David Worked In The Library On Friday And Saturday For A Total Of $7 \frac{3}{4}$ Hours. If He Worked $4 \frac{1}{4}$ Hours On Friday, How Many Hours Did He Work On Saturday?

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Introduction

Time problems can be challenging, especially when dealing with mixed numbers and fractions. In this article, we will explore how to solve a time problem involving a mixed number and a fraction. We will use the example of David working in the library on Friday and Saturday for a total of $7 \frac{3}{4}$ hours. If he worked $4 \frac{1}{4}$ hours on Friday, we will find out how many hours he worked on Saturday.

Understanding the Problem

David worked in the library for a total of $7 \frac{3}{4}$ hours on Friday and Saturday. To find out how many hours he worked on Saturday, we need to subtract the number of hours he worked on Friday from the total number of hours.

Converting Mixed Numbers to Improper Fractions

Before we can subtract the number of hours, 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.

  • 7 \frac{3}{4}$ can be converted to an improper fraction by multiplying the whole number by the denominator and adding the numerator: $7 \times 4 + 3 = 31

  • 4 \frac{1}{4}$ can be converted to an improper fraction by multiplying the whole number by the denominator and adding the numerator: $4 \times 4 + 1 = 17

Converting Improper Fractions to Mixed Numbers

Now that we have the improper fractions, we can convert them back to mixed numbers to make it easier to subtract the number of hours.

  • \frac{31}{4}$ can be converted to a mixed number by dividing the numerator by the denominator: $31 ÷ 4 = 7$ with a remainder of $3$, so the mixed number is $7 \frac{3}{4}

  • \frac{17}{4}$ can be converted to a mixed number by dividing the numerator by the denominator: $17 ÷ 4 = 4$ with a remainder of $1$, so the mixed number is $4 \frac{1}{4}

Subtracting the Number of Hours

Now that we have the mixed numbers, we can subtract the number of hours David worked on Friday from the total number of hours.

734−4147 \frac{3}{4} - 4 \frac{1}{4}

To subtract the mixed numbers, we need to subtract the whole numbers and the fractions separately.

  • Subtracting the whole numbers: $7 - 4 = 3$
  • Subtracting the fractions: $\frac{3}{4} - \frac{1}{4} = \frac{2}{4} = \frac{1}{2}$

Finding the Number of Hours Worked on Saturday

Now that we have the result of the subtraction, we can find the number of hours David worked on Saturday.

3 \frac{1}{2}$ hours Therefore, David worked $3 \frac{1}{2}$ hours on Saturday. **Conclusion** -------------- In this article, we solved a time problem involving a mixed number and a fraction. We converted the mixed numbers to improper fractions, subtracted the number of hours, and found the number of hours David worked on Saturday. This problem demonstrates the importance of understanding fractions and mixed numbers in solving time problems. **Real-World Applications** --------------------------- Time problems like this one are common in real-world applications, such as: * Scheduling: Finding the number of hours worked on a particular day to schedule tasks and appointments. * Budgeting: Calculating the number of hours worked to determine pay and benefits. * Project Management: Estimating the number of hours required to complete a project. **Tips and Tricks** ------------------- When solving time problems involving mixed numbers and fractions, remember to: * Convert mixed numbers to improper fractions before subtracting or adding. * Subtract or add the whole numbers and fractions separately. * Simplify the result to find the final answer. By following these tips and tricks, you can become proficient in solving time problems involving mixed numbers and fractions. **Practice Problems** ------------------- Try solving the following practice problems to reinforce your understanding of time problems involving mixed numbers and fractions: 1. A person worked $5 \frac{2}{3}$ hours on Monday and $3 \frac{1}{3}$ hours on Tuesday. How many hours did they work in total? 2. A group of friends worked $2 \frac{1}{2}$ hours on a project on Friday and $1 \frac{1}{2}$ hours on Saturday. How many hours did they work in total? 3. A person worked $6 \frac{3}{4}$ hours on a project on Monday and $4 \frac{1}{4}$ hours on Tuesday. How many hours did they work in total? **Answer Key** -------------- 1. $5 \frac{2}{3} + 3 \frac{1}{3} = 8 \frac{4}{3}$ hours 2. $2 \frac{1}{2} + 1 \frac{1}{2} = 4$ hours 3. $6 \frac{3}{4} - 4 \frac{1}{4} = 2 \frac{2}{4} = 2 \frac{1}{2}$ hours<br/> **Frequently Asked Questions: Time Problems Involving Mixed Numbers and Fractions** ==================================================================================== **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 $a \frac{b}{c}$, where $a$ is the whole number, $b$ is the numerator, and $c$ is the denominator. **Q: How do I convert a mixed number to an improper fraction?** --------------------------------------------------------- A: To convert a mixed number to an improper fraction, multiply the whole number by the denominator and add the numerator. Then, write the result as a fraction with the denominator. * Example: $7 \frac{3}{4}$ can be converted to an improper fraction by multiplying the whole number by the denominator and adding the numerator: $7 \times 4 + 3 = 31

  • So, $7 \frac{3}{4} = \frac{31}{4}$

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

A: To convert an improper fraction to a mixed number, divide the numerator by the denominator and write the result as a mixed number.

  • Example: $\frac31}{4}$ can be converted to a mixed number by dividing the numerator by the denominator $31 ÷ 4 = 7$ with a remainder of $3$, so the mixed number is $7 \frac{3{4}$

Q: How do I subtract mixed numbers?

A: To subtract mixed numbers, subtract the whole numbers and the fractions separately.

  • Example: $7 \frac{3}{4} - 4 \frac{1}{4}$
  • Subtract the whole numbers: $7 - 4 = 3$
  • Subtract the fractions: $\frac{3}{4} - \frac{1}{4} = \frac{2}{4} = \frac{1}{2}$
  • So, $7 \frac{3}{4} - 4 \frac{1}{4} = 3 \frac{1}{2}$

Q: How do I add mixed numbers?

A: To add mixed numbers, add the whole numbers and the fractions separately.

  • Example: $7 \frac{3}{4} + 4 \frac{1}{4}$
  • Add the whole numbers: $7 + 4 = 11$
  • Add the fractions: $\frac{3}{4} + \frac{1}{4} = \frac{4}{4} = 1$
  • So, $7 \frac{3}{4} + 4 \frac{1}{4} = 11 \frac{1}{4}$

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

A: Time problems involving mixed numbers and fractions have many real-world applications, such as:

  • Scheduling: Finding the number of hours worked on a particular day to schedule tasks and appointments.
  • Budgeting: Calculating the number of hours worked to determine pay and benefits.
  • Project Management: Estimating the number of hours required to complete a project.

Q: How can I practice solving time problems involving mixed numbers and fractions?

A: You can practice solving time problems involving mixed numbers and fractions by:

  • Working on practice problems, such as the ones provided in this article.
  • Using online resources, such as math websites and apps.
  • Asking a teacher or tutor for help.

Q: What are some tips and tricks for solving time problems involving mixed numbers and fractions?

A: Here are some tips and tricks for solving time problems involving mixed numbers and fractions:

  • Convert mixed numbers to improper fractions before subtracting or adding.
  • Subtract or add the whole numbers and fractions separately.
  • Simplify the result to find the final answer.

By following these tips and tricks, you can become proficient in solving time problems involving mixed numbers and fractions.