Definition: A proportion is a statement that two ratios (fractions) are equal.
Boring Example: $\frac{x}{2}=\frac{x+2}{5}$
A Better Example: At a fixed time of the day, the length of a shadow and the height of the object casting the shadow are directly proportional. If a person 2 m tall casts a 5-m shadow, how tall is a fir tree that casts a 40-m shadow?
Another Example of Proportionality: Recipes.
A dessert recipe which makes 4 servings calls for 23g of sugar. What quantity of sugar is needed if we want to make 15 servings?
A Rough Guide: Any time you increase or shrink the size or amount of some THING, but want it to have the same characteristics as the original THING, a proportion may be involved.
Direct Proportionality: The quantity $y$ is directly proportional to $x$ if $y=kx$ where $k$ is some fixed constant.
The constant $k$ is called a proportionality constant.
Example: The number of rows $R$ a particular knitter can knit for a particular design is directly proportional to the time $T$ spent knitting. Tabitha is knitting a scarf and can knit 40 rows in 3.5 hours. How long will it take Tabitha to knit 50 rows? If necessary, round your answer to the nearest tenth.