Question

find the missing values in the ratio table. then write the equivalent ratios in the order they appear in the table.
meters \tminutes
8 \t\t\frac{1}{3}
4 \t\t\square
\square \t\frac{1}{4}
\square \t\frac{2}{15}

Explanation:

Step1: Find the rate (meters per minute)

From the first row, 8 meters in $\frac{1}{3}$ minutes. The rate $r$ is meters divided by minutes: $r = \frac{8}{\frac{1}{3}} = 8\times3 = 24$ meters per minute.

Step2: Find minutes for 4 meters

Let $t$ be the time in minutes. Using $r = \frac{\text{meters}}{\text{minutes}}$, so $t = \frac{\text{meters}}{r}$. For 4 meters, $t = \frac{4}{24} = \frac{1}{6}$ minutes.

Step3: Find meters for $\frac{1}{4}$ minutes

Using $\text{meters} = r\times\text{minutes}$, so $\text{meters} = 24\times\frac{1}{4} = 6$ meters.

Step4: Find meters for $\frac{5}{12}$ minutes

Using $\text{meters} = r\times\text{minutes}$, so $\text{meters} = 24\times\frac{5}{12} = 10$ meters.

Answer:

The missing values (from top to bottom in the "Minutes" and "Meters" columns) are $\frac{1}{6}$, 6, 10. The equivalent ratios are $8:\frac{1}{3}$, $4:\frac{1}{6}$, $6:\frac{1}{4}$, $10:\frac{5}{12}$.