Measurement is related to ratio and proportion in real life in many ways. Here are three types of examples:

First consider conversions. In one example if you compare inches to feet you are looking at a 12:1 ratio and you could solve for the length in feet of an 18 inch model using a proportion 12/1 = 18/x

In my favorite example changes in temperature are proportional at the rate of 5°C increase for every 9°F.

Secondly consider rates, a special type of ratio, often have to do with measurement Miles/hr, Dollars/ft², Miles/gallon

Thirdly there are special cases like scale models, maps, and similar figures where a scale factor exists between proportional objects.

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The primary relationship between measurement and ratio/proportion is in converting units.

For example converting from American standard units to metric requires proportions. To change from inches to centimeters we use the fact that there are 2.54cm per inch.

We also use conversions within a system. For example, converting feet to yards or miles or converting centiliters to liters.

Another connection is using similarity to figure out lengths and angles. This is especially important in scale drawings such as maps and blueprints.

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