Question

find the missing values in the ratio table. then write the equivalent ratios in the order they appear in the table.
flour (cups) oats (cups)
\frac{3}{4} \frac{1}{3}
\square \frac{2}{3}
3 \square
1 \square

Explanation:

Step1: Find the base ratio

First, identify the complete pair: Flour = $\frac{3}{4}$ cups, Oats = $\frac{1}{3}$ cups. The ratio of Flour to Oats is $\frac{\frac{3}{4}}{\frac{1}{3}} = \frac{3}{4} \times 3 = \frac{9}{4}$. This means Flour = $\frac{9}{4} \times$ Oats, or Oats = $\frac{4}{9} \times$ Flour.

Step2: Find missing Flour (Oats = $\frac{2}{3}$)

Use Flour = $\frac{9}{4} \times$ Oats
$\text{Flour} = \frac{9}{4} \times \frac{2}{3} = \frac{18}{12} = \frac{3}{2}$

Step3: Find missing Oats (Flour = 3)

Use Oats = $\frac{4}{9} \times$ Flour
$\text{Oats} = \frac{4}{9} \times 3 = \frac{12}{9} = \frac{4}{3}$

Step4: Find missing Oats (Flour = 1)

Use Oats = $\frac{4}{9} \times$ Flour
$\text{Oats} = \frac{4}{9} \times 1 = \frac{4}{9}$

Step5: List equivalent ratios

Order is Flour : Oats for each row:

1. $\frac{3}{4} : \frac{1}{3}$
2. $\frac{3}{2} : \frac{2}{3}$
3. $3 : \frac{4}{3}$
4. $1 : \frac{4}{9}$

Answer:

Completed Table Values:

Flour (cups): $\frac{3}{2}$
Oats (cups): $\frac{4}{3}$, $\frac{4}{9}$

Equivalent Ratios:

$\frac{3}{4}:\frac{1}{3}$
$\frac{3}{2}:\frac{2}{3}$
$3:\frac{4}{3}$
$1:\frac{4}{9}$