Using Division to Solve the Problem

Oct 13, 2025 by leolavanderia.com.br 126 views

Understanding the Problem

Molly hikes a fraction of a mile every day, and we need to determine how many days she would have to hike to cover a total distance of $$\frac{11}{6}$$ miles. To solve this problem, we need to use division to find the number of days required to hike the given distance.

Breaking Down the Problem

Let's break down the problem step by step:

Molly hikes $$\frac{1}{6}$$ mile every day.
We need to find the number of days she would have to hike to cover a total distance of $$\frac{11}{6}$$ miles.

Using Division to Solve the Problem

To find the number of days required to hike the given distance, we can use division. We can divide the total distance ($$\frac{11}{6}$$ miles) by the daily distance ($$\frac{1}{6}$$ mile) to find the number of days.

\frac{\frac{11}{6}}{\frac{1}{6}} = \frac{11}{6} \div \frac{1}{6}

To divide fractions, we can multiply the first fraction by the reciprocal of the second fraction.

\frac{11}{6} \div \frac{1}{6} = \frac{11}{6} \times \frac{6}{1}

Now, we can multiply the numerators and denominators.

\frac{11}{6} \times \frac{6}{1} = \frac{11 \times 6}{6 \times 1}

\frac{11 \times 6}{6 \times 1} = \frac{66}{6}

Now, we can simplify the fraction by dividing the numerator and denominator by their greatest common divisor, which is 6.

\frac{66}{6} = \frac{66 \div 6}{6 \div 6}

\frac{66 \div 6}{6 \div 6} = \frac{11}{1}

Therefore, Molly would have to hike for 11 days to cover a total distance of $$\frac{11}{6}$$ miles.

Conclusion

In this problem, we used division to find the number of days required to hike a given distance. We divided the total distance by the daily distance to find the number of days. By following the steps of division, we were able to simplify the fraction and find the correct answer.

Key Takeaways

To solve multi-day hiking problems with fractions, we can use division to find the number of days required to hike a given distance.
We can divide fractions by multiplying the first fraction by the reciprocal of the second fraction.
We can simplify fractions by dividing the numerator and denominator by their greatest common divisor.

Practice Problems

Tom hikes $$\frac{1}{4}$$ mile every day. How many days would he have to hike to cover a total distance of $$\frac{17}{4}$$ miles?
Sarah hikes $$\frac{2}{3}$$ mile every day. How many days would she have to hike to cover a total distance of $$\frac{22}{3}$$ miles?

Answer Key

17
11
Frequently Asked Questions (FAQs) about Multi-Day Hiking Problems with Fractions =====================================================================================

Q: What is the formula to solve multi-day hiking problems with fractions?

A: The formula to solve multi-day hiking problems with fractions is:

\frac{\text{Total Distance}}{\text{Daily Distance}} = \text{Number of Days}

Q: How do I divide fractions to solve multi-day hiking problems?

A: To divide fractions, you can multiply the first fraction by the reciprocal of the second fraction. For example:

\frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \times \frac{d}{c}

Q: How do I simplify fractions after dividing?

A: To simplify fractions, you can divide the numerator and denominator by their greatest common divisor (GCD). For example:

\frac{66}{6} = \frac{66 \div 6}{6 \div 6} = \frac{11}{1}

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. For example, the GCD of 12 and 18 is 6.

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

A: There are several ways to find the GCD of two numbers, including:

Using the Euclidean algorithm
Listing the factors of each number and finding the greatest common factor
Using a calculator or online tool

Q: What are some common mistakes to avoid when solving multi-day hiking problems with fractions?

A: Some common mistakes to avoid when solving multi-day hiking problems with fractions include:

Forgetting to simplify fractions after dividing
Not using the correct formula or method
Making errors when multiplying or dividing fractions

Q: How can I practice solving multi-day hiking problems with fractions?

A: You can practice solving multi-day hiking problems with fractions by:

Working through sample problems and exercises
Using online resources and tools, such as calculators or worksheets
Asking a teacher or tutor for help and guidance

Q: What are some real-world applications of multi-day hiking problems with fractions?

A: Some real-world applications of multi-day hiking problems with fractions include:

Planning a hiking trip and determining how many days it will take to complete
Calculating the cost of a hiking trip based on the daily distance and cost per mile
Determining the number of days required to complete a long-distance hike or backpacking trip

Q: Can I use multi-day hiking problems with fractions to solve other types of problems?

A: Yes, you can use multi-day hiking problems with fractions to solve other types of problems, such as:

Calculating the number of days required to complete a project or task
Determining the cost of a project or task based on the daily cost and duration
Solving problems involving rates, ratios, and proportions

Conclusion

In this article, we have covered some frequently asked questions (FAQs) about multi-day hiking problems with fractions. We have discussed the formula for solving these problems, how to divide fractions, and how to simplify fractions after dividing. We have also covered some common mistakes to avoid and provided some tips for practicing and applying these skills in real-world situations.