4.B Ratios and Fractions and How They Relate to Percentage
4.B Ratios and Fractions and How They Relate to Percentage
Chad Flinn and Mark Overgaard
What does a ratio have to do with percentage? What does a fraction have to do with percentage? What is a ratio? These are all good questions, and we’ll answer them here. Percentages, ratios, and fractions are all very similar and can be used to represent numbers in different ways, but with similar outcomes.
We already went through fractions in a past chapter, so we know what those are all about. We should take a bit of time to talk about ratios and what they are.
Mathematically speaking, a ratio is a relationship between two numbers. If we were to once again order a pizza and eat 3 of the 8 slices, we could look at that as a ratio. We ate three-eighths of the pizza. Written as a ratio, this looks like:
[latex]\LARGE3:8[/latex]
Notice how the ratio is written. It has its own style, just like a fraction does. A ratio of 3:8 means that we have eaten 3 of the 8 pieces in the pizza. We could also write a ratio that identified how many pieces of the pizza were eaten and how many were not eaten. The ratio for that would look like:
[latex]\LARGE3:5[/latex]
In this case, 3 pieces of the pizza were eaten while 5 pieces were not. Regardless of which way we describe our pizza eating, what we are dealing with is the relationship between two numbers.
Here is another example: let’s say we are on a job site, and we have to install some pipe. We have 42 feet of plastic pipe and 79 feet of steel pipe to install. What is the ratio of plastic pipe to steel pipe that we need to install?
The answer:
[latex]\LARGE42:79[/latex]
Another question might be how much of the pipe is plastic in relation to how much total pipe we have. In this case, the ratio would look like:
[latex]\LARGE42:121[/latex]
In this case, the 121 is derived from adding the plastic pipe and the steel pipe lengths together.
[latex]\LARGE42+79=121[/latex]
At this point, you might be thinking that this looks and sounds familiar, and you would be correct. Ratios are similar to fractions, and each ratio can be written as a fraction.
[latex]\LARGE\dfrac{42}{121}[/latex]
We would say that 42 feet out of a total of 121 feet of pipe is plastic.
All right: we’ve added a few new things to our math library here, but you might be asking right about now, “Aren’t we dealing with percentages in this chapter? How does all this ratio and fraction stuff relate to percentages?”
The idea is we can take these ratios or fractions and turn them into percentages by making the ratio or fraction out of 100. In truth, we don’t even need to make a ratio or fraction out of 100 to do this, but it’s a good place to start our understanding of the math behind the whole process.
We are at a point where we can finally introduce you to some new people in the story. For the story of percentage, we’re going to use apprentices from carpentry, electrical, and plumbing, in addition to statistics.
Note: all the statistics are just made up.
A trades colleg