A ratio is the mathematic relationship between two numbers, where one is divided by the other. A proportion is an equation where two ratios are equal. A typical use might be something like this. The ratio of boys to girls on the bus is five to four. If the teacher counts fifteen boys, how many girls are on the bus?
Algebra Help's four-page introduction to proportion, means and extremes concludes with a twenty-question worksheet that includes both a manual answer sheet and a step-by-step solution to each problem. "The four parts of the proportion are separated into two groups, the means and the extremes, based on their arrangement in the proportion. Reading from left-to-right and top-to-bottom, the extremes are the very first number, and the very last number."
"In a horror movie featuring a giant beetle, the beetle appeared to be 50 feet long. However, a model was used for the beetle that was really only 20 inches long. A 30-inch tall model building was also used in the movie. How tall did the building seem in the movie?" Math.com's lesson is divided into four steps: First Glance, In Depth, Examples and Workout. The Workout consists of a ten problems with automatic grading. Unfortunately "Check Your Answer" does not work in Firefox 3.5 but does in Internet Explorer 8.
This seven-page lesson from Purple Math has lots of word problems where the work is shown, and the answer explained. "Conversion factors are simplified ratios, so they might be covered around the same time that you're studying ratios and proportions. For instance, suppose you are asked how many feet long an American football field is. You know that its length is 100 yards. You would then use the relationship of 3 feet to 1 yard, and multiply by 3 to get 300 feet."
This all-Flash site is my pick of the day because it explains ratios using interactive manipulatives. Be sure to start with the intro video because it will walk you through a practice problem, explaining the different parts of the screen where the virtual math teacher provides feedback, and where you build the ratio models using virtual blocks. "While guided practice sets encourage students to create models with concrete objects; the independent practice sets help students transition to more abstract representations using paper and pencil."
Today's last site is not another lesson, but rather a tool. There are three ways to represent a ratio: "x:y" or "x/y" or "x to y". Enter a sample ratio in one of the three input boxes, and WebMath will explain a bit about it. For example, entering 3 and 4 in the first line of the tool, produces this. "You entered 3:4. This is a ratio that is read '3 to 4.' Here 3 is called the antecedent, and 4 is called the consequent. The first term is always called the antecedent and the second term is always called the consequent."