Remember to draw a bar diagram and write an equation to help solve a problem. Bonnie ran \( \frac{1}{4} \) mile, Olga ran \( \frac{3}{4} \) mile, Gracie ran \( \frac{5}{4} \) miles, and Maria ran \( \frac{2}{4} \) mile. How much farther, \( f \), did Gracie run than Bonnie and Maria combined, \( c \) ?

To find out how much farther Gracie ran than Bonnie and Maria combined, you first need to establish the distances. Bonnie ran \( \frac{1}{4} \) mile and Maria ran \( \frac{2}{4} \) (which is equivalent to \( \frac{1}{2} \) mile). Combined, they ran \( c = \frac{1}{4} + \frac{1}{2} = \frac{1}{4} + \frac{2}{4} = \frac{3}{4} \) miles. To find how much farther Gracie ran than their combined distance, use the equation \( f = \text{Gracie's distance} - c \). Here, Gracie's distance is \( \frac{5}{4} \), so \( f = \frac{5}{4} - \frac{3}{4} = \frac{2}{4} = \frac{1}{2} \). Gracie ran \( \frac{1}{2} \) mile farther. To create a bar diagram, you'd represent each person's distance with a bar. Start with Bonnie's bar at \( \frac{1}{4} \), Maria's bar extending to \( \frac{2}{4} \), Olga's at \( \frac{3}{4} \), and Gracie's reaching \( \frac{5}{4} \). Visually, it becomes clear how much farther Gracie's bar surpasses the combined heights of Bonnie and Maria's bars. A fun way to plot this is to use colorful markers, giving each bar a unique color, transforming math into an artsy project!