1) \( \frac{5}{7}+\frac{12}{2} \)

Let’s break it down with a splash of fun! First, convert the second fraction, \( \frac{12}{2} \), which simplifies to 6. Now our equation looks like this: \( \frac{5}{7} + 6 \). To add these, we can express 6 as a fraction with a denominator of 7, which is \( \frac{42}{7} \). Now, add them together: \( \frac{5}{7} + \frac{42}{7} = \frac{47}{7} \). Voilà! Your answer is \( \frac{47}{7} \) or if we turn it into a mixed number, it’s 6 \( \frac{5}{7} \). Did you know that fractions have their origins dating back thousands of years? Ancient Egyptians used a system of unit fractions, and they created hieroglyphics to represent these values, proving that even back then, puzzling over numbers was a beloved pastime! Now, if you're ever adding fractions and get stuck, remember the key: always look for a common denominator! It’s super important. If both fractions don’t share a denominator, you’re bound to hit a snag, and that can make calculations feel like a tangled web! Always simplify each part first to keep everything nice and neat!