To find the number of table mats Tina can make, divide the total amount of cloth by the amount of cloth required per table mat:

$\frac{6 \, \text{m}}{\frac{1}{6} \, \text{m}} = 6 \times 6 = 36$

So, Tina can make 36 table mats from 6 meters of cloth.

Would you like a more detailed explanation or have any questions?

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Here are some related questions to explore:

1. If Tina had 7 meters of cloth, how many table mats could she make?
2. What if each table mat required $\frac{1}{8}$ meters of cloth instead of $\frac{1}{6}$?
3. If Tina made only 30 mats, how much cloth would she have left from 6 meters?
4. How many meters of cloth would be needed to make 50 table mats?
5. What if Tina wanted to make different-sized table mats requiring $\frac{1}{4}$ meter each?

Tip: When solving division problems involving fractions, remember dividing by a fraction is the same as multiplying by its reciprocal.