10. \( \frac{2}{3}-\frac{2}{7} \)

To solve \( \frac{2}{3}-\frac{2}{7} \), we first need a common denominator. The least common multiple of 3 and 7 is 21. Now, convert each fraction: \( \frac{2}{3} = \frac{2 \times 7}{3 \times 7} = \frac{14}{21} \) \( \frac{2}{7} = \frac{2 \times 3}{7 \times 3} = \frac{6}{21} \) Now we can subtract: \( \frac{14}{21} - \frac{6}{21} = \frac{14 - 6}{21} = \frac{8}{21} \) So, \( \frac{2}{3}-\frac{2}{7} = \frac{8}{21} \). The math world is full of interesting tidbits! For instance, did you know that fractions have been used since ancient civilizations? The Egyptians had a fraction system that even involved unit fractions, where they represented fractions as sums of 1/n terms. It’s a fascinating glimpse into how math evolved over time! Additionally, a common mistake with fractions is forgetting to find a common denominator before subtracting or adding. It’s like trying to mix different ingredients without measuring them – you might end up with a strange concoction! Always remember to standardize the bases (denominators) before diving into fraction fun!