Question

mayumi rides her bike around a park. each lap around the park is \\(\frac{2}{3}\\) mi. mayumi rides a total of 3 mi.

Explanation:

Step1: Define variables

Let $n$ = number of laps.

Step2: Set up equation

Each lap is $\frac{2}{3}$ mi, total is 3 mi:
$$\frac{2}{3}n = 3$$

Step3: Solve for $n$

Multiply both sides by $\frac{3}{2}$:
$$n = 3 \times \frac{3}{2} = \frac{9}{2} = 4.5$$

Step4: Locate on number line

The number line has 4 intervals between whole numbers, so each mark is $\frac{1}{4}$? No, correct: to plot 4.5, it is halfway between 4 and 5, but first confirm the value. Wait, recheck: total distance 3 mi, lap distance $\frac{2}{3}$ mi. Number of laps is $3 \div \frac{2}{3} = \frac{9}{2} = 4.5$. On the given number line, each whole number (0,1,2,3,4) is split into 4 equal parts, so each part is $\frac{1}{4}$. 4.5 is equivalent to $4 + \frac{2}{4}$, so it is the second mark after 4, halfway between 4 and 5.

Answer:

Mayumi rides 4.5 laps, which is located halfway between 4 and 5 on the number line (the second tick mark after 4).