Question

find the missing values in the ratio table. then write the equivalent ratios in the order they appear in the table.
pages $\frac{1}{4}$ $\frac{3}{4}$ $square$ 5
minutes $\frac{1}{2}$ $square$ 3 $square$
$square:square$
$square:square$
$square:square$
$square:square$

Explanation:

Step1: Find the ratio constant

First, calculate the ratio of pages to minutes using the first pair:
$\text{Ratio} = \frac{\frac{1}{4}}{\frac{1}{2}} = \frac{1}{4} \times \frac{2}{1} = \frac{1}{2}$
This means pages = $\frac{1}{2} \times$ minutes, or minutes = $2 \times$ pages.

Step2: Find missing minutes (second column)

Use minutes = $2 \times$ pages. Pages = $\frac{3}{4}$
$\text{Minutes} = 2 \times \frac{3}{4} = \frac{6}{4} = \frac{3}{2}$

Step3: Find missing pages (third column)

Use pages = $\frac{1}{2} \times$ minutes. Minutes = 3
$\text{Pages} = \frac{1}{2} \times 3 = \frac{3}{2}$

Step4: Find missing minutes (fourth column)

Use minutes = $2 \times$ pages. Pages = 5
$\text{Minutes} = 2 \times 5 = 10$

Step5: List equivalent ratios

Write each pages:minutes pair in order.

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

Answer:

Missing table values (pages, minutes): $\frac{3}{2}$, $\frac{3}{2}$, $10$
Equivalent ratios:
$\frac{1}{4}:\frac{1}{2}$
$\frac{3}{4}:\frac{3}{2}$
$\frac{3}{2}:3$
$5:10$