aka “negative fractions have never show’d up in my math classes until today but apparently I’m already supposed to know what they are”

In: 4

A fraction is just a type of number. It may help to think of 2/3 as a *thing in and of itself* in the same way that “2” or “-17” are, not as “two thirds of something”, in this context (and in many others, because that way of thinking about fractions falls apart quickly once you start doing algebra).

In the same way that you can add two numbers, you can add two fractions, because fractions are just numbers. Similarly, in the same way you can subtract, multiply, or divide numbers, you can subtract, multiply, or divide fractions. And you can take their negatives, which has the same meaning for fractions that it does for integers: -1/2 is the number that, if you add it to 1/2, gives you zero, in the same way that -3 is the number that, if you add it to 3, gives you zero.

The easiest way to think about is to put negative fractions on a number line. If 0 is in the middle, positive numbers are to the right and negative numbers are to the left. -1/2 is between 0 and -1 just like how 1/2 is between 0 and 1

A negative fraction could be thought of as a fraction of a negative thing.

If you can accept that -2 is a thing, then -2/3 would be a third of that.

You know your left and right, correct? Five years old, you have heard the Hokey Pokey song.

Take one step right. Take one step left. You are back where you started, correct?

Same thing if you take one step left, then one step right. You’re back where you started.

In math, we call left “negative,” we call right “positive,” and we call where you started “zero.”

So translate “negative one-half” in your head to “one half step left.”

What is 2 thirds minus 1 third? Thats a practical example of a negative fraction.

Another would be that -1/2 = -0.5