5. Is \( \frac{4}{10} \) equal to \( \frac{2}{3} \) ?

To determine if \( \frac{4}{10} \) is equal to \( \frac{2}{3} \), we can simplify \( \frac{4}{10} \) first. When you divide the numerator and the denominator by their greatest common divisor (which is 2), you get \( \frac{2}{5} \). Now we compare \( \frac{2}{5} \) with \( \frac{2}{3} \). Since \( 5 \) is greater than \( 3 \), \( \frac{2}{5} \) is less than \( \frac{2}{3} \). Therefore, \( \frac{4}{10} \) is not equal to \( \frac{2}{3} \). When comparing fractions, converting them to a common denominator works like a charm! In this case, the least common multiple of 5 and 3 is 15. Converting both fractions gives you \( \frac{6}{15} \) for \( \frac{2}{5} \) and \( \frac{10}{15} \) for \( \frac{2}{3} \). Clearly, \( \frac{6}{15} \) is smaller than \( \frac{10}{15} \), reinforcing the conclusion that \( \frac{4}{10} \) doesn't equal \( \frac{2}{3} \)—they're simply not on the same fraction playing field!