How do you use a complement in math with percents? - Answers

The definition of a complement is to do with "sets". Without getting too technical, the complement of a set of things is everything of interest apart from the set of things. So if you're working with the primary colours we have Red, Green, Blue. The compliment of Red, sometimes written Redc, is Green and Blue. With percentages it's quite simple: If 40% of a group of people have a dog, then you know 60% of those people don't have a dog. This is because everyone (100%) must either have a dog or not have a dog. Let's say that there's still 40% of the group who own a dog, and 30% of people own a cat. It might be tempting to say that 30% have no dog or cat because 100%-30%-40% is 30%. But the problem with that logic is that some people could have a dog AND a cat. Then you would be counting them twice. We would need to know how many people had both a dog and a cat, let's say it's 5%. So of the people, 40% have a dog. That leaves 60%. 30% have a cat. That's 30%, but 5% of the people have been counted twice, for dogs and cats. SO we need to add them back on. So 35% of people have neither a cat or a dog in this example.