Calculating the Total Length of Tape Used

Oct 13, 2025 by miodeya.com 69 views

Introduction

In this problem, we are given a 50-foot roll of packing tape and asked to find out how much tape is left after using two $8 \frac{5}{6}$ -foot lengths. To solve this problem, we need to subtract the total length of the tape used from the initial length of the roll.

Calculating the Total Length of Tape Used

First, let's convert the mixed number $8 \frac{5}{6}$ to an improper fraction. We can do this by multiplying the whole number part (8) by the denominator (6) and then adding the numerator (5). This gives us:

8 \frac{5}{6} = \frac{(8 \times 6) + 5}{6} = \frac{48 + 5}{6} = \frac{53}{6}

Now that we have the length of each piece of tape as an improper fraction, we can find the total length of tape used by adding the two lengths together:

\frac{53}{6} + \frac{53}{6} = \frac{106}{6}

Simplifying the Fraction

To simplify the fraction $\frac{106}{6}$ , we can divide both the numerator and the denominator by their greatest common divisor, which is 2. This gives us:

\frac{106}{6} = \frac{53}{3}

Calculating the Remaining Tape

Now that we have the total length of tape used as a simplified fraction, we can subtract this from the initial length of the roll to find the remaining tape:

50 - \frac{53}{3}

To subtract a fraction from a whole number, we need to convert the whole number to a fraction with the same denominator. In this case, we can convert 50 to a fraction with a denominator of 3:

50 = \frac{150}{3}

Now we can subtract the two fractions:

\frac{150}{3} - \frac{53}{3} = \frac{97}{3}

Converting the Fraction to a Mixed Number

To convert the improper fraction $\frac{97}{3}$ to a mixed number, we can divide the numerator (97) by the denominator (3). This gives us:

\frac{97}{3} = 32 \frac{1}{3}

Conclusion

In this problem, we were given a 50-foot roll of packing tape and asked to find out how much tape is left after using two $8 \frac{5}{6}$ -foot lengths. We converted the mixed number to an improper fraction, added the two lengths together, simplified the fraction, subtracted the total length of tape used from the initial length of the roll, and finally converted the improper fraction to a mixed number. The remaining tape is $32 \frac{1}{3}$ feet.

Calculating the Remaining Tape in Decimal Form

To convert the mixed number $32 \frac{1}{3}$ to a decimal, we can divide the numerator (1) by the denominator (3) and then add the result to the whole number part (32):

32 + \frac{1}{3} = 32 + 0.33 = 32.33

Conclusion

In this problem, we were given a 50-foot roll of packing tape and asked to find out how much tape is left after using two $8 \frac{5}{6}$ -foot lengths. We converted the mixed number to an improper fraction, added the two lengths together, simplified the fraction, subtracted the total length of tape used from the initial length of the roll, converted the improper fraction to a mixed number, and finally converted the mixed number to a decimal. The remaining tape is 32.33 feet.

Calculating the Percentage of Tape Used

To calculate the percentage of tape used, we can divide the total length of tape used by the initial length of the roll and then multiply by 100:

\frac{\frac{53}{3}}{50} \times 100 = \frac{53}{3} \times \frac{100}{50} = \frac{53}{3} \times 2 = \frac{106}{3}

To simplify the fraction $\frac{106}{3}$ , we can divide both the numerator and the denominator by their greatest common divisor, which is 1. This gives us:

\frac{106}{3} = 35.33

Conclusion

In this problem, we were given a 50-foot roll of packing tape and asked to find out how much tape is left after using two $8 \frac{5}{6}$ -foot lengths. We converted the mixed number to an improper fraction, added the two lengths together, simplified the fraction, subtracted the total length of tape used from the initial length of the roll, converted the improper fraction to a mixed number, converted the mixed number to a decimal, and finally calculated the percentage of tape used. The remaining tape is 32.33 feet, and the percentage of tape used is 35.33%.

Introduction

In the previous article, we calculated the remaining packing tape after using two $8 \frac{5}{6}$ -foot lengths from a 50-foot roll. In this article, we will answer some frequently asked questions related to the problem.

Q: What is the total length of tape used?

A: The total length of tape used is $\frac{53}{3}$ feet.

Q: How do I convert the mixed number $8 \frac{5}{6}$ to an improper fraction?

A: To convert the mixed number $8 \frac{5}{6}$ to an improper fraction, you can multiply the whole number part (8) by the denominator (6) and then add the numerator (5). This gives you:

8 \frac{5}{6} = \frac{(8 \times 6) + 5}{6} = \frac{48 + 5}{6} = \frac{53}{6}

Q: How do I add the two lengths of tape together?

A: To add the two lengths of tape together, you can add the two improper fractions:

\frac{53}{6} + \frac{53}{6} = \frac{106}{6}

Q: How do I simplify the fraction $\frac{106}{6}$ ?

A: To simplify the fraction $\frac{106}{6}$ , you can divide both the numerator and the denominator by their greatest common divisor, which is 2. This gives you:

\frac{106}{6} = \frac{53}{3}

Q: How do I subtract the total length of tape used from the initial length of the roll?

A: To subtract the total length of tape used from the initial length of the roll, you can convert the whole number to a fraction with the same denominator as the fraction representing the total length of tape used. In this case, you can convert 50 to a fraction with a denominator of 3:

50 = \frac{150}{3}

Now you can subtract the two fractions:

\frac{150}{3} - \frac{53}{3} = \frac{97}{3}

Q: How do I convert the improper fraction $\frac{97}{3}$ to a mixed number?

A: To convert the improper fraction $\frac{97}{3}$ to a mixed number, you can divide the numerator (97) by the denominator (3). This gives you:

\frac{97}{3} = 32 \frac{1}{3}

Q: How do I convert the mixed number $32 \frac{1}{3}$ to a decimal?

A: To convert the mixed number $32 \frac{1}{3}$ to a decimal, you can divide the numerator (1) by the denominator (3) and then add the result to the whole number part (32):

32 + \frac{1}{3} = 32 + 0.33 = 32.33

Q: How do I calculate the percentage of tape used?

A: To calculate the percentage of tape used, you can divide the total length of tape used by the initial length of the roll and then multiply by 100:

\frac{\frac{53}{3}}{50} \times 100 = \frac{53}{3} \times \frac{100}{50} = \frac{53}{3} \times 2 = \frac{106}{3}

To simplify the fraction $\frac{106}{3}$ , you can divide both the numerator and the denominator by their greatest common divisor, which is 1. This gives you:

\frac{106}{3} = 35.33

Conclusion

In this article, we answered some frequently asked questions related to the problem of calculating the remaining packing tape after using two $8 \frac{5}{6}$ -foot lengths from a 50-foot roll. We hope that this Q&A article has helped to clarify any confusion and provided a better understanding of the problem.