A ratio of two measures with different units can be expressed by combining the two units into a single, coherent expression. For example, if you have a ratio of 5 meters to 2 seconds, it can be written as 5 m / 2 s, which represents a speed of 2.5 meters per second. This ratio provides meaningful information about the relationship between the two measures, allowing for comparisons or calculations relevant to the context. However, it's important to ensure that the units are compatible for the specific application being considered.
In that case, the units don't cancel, and you have to keep the units. For example, if you travel 100 km in 2 hours, the ratio is 100 km / 2 hours or 50 km/hour. You have to keep the units, for the result to be meaningful (although the units are quite often implied).
An example of a ratio comparing two quantities with different units is the speed of a car, expressed as miles per hour (mph). For instance, if a car travels 120 miles in 2 hours, the ratio of distance to time would be 120 miles:2 hours, which simplifies to a speed of 60 mph. This ratio highlights the relationship between distance (miles) and time (hours), despite their differing units.
A rate compares two different units. Ex. 1 mile / 1 hour A ratio compares two of the same units. Ex. 1 mile / 2 miles
3 feet = 36 inches so a ratio which uses the same units of measurement for both measures, would be 36:24 which is equivalent to 3:2
If the measurements are of like things (eg distances) to find the ratio convert one of them into the units of the other, then the units an be dropped and the ratio simplified; eg: What is the ratio of 2 cm = 1 km? 1 m = 100 cm 1 km = 1000 m = 1000 × 100 cm = 100,000 cm → 2 cm : 1 km = 2 cm : 100,000 cm = 2 : 100,000 = 1 : 50,000 (This is the scale of the OS Landranger maps). If they are different things, then the units cannot be dropped, and the ratio requires them, eg making a brine solution may require 1 g of salt per 100 ml of distilled water the ratio of salt : water = 1 g : 100 ml.
One term for such a ratio is a "conversion factor".
ratio that compares 2 quantities measured in diiferent units
In that case, the units don't cancel, and you have to keep the units. For example, if you travel 100 km in 2 hours, the ratio is 100 km / 2 hours or 50 km/hour. You have to keep the units, for the result to be meaningful (although the units are quite often implied).
A rate compares two different units. Ex. 1 mile / 1 hour A ratio compares two of the same units. Ex. 1 mile / 2 miles
The rise is 2 and the run is 5. The ratio is called the slope, which in this case is 2/5 or 0.4.
3 feet = 36 inches so a ratio which uses the same units of measurement for both measures, would be 36:24 which is equivalent to 3:2
Means for every 100 units of one, you add 12 units of 2. Or a 20/3 ratio (expressed in percent).
If the measurements are of like things (eg distances) to find the ratio convert one of them into the units of the other, then the units an be dropped and the ratio simplified; eg: What is the ratio of 2 cm = 1 km? 1 m = 100 cm 1 km = 1000 m = 1000 × 100 cm = 100,000 cm → 2 cm : 1 km = 2 cm : 100,000 cm = 2 : 100,000 = 1 : 50,000 (This is the scale of the OS Landranger maps). If they are different things, then the units cannot be dropped, and the ratio requires them, eg making a brine solution may require 1 g of salt per 100 ml of distilled water the ratio of salt : water = 1 g : 100 ml.
It is a rate. For instance, if the quantities are 10 km and 2 hours, then the ratio (10 km)/(2 hours) = 10/2 km/hour = 5 km/h, which is a rate of speed.
If two shapes are similar, then each length is in the same ratio. The ratio of the heights is 10 : 2 Thus the radii are in the same ratio, ie 4 : x = 10 : 2 → x = 2 × 4 ÷ 10 = 0.8 units
The aspect ratio of 5x7.5 can be expressed as a fraction, which simplifies to 2:3. This means that for every 2 units in width, there are 3 units in height. Therefore, the aspect ratio reflects a rectangular shape that is wider than it is tall.
There are many instances: for example, speed is measured in kilometres per hour where the ratio is measured between a distance (measured in kilometres) and time (measured in hours). So it is no big deal except that you need to mention the units.