Molly Completes 3 10 \frac{3}{10} 10 3 ​ Of Her Science Project In 4 5 \frac{4}{5} 5 4 ​ Hour.How Much Of The Science Project Does Molly Complete Per Hour?Molly Completes □ \square □ Of The Science Project Per Hour.

Understanding the Problem

Molly is working on a science project and wants to know how much of it she completes per hour. To solve this problem, we need to understand the concept of fractions and division. We will use the given information to calculate Molly's completion rate per hour.

Given Information

• Molly completes $\frac{3}{10}$ of her science project.
• She completes this amount in $\frac{4}{5}$ hour.

Calculating Completion Rate

To find out how much of the science project Molly completes per hour, we need to divide the amount she completes by the time it takes her to complete it. In other words, we need to divide $\frac{3}{10}$ by $\frac{4}{5}$.

Division of Fractions

When we divide one fraction by another, we can multiply the first fraction by the reciprocal of the second fraction. The reciprocal of a fraction is obtained by swapping its numerator and denominator.

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

In this case, we have:

$\frac{3}{10} \div \frac{4}{5} = \frac{3}{10} \times \frac{5}{4}$

Multiplying Fractions

To multiply fractions, we multiply their numerators and denominators separately.

$\frac{3}{10} \times \frac{5}{4} = \frac{3 \times 5}{10 \times 4} = \frac{15}{40}$

Simplifying the Fraction

We can simplify the fraction $\frac{15}{40}$ by dividing both its numerator and denominator by their greatest common divisor (GCD). The GCD of 15 and 40 is 5.

$\frac{15}{40} = \frac{15 \div 5}{40 \div 5} = \frac{3}{8}$

Conclusion

Molly completes $\frac{3}{8}$ of the science project per hour.

Real-World Application

This problem can be applied to real-life situations where we need to calculate rates or completion times. For example, if a construction worker completes $\frac{3}{10}$ of a building in $\frac{4}{5}$ hour, we can use this method to calculate how much of the building they complete per hour.

Practice Problems

1. A student completes $\frac{2}{3}$ of a math problem in $\frac{3}{4}$ hour. How much of the math problem does the student complete per hour?
2. A worker completes $\frac{5}{6}$ of a project in $\frac{2}{3}$ hour. How much of the project does the worker complete per hour?

Answer Key

1. $\frac{8}{9}$
2. $\frac{5}{4}$
   Molly's Science Project: Q&A =============================

Q: What is the main concept behind Molly's science project?

A: The main concept behind Molly's science project is to calculate her completion rate per hour. This involves understanding fractions and division.

Q: What is the given information in the problem?

A: The given information is that Molly completes $\frac{3}{10}$ of her science project in $\frac{4}{5}$ hour.

Q: How do we calculate Molly's completion rate per hour?

A: To calculate Molly's completion rate per hour, we need to divide the amount she completes by the time it takes her to complete it. In other words, we need to divide $\frac{3}{10}$ by $\frac{4}{5}$.

Q: What is the formula for dividing fractions?

A: The formula for dividing fractions is:

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

Q: How do we multiply fractions?

A: To multiply fractions, we multiply their numerators and denominators separately.

Q: What is the greatest common divisor (GCD) and how do we use it to simplify fractions?

A: The greatest common divisor (GCD) is the largest number that divides two numbers without leaving a remainder. We can simplify a fraction by dividing both its numerator and denominator by their GCD.

Q: How do we simplify the fraction $\frac{15}{40}$?

A: We can simplify the fraction $\frac{15}{40}$ by dividing both its numerator and denominator by their GCD, which is 5.

$\frac{15}{40} = \frac{15 \div 5}{40 \div 5} = \frac{3}{8}$

Q: What is the final answer to the problem?

A: Molly completes $\frac{3}{8}$ of the science project per hour.

Q: How can we apply this problem to real-life situations?

A: This problem can be applied to real-life situations where we need to calculate rates or completion times. For example, if a construction worker completes $\frac{3}{10}$ of a building in $\frac{4}{5}$ hour, we can use this method to calculate how much of the building they complete per hour.

Q: What are some practice problems that we can use to reinforce our understanding of the concept?

A: Here are some practice problems that we can use to reinforce our understanding of the concept:

1. A student completes $\frac{2}{3}$ of a math problem in $\frac{3}{4}$ hour. How much of the math problem does the student complete per hour?
2. A worker completes $\frac{5}{6}$ of a project in $\frac{2}{3}$ hour. How much of the project does the worker complete per hour?

Q: What are the answers to the practice problems?

A: Here are the answers to the practice problems:

1. $\frac{8}{9}$
2. $\frac{5}{4}$