A **proportion** is an equation indicating two ratios are equal.

If *a* is to *b* as *c* is to *d*, then $\genfrac{}{}{0.07ex}{}{a}{b}=\genfrac{}{}{0.07ex}{}{c}{d}$.

If $\genfrac{}{}{0.07ex}{}{a}{b}=\genfrac{}{}{0.07ex}{}{c}{d}$, then, using cross multiplication,
$ad=bc$.

Then, by rewriting the equation,
$\genfrac{}{}{0.07ex}{}{a}{c}=\genfrac{}{}{0.07ex}{}{b}{d}$.

Similarly,
$\genfrac{}{}{0.07ex}{}{d}{b}=\genfrac{}{}{0.07ex}{}{c}{a}$ and $\genfrac{}{}{0.07ex}{}{b}{a}=\genfrac{}{}{0.07ex}{}{d}{c}$.

1 is to 2 can be written as $\genfrac{}{}{0.07ex}{}{1}{2}$. 3 is to *n* can be written as $\genfrac{}{}{0.07ex}{}{3}{n}$.

So, $\genfrac{}{}{0.07ex}{}{1}{2}=\genfrac{}{}{0.07ex}{}{3}{n}$.

Now, write all the possible variations of the proportion.

$\genfrac{}{}{0.07ex}{}{1}{3}=\genfrac{}{}{0.07ex}{}{2}{n}\text{}\genfrac{}{}{0.07ex}{}{n}{2}=\genfrac{}{}{0.07ex}{}{3}{1}\text{}\genfrac{}{}{0.07ex}{}{n}{3}=\genfrac{}{}{0.07ex}{}{2}{1}$

A table can be used to organize the information before writing the proportion.

| Recipe A | Recipe B |

Batches | 1 | 3 |

Eggs | 2 | *E* |

1 batch is to 2 eggs as 3 batches is to

*E* can be written as follows.

$\genfrac{}{}{0.07ex}{}{1\text{batch}}{2\text{eggs}}=\genfrac{}{}{0.07ex}{}{3\text{batches}}{E}$

The recipe calls for 2 eggs per batch.

Use that unit rate to solve for the number of eggs in 2, 3, and 4 batches.

2 eggs/1 batch × 2 batches = 4 eggs

2 eggs/1 batch × 3 batches = 6 eggs

2 eggs/1 batch × 4 batches = 8 eggs

The input-output table and graph are shown below.

**Sonya's Cookie Recipe**
Number of Batches |
Number of Eggs |
1 | 2 |
2 | 4 |
3 | 6 |
4 | 8 |
| | |