Calculating the Total Amount of Thread Cut

Oct 13, 2025 by vinooalluri.com 105 views

The Great Thread Heist: Calculating the Change in Thread on a Spool

When it comes to mathematics, problems often involve real-world scenarios that require critical thinking and calculation. In this article, we will delve into a problem that involves seven students cutting thread from a spool for a school project. We will explore the concept of change in the amount of thread on the spool and calculate the number that represents this change.

Seven students each cut $$5 \frac{3}{4}$$ inches of thread from a spool for a school project. To find the change in the amount of thread on the spool, we need to calculate the total amount of thread cut by the students and then determine the difference between the initial and final amounts of thread on the spool.

Calculating the Total Amount of Thread Cut

To calculate the total amount of thread cut by the students, we need to multiply the amount of thread cut by each student by the number of students.

\text{Total amount of thread cut} = 7 \times 5 \frac{3}{4}

To multiply a mixed number by a whole number, we need to convert the mixed number to an improper fraction. We can do this by multiplying the whole number part by the denominator and then adding the numerator.

5 \frac{3}{4} = \frac{(5 \times 4) + 3}{4} = \frac{20 + 3}{4} = \frac{23}{4}

Now we can multiply the improper fraction by the whole number.

\text{Total amount of thread cut} = 7 \times \frac{23}{4} = \frac{7 \times 23}{4} = \frac{161}{4}

Converting the Improper Fraction to a Mixed Number

To make it easier to understand the total amount of thread cut, we can convert the improper fraction to a mixed number.

\frac{161}{4} = 40 \frac{1}{4}

Calculating the Change in the Amount of Thread on the Spool

To calculate the change in the amount of thread on the spool, we need to subtract the total amount of thread cut from the initial amount of thread on the spool. However, since we are not given the initial amount of thread on the spool, we can assume that the problem is asking for the change in the amount of thread on the spool in terms of the amount of thread cut.

The Change in the Amount of Thread on the Spool

Since the problem is asking for the change in the amount of thread on the spool in terms of the amount of thread cut, we can conclude that the change in the amount of thread on the spool is equal to the total amount of thread cut.

\text{Change in the amount of thread on the spool} = \text{Total amount of thread cut} = 40 \frac{1}{4}

In conclusion, the change in the amount of thread on the spool is represented by the number $$40 \frac{1}{4}$$ inches. This is the total amount of thread cut by the seven students, which is the change in the amount of thread on the spool.

The correct answer is A. $$-40 \frac{1}{4}$$ inches.
Frequently Asked Questions: The Great Thread Heist

In our previous article, we explored the concept of change in the amount of thread on a spool and calculated the number that represents this change. In this article, we will answer some frequently asked questions related to the problem.

Q: What is the initial amount of thread on the spool?

A: Unfortunately, the problem does not provide the initial amount of thread on the spool. However, we can assume that the problem is asking for the change in the amount of thread on the spool in terms of the amount of thread cut.

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 then add the numerator. For example, to convert $$5 \frac{3}{4}$$ to an improper fraction, you would multiply 5 by 4 and add 3, resulting in $$\frac{20 + 3}{4} = \frac{23}{4}$$.

Q: How do I multiply a mixed number by a whole number?

A: To multiply a mixed number by a whole number, you need to convert the mixed number to an improper fraction and then multiply the improper fraction by the whole number. For example, to multiply $$5 \frac{3}{4}$$ by 7, you would convert the mixed number to an improper fraction $$\frac{23}{4}$$ and then multiply it by 7, resulting in $$\frac{7 \times 23}{4} = \frac{161}{4}$$.

Q: What is the difference between the initial and final amounts of thread on the spool?

A: Since we are not given the initial amount of thread on the spool, we cannot calculate the difference between the initial and final amounts of thread on the spool. However, we can conclude that the change in the amount of thread on the spool is equal to the total amount of thread cut.

Q: Why is the change in the amount of thread on the spool negative?

A: The change in the amount of thread on the spool is negative because the students are cutting thread from the spool, resulting in a decrease in the amount of thread on the spool.

Q: What is the total amount of thread cut by the students?

A: The total amount of thread cut by the students is $$40 \frac{1}{4}$$ inches.

Q: What is the change in the amount of thread on the spool?

A: The change in the amount of thread on the spool is $$-40 \frac{1}{4}$$ inches.

In conclusion, we have answered some frequently asked questions related to the problem of the great thread heist. We hope that this article has provided you with a better understanding of the concept of change in the amount of thread on a spool and how to calculate it.

If you are interested in learning more about fractions and mixed numbers, we recommend checking out the following resources:

Khan Academy: Fractions and Mixed Numbers
Mathway: Fractions and Mixed Numbers
IXL: Fractions and Mixed Numbers

We hope that this article has been helpful in answering your questions and providing you with a better understanding of the concept of change in the amount of thread on a spool.