Trying to understand fractions is risky business

I’m not very good with fractions. Oh, I do all right with things like one-half, one-third or one-fourth. But as soon as it goes any further, I get a little confused. For example, can you easily cut a pie into fifths? OK, I’ll let you cut, but I get first choice of the pieces.

Fractions are ratios. While we learn to manipulate them in school, I just don’t grasp what they mean very well. A ratio is a relationship between two numbers that indicates how the first number is related to the second. We have one pie, and it is cut into five equal pieces. (But I still get the biggest one.) We use ratios, and therefore fractions, when we talk about cutting up pie (or pi), when discussing speed as in miles per hour, or when contemplating the risk of dying in a fire.

I think I have trouble understanding risk because risk is described as a fraction. We call risk fractions “probability.” For example, if I roll a single die with six numbers on it, the probability of rolling a two is one chance in six. The one chance in six is written as the fraction 1/6, which is further calculated as being one divided by six, or 0.1667. I understand the one in six part, but I don’t grasp 0.1667.

So I’m afraid I tend to worry about things that aren’t really risky and ignore many risky behaviors. For example, government has set flammability standards for children’s clothing. That sounds good. Yet the chance of dying in a fire are said to be 0.00001 (that’s 1 in 100,000) and one in three children (0.33) are said to live in homes without smoke detectors.

According to the National Safety Council, three out of 10 people do not wear safety belts. Yeah, sometimes I forget. And sometimes I’m just lazy. Now driving is six times more deadly than flying, but I never forget to buckle up on an airplane.

Then there’s this: 227 out of 372 people are overweight. (No, forget it, I ain’t telling which group I’m in.) Further, 44 percent of overweight people are obese. So is that 44 out of 227, or 44 out of 100 that are obese? I get confused. Anyway, obviously I don’t worry about that enough.

The National Institute of Occupational Health and Safety claims that 20 people are murdered on the job each day. Did you know that working as a retail sales counter clerk is nearly three times more deadly than being a firefighter? The risk of dying during childbirth is one in 5,000 (0.0002) in the developed world. The risk of dying from a gunshot wound is one in 25,000 (0.00004). I wonder which of these we should declare illegal.

How about this one? The chances of dying from a bee sting are about one in 14 million (0.00000007). The risk of dying in a fire is one in 100,000 (0.00001). Yet people who don’t want bees in their yards put fireplaces in their homes. The risk of dying while riding a bike is about one in 400,000 (0.0000025), while the risk of being killed in a car accident is one in 20,000 (0.00005).

I decided to calculate how my chances of survival might improve if I prepare myself for the risky things that can happen. This is sort of the opposite of risk: the probability of benefit from being prepared. Being new at this, and poor with fractions, I stayed away from traditional approaches. I figured a thumbnail estimate would be more helpful.

So I have based my analysis on two well-known situations. If a stitch in time saves nine, and an ounce of prevention is worth a pound of cure, then there is a ratio of 12.5 to 1 advantage to being prepared.

# # #

Gary McCallister is professor of biology at Mesa State College.


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