To determine how much ribbon the dressmaker still needs, we'll subtract the length of ribbon she has from the total length she requires.

The dressmaker needs:

• $21 \frac{7}{8}$ meters of ribbon.

She has:

• $\frac{5}{8}$ meters of ribbon.

Step 1: Convert the mixed number to an improper fraction

First, convert $21 \frac{7}{8}$ to an improper fraction:

$21 \frac{7}{8} = \frac{21 \times 8 + 7}{8} = \frac{168 + 7}{8} = \frac{175}{8}$

Step 2: Subtract the fractions

Now, subtract the length of ribbon she has from the length she needs:

$\frac{175}{8} - \frac{5}{8} = \frac{175 - 5}{8} = \frac{170}{8}$

Step 3: Simplify the fraction

Simplify $\frac{170}{8}$:

$\frac{170}{8} = \frac{85}{4} = 21 \frac{1}{4} \text{ meters}$

Conclusion

The dressmaker still needs 21¼ meters of ribbon.

Why? The subtraction shows how much more ribbon is required to meet the total needed length. Simplifying the improper fraction helps express this in a more understandable form (mixed number), which in this case is 21¼ meters.

Would you like further details, or do you have any more questions?

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Here are five related questions you might find interesting:

1. If the dressmaker finds another piece of ribbon that is 10 meters long, how much more will she need?
2. How much ribbon does she need if she uses 5 meters from her available supply?
3. If she needs a total of 25 meters instead of 21⅞ meters, how much more does she need?
4. What percentage of the total required ribbon does she already have?
5. If she can only purchase ribbon in whole meters, how many meters should she buy to meet her needs?

Tip: When working with fractions, converting mixed numbers to improper fractions can make operations like subtraction or addition more straightforward.