Question

find the missing values in the ratio table. then write the equivalent ratios in the order they appear in the table.
meters 8 4 □ □
minutes \\(\frac{1}{3}\\) □ \\(\frac{1}{4}\\) \\(\frac{5}{12}\\)
□:□

Explanation:

Step1: Find the constant ratio

First, calculate the ratio of meters to minutes using the first complete pair.
$\text{Ratio} = \frac{8}{\frac{1}{3}} = 8 \times 3 = 24$
This means the speed is 24 meters per minute, so $\text{Meters} = 24 \times \text{Minutes}$ and $\text{Minutes} = \frac{\text{Meters}}{24}$.

Step2: Find missing minutes (2nd row)

Use the ratio to find minutes for 4 meters.
$\text{Minutes} = \frac{4}{24} = \frac{1}{6}$

Step3: Find missing meters (3rd row)

Use the ratio to find meters for $\frac{1}{4}$ minutes.
$\text{Meters} = 24 \times \frac{1}{4} = 6$

Step4: Find missing meters (4th row)

Use the ratio to find meters for $\frac{5}{12}$ minutes.
$\text{Meters} = 24 \times \frac{5}{12} = 10$

Step5: List equivalent ratios

Write each pair as a ratio in meters:minutes order.

1. $8:\frac{1}{3}$
2. $4:\frac{1}{6}$
3. $6:\frac{1}{4}$
4. $10:\frac{5}{12}$

Answer:

Missing values: $\frac{1}{6}$ (minutes, 2nd column), $6$ (meters, 3rd column), $10$ (meters, 4th column)
Equivalent ratios:
$8:\frac{1}{3}$, $4:\frac{1}{6}$, $6:\frac{1}{4}$, $10:\frac{5}{12}$