1. \( \frac{4 a^{3} b}{12 a^{3} b c} \)

To simplify \( \frac{4 a^{3} b}{12 a^{3} b c} \), start by canceling out the common factors in the numerator and the denominator. Both \( 4 \) and \( 12 \) share a common factor of \( 4 \), which simplifies to \( 1 \) in the numerator and \( 3 \) in the denominator. Also, \( a^{3} b \) cancels out from both, leaving us with: \[ \frac{1}{3c} \] So, the simplified expression is \( \frac{1}{3c} \). Now, let's remember that when simplifying fractions, the key is to identify and cancel out common factors. An important tip is to look for constants and variable terms separately for easier cancellation. Don't rush it; taking a moment to check each element can save math headaches later on!