Richard Needed To Read 5 Books For His Summer Reading Assignment. It Took Him 4 5 8 4 \frac{5}{8} 4 8 5 Hours To Read The First 2 Books And 7 7 8 7 \frac{7}{8} 7 8 7 Hours To Read The Remaining 3 Books. How Long Did It Take Richard To Read All 5 Books?A.

Mar 13, 2025 by ADMIN 259 views

**Richard's Summer Reading Assignment: A Mathematical Puzzle**

Introduction

Summer reading assignments are a great way to encourage students to read and explore new books. However, they can also be a source of frustration, especially when it comes to calculating the time it takes to read a certain number of books. In this article, we will explore a mathematical puzzle that involves calculating the time it takes to read a certain number of books. We will use the concept of mixed numbers and fractions to solve this problem.

The Problem

Richard needed to read 5 books for his summer reading assignment. It took him $4 \frac{5}{8}$ hours to read the first 2 books and $7 \frac{7}{8}$ hours to read the remaining 3 books. How long did it take Richard to read all 5 books?

Step 1: Convert Mixed Numbers to Improper Fractions

To solve this problem, we need to convert the mixed numbers to improper fractions. An improper fraction is a fraction where the numerator is greater than or equal to the denominator.

$4 \frac{5}{8}$ can be converted to an improper fraction as follows:
$4 \frac{5}{8} = \frac{(4 \times 8) + 5}{8} = \frac{32 + 5}{8} = \frac{37}{8}$
$7 \frac{7}{8}$ can be converted to an improper fraction as follows:
$7 \frac{7}{8} = \frac{(7 \times 8) + 7}{8} = \frac{56 + 7}{8} = \frac{63}{8}$

Step 2: Add the Fractions

Now that we have converted the mixed numbers to improper fractions, we can add them together to find the total time it took Richard to read the first 2 books and the remaining 3 books.

To add the fractions, we need to have the same denominator, which is 8 in this case.
$\frac{37}{8} + \frac{63}{8} = \frac{37 + 63}{8} = \frac{100}{8}$

Step 3: Simplify the Fraction

The fraction $\frac{100}{8}$ can be simplified by dividing both the numerator and the denominator by their greatest common divisor, which is 4.

$\frac{100}{8} = \frac{100 ÷ 4}{8 ÷ 4} = \frac{25}{2}$

Step 4: Convert the Fraction to a Mixed Number

To make it easier to understand, we can convert the improper fraction $\frac{25}{2}$ to a mixed number.

$\frac{25}{2} = 12 \frac{1}{2}$

Conclusion

In conclusion, it took Richard $12 \frac{1}{2}$ hours to read all 5 books. This problem required us to convert mixed numbers to improper fractions, add the fractions, simplify the fraction, and convert the fraction to a mixed number. By following these steps, we were able to solve the problem and find the total time it took Richard to read all 5 books.

Key Takeaways

Mixed numbers can be converted to improper fractions by multiplying the whole number part by the denominator and adding the numerator.
To add fractions, we need to have the same denominator.
Fractions can be simplified by dividing both the numerator and the denominator by their greatest common divisor.
Improper fractions can be converted to mixed numbers by dividing the numerator by the denominator and writing the remainder as the new numerator.

Real-World Applications

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

Time management: Calculating the time it takes to complete a task is essential in time management.
Finance: Calculating interest rates and investment returns requires the use of fractions and mixed numbers.
Science: Calculating the time it takes for a chemical reaction to occur or the time it takes for a physical system to reach equilibrium requires the use of fractions and mixed numbers.

Final Thoughts

Introduction

In our previous article, we explored a mathematical puzzle that involved calculating the time it took Richard to read 5 books for his summer reading assignment. We used the concept of mixed numbers and fractions to solve this problem. In this article, we will provide a Q&A section to help clarify any doubts and provide additional information on the topic.

Q: What is a mixed number?

A: A mixed number is a combination of a whole number and a fraction. It is written in the form of a whole number followed by a fraction, such as $4 \frac{5}{8}$ .

Q: How do I convert a mixed number to an improper fraction?

A: To convert a mixed number to an improper fraction, you need to multiply the whole number part by the denominator and add the numerator. Then, write the result as a fraction with the denominator as the original denominator. For example, $4 \frac{5}{8}$ can be converted to an improper fraction as follows:

4 \frac{5}{8} = \frac{(4 \times 8) + 5}{8} = \frac{32 + 5}{8} = \frac{37}{8}

Q: How do I add fractions with different denominators?

A: To add fractions with different denominators, you need to have the same denominator. You can do this by finding the least common multiple (LCM) of the two denominators and then converting both fractions to have the LCM as the denominator. For example, to add $\frac{1}{2}$ and $\frac{1}{3}$ , you need to find the LCM of 2 and 3, which is 6. Then, convert both fractions to have 6 as the denominator:

\frac{1}{2} = \frac{1 \times 3}{2 \times 3} = \frac{3}{6}

\frac{1}{3} = \frac{1 \times 2}{3 \times 2} = \frac{2}{6}

Now, you can add the fractions:

\frac{3}{6} + \frac{2}{6} = \frac{3 + 2}{6} = \frac{5}{6}

Q: How do I simplify a fraction?

A: To simplify a fraction, you need to divide both the numerator and the denominator by their greatest common divisor (GCD). For example, to simplify $\frac{12}{18}$ , you need to find the GCD of 12 and 18, which is 6. Then, divide both the numerator and the denominator by 6:

\frac{12}{18} = \frac{12 ÷ 6}{18 ÷ 6} = \frac{2}{3}

Q: How do I convert an improper fraction to a mixed number?

A: To convert an improper fraction to a mixed number, you need to divide the numerator by the denominator and write the remainder as the new numerator. For example, to convert $\frac{25}{2}$ to a mixed number, you need to divide 25 by 2:

\frac{25}{2} = 12 \frac{1}{2}

Q: What are some real-world applications of fractions and mixed numbers?

A: Fractions and mixed numbers have many real-world applications in various fields, such as:

Time management: Calculating the time it takes to complete a task is essential in time management.
Finance: Calculating interest rates and investment returns requires the use of fractions and mixed numbers.
Science: Calculating the time it takes for a chemical reaction to occur or the time it takes for a physical system to reach equilibrium requires the use of fractions and mixed numbers.

Conclusion

In conclusion, this Q&A section provides additional information and clarification on the topic of fractions and mixed numbers. We hope that this article has been helpful in understanding the concept of mixed numbers and fractions and how to apply them in real-world situations. If you have any further questions or concerns, please feel free to ask.