by Jason Marshall

## What are Fractions?

### The easiest type of fractions to understand are built by turning the integers on their heads. Every integer has what’s called a reciprocal which is obtained by dividing one by that integer. For example: the reciprocal of 1 is 1/1, the reciprocal of 2 is 1/2, the reciprocal of 3 is 1/3, and so on. You could conceivably create a list of all such fractions by walking positive integer steps along the number line and calling out the reciprocal of the integer at each position. Eventually, you’d start getting to big numbers: 1/99, 1/100, and then eventually even bigger: 1/999, 1/1000, and then even bigger, and bigger, forever.

The apparently empty spaces between the integers on the number line are actually teeming with infinitely many numbers known as fractions.

## Wrap Up

### That’s all the math we have time for today. But rest assured we’ll be talking a lot more about fractions and how to interpret and work with them in upcoming articles (next week we'll cover numerators and denominators). In the meantime, here’s a problem for you to think about: Why can’t the denominator (that is, the bottom number) of a fraction be zero? Look for my explanation in the weekly “solutions” video posted each week to the videos section of the Math Dude’s Facebook page and to YouTube.

Please join our growing community of social networking math fans on Twitter and Facebook, ask questions, and chat with other math enthusiasts. Check it out! You can also submit a question to me at mathdude@quickanddirtytips.com.