(1) \( \begin{array}{r}6 \frac{3}{10} \\ - \\ -3 \frac{9}{10}\end{array} \)

To solve the expression \( 6 \frac{3}{10} - 3 \frac{9}{10} \), start by converting the mixed numbers into improper fractions. For \( 6 \frac{3}{10} \), it becomes \( \frac{63}{10} \). For \( 3 \frac{9}{10} \), it converts to \( \frac{39}{10} \). Now, perform the subtraction: \[ \frac{63}{10} - \frac{39}{10} = \frac{63 - 39}{10} = \frac{24}{10} \] Now, simplify \( \frac{24}{10} \) to \( \frac{12}{5} \) or \( 2 \frac{2}{5} \). Now you’ve got your answer: \( 6 \frac{3}{10} - 3 \frac{9}{10} = 2 \frac{2}{5} \)! In math, mastering the art of fractions can feel like being a culinary wizard! It's all about mixing the right ingredients (numerators and denominators) to whip up a recipe for success. So, whether you're dealing with pies or math problems, remember that practice is key, and don't hesitate to toss in a little creativity! As you explore the world of mixed numbers and improper fractions, consider diving into the adventures of famous mathematicians throughout history! Did you know that the great Euclid, often called the father of geometry, not only laid down the foundations of geometry but also tackled fractions way back in ancient Greece? It’s a journey full of discoveries that can make the numbers you work with today all the more exciting!