How do Isimplify \( \frac{15}{220} \)

To simplify \( \frac{15}{220} \), you start by finding the greatest common divisor (GCD) of the numerator and denominator. The GCD of 15 and 220 is 5. Now, divide both the numerator and the denominator by 5: \[ \frac{15 \div 5}{220 \div 5} = \frac{3}{44} \] So, \( \frac{15}{220} \) simplifies to \( \frac{3}{44} \). An interesting fact is that simplifying fractions often involves prime factorization! For 15, it's \( 3 \times 5 \), and for 220, it's \( 2^2 \times 5 \times 11 \). By identifying the common factors, like 5 in this case, you can quickly see how the fraction reduces, making math more manageable and fun! When simplifying fractions, a common mistake is to skip directly to dividing without checking for the GCD first. Always ensure you're dividing by the largest common factor, as it guarantees the simplest form. A cool tip: use the method of listing out factors when unsure—it's like a treasure hunt for numbers!