Question

find the missing values in the ratio table. then write the equivalent ratios in the order they appear in the table.
feet
inches
$\frac{1}{24}$
$square$
$\frac{1}{8}$
$square$
$\frac{1}{2}$
1
$square$
$\frac{1}{4}$

Explanation:

First, establish the conversion factor: 1 foot = 12 inches, so the ratio of inches to feet is $12:1$, or $\frac{\text{inches}}{\text{feet}} = 12$.

Step1: Find missing inch value

Given feet = $\frac{1}{24}$, calculate inches.
$\text{Inches} = \frac{1}{24} \times 12 = \frac{12}{24} = \frac{1}{2}$ (matches given, confirms ratio)

Step2: Find missing feet value

Given inches = 1, calculate feet.
$\text{Feet} = \frac{1}{12}$

Step3: Find missing inch value

Given feet = $\frac{1}{8}$, calculate inches.
$\text{Inches} = \frac{1}{8} \times 12 = \frac{12}{8} = \frac{3}{2}$

Step4: Find missing feet value

Given inches = $\frac{1}{4}$, calculate feet.
$\text{Feet} = \frac{1}{4} \div 12 = \frac{1}{4} \times \frac{1}{12} = \frac{1}{48}$

Step5: List equivalent ratios

Pair each inch value with its foot value.

1. $\frac{1}{2}:\frac{1}{24}$
2. $1:\frac{1}{12}$
3. $\frac{3}{2}:\frac{1}{8}$
4. $\frac{1}{4}:\frac{1}{48}$

Answer:

Missing values in the table (Feet column): $\frac{1}{12}$, $\frac{1}{48}$
Missing values in the table (Inches column): $\frac{3}{2}$

Equivalent ratios:
$\frac{1}{2}:\frac{1}{24}$
$1:\frac{1}{12}$
$\frac{3}{2}:\frac{1}{8}$
$\frac{1}{4}:\frac{1}{48}$