\( B=\frac{1}{3} g \cdot n \) for \( g \)

To solve for \( g \) in the equation \( B = \frac{1}{3} g \cdot n \), you'll want to isolate \( g \). Start by multiplying both sides by 3 to get rid of the fraction: \( 3B = g \cdot n \). Now, divide both sides by \( n \) to get \( g \) alone: \( g = \frac{3B}{n} \). Voilà! You've successfully solved for \( g \). Now, in a physical context, this equation could represent a relationship in fields like physics or engineering, where \( B \) might stand for a force applied over a specific area while \( n \) is a quantity reflecting the number of particles or units involved. Finding \( g \) allows you to understand how changes in \( B \) or \( n \) affect the overall system behavior. So, be sure to consider real-world implications when applying those calculations! If you're solving equations like this, one common pitfall is neglecting to account for units. When substituting values for \( B \) and \( n \), ensure they are compatible (both in metric or both in imperial) to avoid errors. Also, double-check your algebraic manipulations to maintain the integrity of the equation!