2 Attachment(s)

Multiplying & Dividing Fractions - Application

**From the book:**

"About 1/3 of all plant and animal species in the United States are at risk of becoming extinct. There are 20,439 known species of plants and animals in the United States. How many species are at risk of extinction? (*Source:* The Nature Conservancy)"

Not so amusingly (being that I'm cramming), my solution results in 338,661 *more* species than there are known to be in the United States.

The steps I took to solve the problem are illustrated in figure 1. The steps I took to list all the prime factors of the number 20,439 are illustrated in figure 2. I made my notes as clear as possible.

Any hints regarding where I took a wrong step?

How do I tell if a very large number is a prime?

That's not necessarily where I left the right path of truth. It's just an added mistake that I added rather than multiplying -- which wouldn't have worked either, of course.

The place where I'm taking a wrong step is in not being able to determine whether very large numbers are prime numbers. When I pared 20,439 down to $\displaystyle 20439=3^3 \cdot 757$, I attempted to keep paring away. This was because I did not know how to determine whether 757 is a prime number.

I know about certain tricks that can be used to divide numbers evenly, such as whether the sum of a number's digits is divisible by 9, or 3, or whether the last digit is divisible by 2, 5 or 10.

Looking at 757, its last digit is a prime number, and the sum of its digits equals 19, also a prime number. Is this a number's way of saying, "I'm a prime?"