rate?

A: To rewrite a rate as a unit rate, you need to divide the numerator by the denominator and simplify the result.

Q: What is the difference between a rate and a unit rate?

A: A rate is a ratio of two quantities, while a unit rate is a rate with a denominator of 1.

Q: How do I simplify a fraction to get a unit rate?

A: To simplify a fraction to get a unit rate, you need to divide the numerator and denominator by their greatest common divisor (GCD).

Q: What is the reciprocal of a fraction?

A: The reciprocal of a fraction is obtained by swapping the numerator and denominator.

Q: How do I use the reciprocal of a fraction to divide it by another fraction?

A: To use the reciprocal of a fraction to divide it by another fraction, you need to multiply the first fraction by the reciprocal of the second fraction.

Q: What is the greatest common divisor (GCD) of two numbers?

A: The greatest common divisor (GCD) of two numbers is the largest number that divides both numbers without leaving a remainder.

Q: How do I find the GCD of two numbers?

A: To find the GCD of two numbers, you can use the Euclidean algorithm or list the factors of each number and find the largest common factor.

Q: What are some common mistakes to avoid when working with unit rates?

A: Some common mistakes to avoid when working with unit rates include:

Failing to simplify fractions
Not using the reciprocal of a fraction when dividing
Not multiplying the numerators and denominators when dividing fractions
Not simplifying the result by dividing the numerator and denominator by their GCD

Q: How do I apply unit rates to real-world applications?

A: Unit rates can be applied to many real-world applications, such as:

Calculating interest rates on loans and investments
Determining the cost of goods and services
Measuring the efficiency of machines and processes
Analyzing data and making informed decisions

Q: What are some tips and tricks for working with unit rates?

A: Some tips and tricks for working with unit rates include:

Always simplify fractions by dividing the numerator and denominator by their GCD
Use the reciprocal of a fraction to divide it by another fraction
Multiply the numerators and denominators when dividing fractions
Simplify the result by dividing the numerator and denominator by their GCD

Conclusion

In conclusion, unit rates are an important concept in mathematics that can be applied to many real-world applications. By understanding how to rewrite rates as unit rates and avoiding common mistakes, you can become proficient in working with unit rates and apply them to real-world problems.