How Many 8 1/4 Inch Yarn Pieces Can Be Cut from a 96-inch Roll?

Suppose you have a roll of yarn that measures 96 inches. If you need to cut pieces that are 8 1/4 inches long, can you determine how many such pieces can be obtained? Let us break down the process step by step and provide a detailed explanation.

Step-by-step Calculation

First, let's convert the mixed fraction 8 1/4 inches into an improper fraction for easier calculation.

Conversion to Improper Fraction

8 1/4 inches can be written as:

8 1/4? (8 × 4 1) / 4? 32/4 1/4? 33/4 inches

Now, to find out how many 8 1/4 inch pieces can be cut from a 96-inch roll, we divide the total length by the length of each piece:

Number of pieces 96 / (33/4)? 96 × (4/33)? 384/33

Perform the division:

384 ÷ 33 ≈ 11.6363

Expressing the Result as a Mixed Number

To express 11.6363 as a mixed number, separate the whole part from the fractional part:

11 whole pieces with a remainder of 384 - (33 × 11) 384 - 363 21

This means:

384/33 11 and 21/33

Simplify the fraction 21/33 by dividing the numerator and denominator by 3:

21/33 7/11

Therefore, the final answer is:

11 7/11 pieces

So, you can cut 11 7/11 pieces of yarn from a 96-inch roll.

Further Breakdown and Verification

Let's verify this using another method to ensure accuracy:

Bivariate Solution

Let t represent the number of pieces of yarn required:

33t/4 96

Solve for t:

t 96 × 4 / 33 128 / 11 11 and 7/11 pieces

This confirms our earlier result, as 11 7/11 can be split into 11 full pieces and an additional fractional piece.

Half of the Answer Explained

If 11 7/11 pieces can be cut, half of this answer would be:

11 7/11 ÷ 2 11 (7/11 ÷ 2) 11 7/22 11 7/22 or 11.318

This aligns with the initial statement of 11 7/11 pieces being cut, with half of that being 64/11 or 5 9/11 pieces.

Conclusion

Based on the detailed calculations and the verification steps provided, we can conclude that:

You can cut 11 7/11 pieces of yarn from a 96-inch roll, with the piece being 8 1/4 inches long. Half of the answer, or 64/11 pieces, also holds true when considering the fractional part.

These calculations demonstrate the practical application of fraction arithmetic in real-world scenarios, such as dividing yarn.