Arliss Has Two Pieces Of Carpet Runner. One Is $2 \frac{1}{3}$ Yards Long, And The Other Is $3 \frac{1}{3}$ Yards Long. She Needs 10 Yards Of Carpet Runner Altogether. How Much More Does She Need To Buy?1. Write And Solve The

Arliss's Carpet Runner Conundrum: A Math Problem

In this article, we will delve into a real-world math problem involving carpet runners. Arliss, a homeowner, has two pieces of carpet runner that she needs to use for her home. One piece is $2 \frac{1}{3}$ yards long, and the other is $3 \frac{1}{3}$ yards long. However, she needs a total of 10 yards of carpet runner to complete her project. The question is, how much more does she need to buy?

To solve this problem, we need to first understand the measurements involved. Arliss has two pieces of carpet runner, one measuring $2 \frac{1}{3}$ yards and the other measuring $3 \frac{1}{3}$ yards. We need to find out how much carpet runner she already has and how much more she needs to buy.

Converting Mixed Numbers to Improper Fractions

Before we can add the two pieces of carpet runner together, we need to convert the mixed numbers to improper fractions. To do this, we multiply the whole number part by the denominator and add the numerator.

• $2 \frac{1}{3} = \frac{(2 \times 3) + 1}{3} = \frac{6 + 1}{3} = \frac{7}{3}$
• $3 \frac{1}{3} = \frac{(3 \times 3) + 1}{3} = \frac{9 + 1}{3} = \frac{10}{3}$

Adding the Two Pieces of Carpet Runner

Now that we have converted the mixed numbers to improper fractions, we can add the two pieces of carpet runner together.

• $\frac{7}{3} + \frac{10}{3} = \frac{17}{3}$

Converting the Sum Back to a Mixed Number

To make it easier to understand, we can convert the sum back to a mixed number.

• $\frac{17}{3} = 5 \frac{2}{3}$

Finding Out How Much More Arliss Needs to Buy

Now that we know Arliss has $5 \frac{2}{3}$ yards of carpet runner, we can find out how much more she needs to buy. Since she needs a total of 10 yards, we can subtract the amount she already has from the total amount needed.

• $10 - 5 \frac{2}{3} = 4 \frac{1}{3}$

In conclusion, Arliss needs to buy $4 \frac{1}{3}$ yards of carpet runner to complete her project. This problem required us to convert mixed numbers to improper fractions, add the two pieces of carpet runner together, and then convert the sum back to a mixed number. By following these steps, we were able to find out how much more Arliss needs to buy.

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

• Home improvement: When planning a home renovation project, it's essential to calculate the amount of materials needed to avoid running out or having too much waste.
• Construction: In construction, accurate measurements are crucial to ensure that the project is completed on time and within budget.
• Manufacturing: In manufacturing, accurate measurements are necessary to produce products that meet the required specifications.

Here are some tips and tricks to help you solve similar problems:

• Use a calculator: When working with fractions, it's often easier to use a calculator to simplify the calculations.
• Convert mixed numbers to improper fractions: Converting mixed numbers to improper fractions can make it easier to add and subtract fractions.
• Check your work: Always check your work to ensure that you have the correct answer.

Here are some common mistakes to avoid when solving similar problems:

• Not converting mixed numbers to improper fractions: Failing to convert mixed numbers to improper fractions can lead to incorrect answers.
• Not checking your work: Not checking your work can result in incorrect answers.
• Not using a calculator: Not using a calculator can make calculations more time-consuming and prone to errors.

In conclusion, solving math problems like Arliss's carpet runner conundrum requires attention to detail, accuracy, and a clear understanding of the concepts involved. By following the steps outlined in this article, you can solve similar problems and apply the concepts to real-world situations.
Arliss's Carpet Runner Conundrum: A Math Problem Q&A

In our previous article, we solved a real-world math problem involving carpet runners. Arliss, a homeowner, had two pieces of carpet runner that she needed to use for her home. One piece was $2 \frac{1}{3}$ yards long, and the other was $3 \frac{1}{3}$ yards long. However, she needed a total of 10 yards of carpet runner to complete her project. The question was, how much more does she need to buy?

Q: What is the first step in solving this problem?

A: The first step is to convert the mixed numbers to improper fractions. This will make it easier to add the two pieces of carpet runner together.

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

A: To convert a mixed number to an improper fraction, you multiply the whole number part by the denominator and add the numerator. For example, $2 \frac{1}{3} = \frac{(2 \times 3) + 1}{3} = \frac{6 + 1}{3} = \frac{7}{3}$.

Q: What is the sum of the two pieces of carpet runner?

A: The sum of the two pieces of carpet runner is $\frac{7}{3} + \frac{10}{3} = \frac{17}{3}$.

Q: How do I convert the sum back to a mixed number?

A: To convert the sum back to a mixed number, you divide the numerator by the denominator and write the remainder as the new numerator. For example, $\frac{17}{3} = 5 \frac{2}{3}$.

Q: How much more carpet runner does Arliss need to buy?

A: Arliss needs to buy $4 \frac{1}{3}$ yards of carpet runner to complete her project.

Q: What are some real-world applications of this problem?

A: This problem has real-world applications in various fields, such as home improvement, construction, and manufacturing. Accurate measurements are crucial in these fields to ensure that projects are completed on time and within budget.

Q: What are some tips and tricks for solving similar problems?

A: Here are some tips and tricks to help you solve similar problems:

• Use a calculator to simplify calculations.
• Convert mixed numbers to improper fractions.
• Check your work to ensure that you have the correct answer.

Q: What are some common mistakes to avoid when solving similar problems?

A: Here are some common mistakes to avoid when solving similar problems:

• Not converting mixed numbers to improper fractions.
• Not checking your work.
• Not using a calculator.

In conclusion, solving math problems like Arliss's carpet runner conundrum requires attention to detail, accuracy, and a clear understanding of the concepts involved. By following the steps outlined in this article and using the tips and tricks provided, you can solve similar problems and apply the concepts to real-world situations.

Q: What is the difference between a mixed number and an improper fraction?

A: A mixed number is a combination of a whole number and a fraction, while an improper fraction is a fraction with a numerator that is greater than or equal to the denominator.

Q: How do I add fractions with different denominators?

A: To add fractions with different denominators, you need to find the least common multiple (LCM) of the denominators and then convert each fraction to have the LCM as the denominator.

Q: What is the least common multiple (LCM) of two numbers?

A: The LCM of two numbers is the smallest number that is a multiple of both numbers.

Q: How do I convert a fraction to a decimal?

A: To convert a fraction to a decimal, you divide the numerator by the denominator.

In conclusion, this Q&A session has provided you with a better understanding of the concepts involved in solving math problems like Arliss's carpet runner conundrum. By following the steps outlined in this article and using the tips and tricks provided, you can solve similar problems and apply the concepts to real-world situations.