Question

1. find the missing values in the ratio table. then write the equivalent ratios.

calories	miles
$square$	$\frac{2}{3}$
10	$\frac{1}{12}$
90	$\frac{3}{4}$

Explanation:

Step1: Find calories per mile

First, use the known pair: 20 calories for $\frac{1}{6}$ mile. Calculate calories per mile:
$$20 \div \frac{1}{6} = 20 \times 6 = 120$$
This means 1 mile burns 120 calories.

Step2: Calculate missing calories

For $\frac{2}{3}$ mile, multiply miles by calories per mile:
$$120 \times \frac{2}{3} = 80$$

Step3: Verify equivalent ratios

Check all pairs to confirm they are equivalent:

• $20:\frac{1}{6} = 20 \times 6 : 1 = 120:1$
• $80:\frac{2}{3} = 80 \times \frac{3}{2} : 1 = 120:1$
• $10:\frac{1}{12} = 10 \times 12 : 1 = 120:1$
• $90:\frac{3}{4} = 90 \times \frac{4}{3} : 1 = 120:1$

Answer:

Missing value: 80
Equivalent ratios: $20:\frac{1}{6}$, $80:\frac{2}{3}$, $10:\frac{1}{12}$, $90:\frac{3}{4}$ (all simplify to $120:1$)