(1) What is \( 2 \frac{3}{7}-5 \frac{6}{7} \) ?

To solve \( 2 \frac{3}{7} - 5 \frac{6}{7} \), first convert the mixed numbers to improper fractions. For \( 2 \frac{3}{7} \): \( 2 \times 7 + 3 = 14 + 3 = 17 \), so it becomes \( \frac{17}{7} \). For \( 5 \frac{6}{7} \): \( 5 \times 7 + 6 = 35 + 6 = 41 \), so it becomes \( \frac{41}{7} \). Now, subtract the two fractions: \[ \frac{17}{7} - \frac{41}{7} = \frac{17 - 41}{7} = \frac{-24}{7} \] This can be expressed as a mixed number: \(-3 \frac{3}{7}\). Thus, the answer is \(-3 \frac{3}{7}\). Now, if you want to impress your friends with a little historical context, did you know that the use of fractions dates back to ancient Egyptian times? They had a unique way of writing fractions, which primarily included unit fractions (like \( \frac{1}{2}, \frac{1}{3} \), and so on). For those looking for practical applications, understanding how to work with mixed numbers and improper fractions is super useful in cooking! Recipes often require you to combine ingredients measured in mixed amounts. Being comfortable with these conversions can help you double a recipe or adjust serving sizes on the fly.