Question

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

Explanation:

Step1: Find the ratio constant

First, calculate the ratio of oats to flour using the first pair:
$\text{Ratio } r = \frac{\frac{1}{3}}{\frac{3}{4}} = \frac{1}{3} \times \frac{4}{3} = \frac{4}{9}$
Alternatively, ratio of flour to oats is $\frac{9}{4}$.

Step2: Find missing flour value

Use the oats value $\frac{2}{3}$. Let flour be $f$. Since $\frac{f}{\frac{2}{3}} = \frac{9}{4}$, solve for $f$:
$f = \frac{9}{4} \times \frac{2}{3} = \frac{18}{12} = \frac{3}{2}$

Step3: Find missing oats for 3 cups flour

Let oats be $o$. Use $o = 3 \times \frac{4}{9} = \frac{12}{9} = \frac{4}{3}$

Step4: Find missing oats for 1 cup flour

Let oats be $o$. Use $o = 1 \times \frac{4}{9} = \frac{4}{9}$

Step5: Write equivalent ratios

Pair each flour value with its oats value, in order.

Answer:

First, the completed table values:
Flour (cups): $\frac{3}{4}$, $\frac{3}{2}$, $3$, $1$
Oats (cups): $\frac{1}{3}$, $\frac{2}{3}$, $\frac{4}{3}$, $\frac{4}{9}$

The equivalent ratios:
$\frac{3}{4}:\frac{1}{3}$
$\frac{3}{2}:\frac{2}{3}$
$3:\frac{4}{3}$
$1:\frac{4}{9}$