Dividing Ribbon Lengths: A Step-by-Step Guide

In many crafting projects, dividing a length of ribbon into equal pieces is a common task. This article will guide you through the process of determining the length of each piece of ribbon when you have a total length given in a mixed number. Let's explore a specific case where we have a total length of 10 1/3 yards, and the ribbon needs to be divided into 4 equal pieces. Follow the steps below to find the length of each piece.

Step 1: Convert the Mixed Number to an Improper Fraction

To work with the given length in a more manageable form, let's start by converting the mixed number 10 1/3 to an improper fraction.

Convert 10 1/3 to an Improper Fraction

First, multiply the whole number by the denominator of the fraction:

10 × 3 30

Next, add the numerator of the fraction to this product:

30 1 31

Finally, place the sum over the same denominator:

10 1/3 31/3

Step 2: Divide the Total Length by the Number of Pieces

The next step is to determine the length of each of the four equal pieces by dividing the total length by 4. This can be expressed mathematically as:

31/3 ÷ 4 31/3 × 1/4

Multiplying the fractions together gives us:

31/12

Step 3: Convert the Result to a Mixed Number

To make it easier to work with, especially for physical cutting purposes, it's useful to convert the improper fraction 31/12 back into a mixed number.

Perform the division:

31 ÷ 12 2 R 7

This means the whole number is 2 and the remainder over the same denominator is 7/12. Therefore, the length of each piece of ribbon is:

2 7/12 yards

Step 4: Convert the Result to Inches

If you need the length in inches, remember that:

1 yard 36 inches

Thus, we first convert the improper fraction to inches:

31/12 yd × 36 in/yd 1188 in/12 93 in

So, each piece of ribbon is 93 inches or 2 7/12 yards long.

Alternative Solution: Convert to Inches Directly

Alternatively, you can convert the total length of the ribbon directly to inches, and then divide by the number of pieces:

Convert 10 1/3 yards to Inches

First, convert 10 1/3 yards to an improper fraction:

10 × 3 30

30 1 31

10 1/3 31/3

Then convert yards to inches:

31/3 × 36 372 inches

Divide this total length by the number of pieces:

372 ÷ 4 93 inches

This confirms that each piece of ribbon is 93 inches or 7 feet 9 inches.

Conclusion

By following these detailed steps, you can easily determine the length of each piece of ribbon when given a total length in a mixed number. Whether you need to work with the length in yards or inches, this guide covers all the necessary calculations. The key steps involve converting mixed numbers to improper fractions, dividing by the number of pieces, and converting to inches if needed.